Anti-Competitive Effects of resale-Below-Cost Laws
Marie-Laure Allain, Claire Chambolle
To cite this version:
Marie-Laure Allain, Claire Chambolle. Anti-Competitive Effects of resale-Below-Cost Laws.
International Journal of Industrial Organization, Elsevier, 2011, 29 (4), pp.373-385. <hal00367492>
HAL Id: hal-00367492
https://hal.archives-ouvertes.fr/hal-00367492
Submitted on 11 Mar 2009
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ECOLE POLYTECHNIQUE
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE
ANTI-COMPETITIVE EFFECTS OF RESALE-BELOW-COST
LAWS
Marie-Laure ALLAIN
Claire CHAMBOLLE
January 2009
Cahier n° 2009-09
DEPARTEMENT D'ECONOMIE
Route de Saclay
91128 PALAISEAU CEDEX
(33) 1 69333033
http://www.enseignement.polytechnique.fr/economie/
mailto:[email protected]
   

    

         
        
          
           
          
          
            
 
    
       


           
           
           
        

           
     

            
 

             
              
      

             
               
           
   
            
            
            
              
               
           
          
             
            
              
          
          
              
            
            
          
           
           
             
            
            
              
            
               

              
            

                
             
    

               

         
            
           
              
        
            
              
        
               
     
              
          
             
              
           
             
              
            
             
             
    
          
            
           
             

             
            
            
             
                
          

            
             
                
              
                  
 

            
              
             
             
            
            
            
           
            
            
     
             
            
          
           
               
              
          
               
              
              
  
            
           
        
          
            
            
             
            
            
            

              
             
                  

      
            
             
            
           
               
             
              
             
            
             
             
            
              
              
            
            
            
             
             
           
             
               
              
  


 
  
             
           
            
           

              
             
            
          
             
          
            
             
          
          
            
              
              
             
             
             
            

 
            
             
            
             
             
          
            
            

        
          

             
  

             
                
               
              
      


              
                    
               
                
               
            
                
              
      
             
             
             
            
              

    
               
            
             
            
             
            
             
             
         
             
             
             
             
            
           

             
                
            

            
              
              
              
             
       
              
             
              
            
              
           
             
               
         


 

           
              
             
            
       
             
             
               
                
     
                  

            
           
              

         
            
                 
                
                   
    
         
    
                 
              
            
              
     
              


              
           
            
            
              

             

 



          
               





            
                 
               
             
                
                 
              
         

              
             
                
            
             

               
           
              
               
             
             
           
           
            
          
               
             
              
          
           
             
           
              
            
            
              
              
             
               
                  
              
              
            
             
              
             

               
               
  


    
          
               
               
               
           
              
             
           
           
           
              
          
              
              
              
             
             
          
             
             
            
              

               
              
                
                 
              
                 
                
             
        

           

            
             
            
              

            
           
               
                 
               
             
           
            
  



    
               
             
           
            
            
    
          

      







              
                
              
             
               
           
            
          
           
                  
        

         

          
    
           
   
                
             
               
               
                
            
            
             
                 
             
           
             
              
     
               
              
              
            
              
               
            
               
             
               
           

                
                
                   
                 
       


 
             
              
               
      
             
 
 


  
            
      

      
      
          
             
             
               
             
             
              
            
             
           
    
         
          
   
             
                 
           
  


              
              
           
            
            
             

               
               

               
                
              
               
             
           
 
         
          
      
    
            
             
              
             
               
         
          
             
   
            
             
           
       
     
          
         
             
              
              
          
            
              


     
               
                
            
                 
                  
            
                

 
             
            
         
           
                     
              
            
            
                
               
               
       
    

       
       


  
    
             
                  
   
            
  
             
              
          
     
       
       
            

            
              
       
       
              
    
           
  
              
               
         
      
           
       

           
      
   
      
        
             
                 
              
              
          
    
           
              
              
         
   
      
        


           
   
            
             
          
     
          
            
               
            
              
           
         

            
          
    
              
         
       
  
        


  
      
  
      
   
          
         
    
             
             
   
             
         

  
            
          
  


      

 


 






            
   

 
               
     


Equilibrium prices
0.6
ŵ
0.55
0.5
~
w
w
0.45
p*
0.35
0.25
0.15
~
0.25 α
0.5
α
0.75
α̂
1
α
 
            
         

   
          
    

             
      
      
    
      
       
      
         
    
               
             
           
              
               
                     
                  

                    
              
   
            
       
         
    
   
           

              
 
                
              
             
  
             
               
            
                 
         
   
            
             
  

              
         
           
            
              
       
             
             
              
              
           
   
               
  
            
            
              


   
           
         
             
           
           
             
             
                
   
            
              
          
              
           
      
         

    
           
             
  
    
              
  
              
   
    
     
    
   
            
            
         
             
               

       
            
            

               
               
  
               
            
           
    

            
   
             
             
            
                
            
               
            
           
               
   
           
             
   
       
               
         
               
               
              
             
               
  
             
                  
            
 


   
           
  
               
      
             
              
            
              
           
            
     
      
          
               
         
          
          
           
             
           
         
               
    
    
           
              
                   
       
        
          
         
          
            
    
             

    
       
          
                   
          
 
             
   
    
              
   
           
          
            
           
          
   
Impact of downstream competition (b )
Impact of upstream competition (a )
ŵ
Final prices
pM
α~

p*
w
RPM
2− b
3− b
ŵ
Final prices
4 − 2b
4− b
1
pM
α
p*
w
RPM
α~
2−b
3−b
4 − 2b
4−b
1
α
 
            
            
                
               
                
                 
          
                    
                    
                
       

               
       


            
             
           
           
            
         
     
              

 
        

       
            
           
            
               
             
          
             
             
             
            
          
              
     
             
               
   


     
         
       



     
              
                
             

         

               
             
               
Final Price Equilibria
1/2
1 − ab
2 − ab
Price-Floor
Price-floor
1− b
2−b
Without restriction
RPM
0
1
α
 
           
            
             
                
                 
 

           
                
   


                   


                
               
             
                        
       
        
          


             

     

             
            
               
              
           
        
           
          
            
              
             
                
              
              
               
             
              
           
                 
               
    
           
    
              
           
              
             
           
   

             


              
 


  

 
              
              
          
          
             
             
               
            
                  
               
           
              
            
           
    
   
            
             
            
               
              
              
             
             
     

   
           
            

  

              
 
          
           
            
              
            
            
            
               
             
             
               
          
          
            
             
                
            
             
             

            
             
            
               
             
              
               
          
           
              
            

         

               
           
              
              
             
         
              
              
 


            
         
    
          
         
              
            
           
           
              
               
 
              
              
             
               
             
          
          
               
           
          
               

            
            
                
   
              
               
            
              
             
            
            
              
          
           



          
         
  
         
     
          
         
         
       
             
        
            
          
  

             
  

                

           
          

          
     
         
            
  
           
            

         
        
             
        
           
       
          
        
          
         
  
           
         
          
    
           
         
         
         
   
         
  
          
      

         
    
      
            
      
            
  
            
 
            
     
          
   
          
         
            
         
         
        
         
           
         
     



    
            
     

              
        


 
                 
               
                  
               
            
                
              
      
        
                            
 
          
 
 

            

                 
              



        

 
              
            
        

                   
             
               
            
           
            

  
               
              
   
               

    





    
          




    
       





      
          





    
         
           
           
             
               
           
              
          
             
               
              
                 
                 
                
              


      


      
 

 

                 
    
          
                
          


 



                  
                
                  
           

            
                  
               
    

          
    
          
  

     
   

     
     
            
             
                   
      
   




 
              
                 
                  
         
 


           

          

           
             
             
        
    
         
          


    
 
  






   
 
     
 



  
  

   

             
             
 
    
             
              
     
        

          
  
    

 

   
   
          



     
 


  




            
               
            
                
             

  
 

   











   
 







              
            
 

  
               
            
               
                  
   

 
 
   
 
   

             
  


  

       


 
     
            

            
               
  

     
  

 
 
       

  

 

   
 

                 
                         
      
       


    
       

         
 

 


 
      
              
           

                           
      

              
 
              
  
            
           
    
  



 
         
 
     

 
  
 
    

  
      

           
  
            
  
   



       
  

             
 
      
          
            

            



        
  
 
 
  

     
           
       
             
     
              
              
  
                 






     
     
     
        
  

              
               
        
    
     
      
        
             
      
         
            
            

                 
              
     

              
               
                 
               
               
   
             
                
     
          
              
 

  

 
         



           
               
 
               

 

      

     

 




    














 
              
               
            
                   
             
            

        
        
             
           
            
              
           
           
  
    



            






         





            
    

              
                
           
              
              
            
          
              
   
 
 
           

         
            
     
           

          
       
  
            
         
       
                 
                     
           


   
          
    
   
              

           


               
   

              
                
           

             
      



       
                 
                     
                
  



     
   
 
 
 

   
                


      
          
              

              

 



         
   



                   
           
                
               
               
           
                
                
               
              
               
     
    

   
       
         
  


     
     
         
    
            
    
          
        
      
      
   
               


 

         


 


            
        





                  
      

          

 
           
              
                  

 
              
              




     
 
   
 
   


      

 

     

 


            
               
                

   
 

              
         
                
       

   
  
  
     

   




         
       

   
       

             
            
            
             
                  
                
 
  


 
    
             

 
          

        
   

   




    
                      
               
            
  
        
  


               
                


  
  
     




         
          



  
                  
             

                 
           



           
 
  


             
  
 


              
 
                
             
            
         
             
                   
            

 
               
          
    
         
      
 

               
               
                
               
                     
            
              
         
       







 


                        
              
              
            

             
         
 

 

           
              
                
                  
                
             
             
               
            






 



 
    
 
    

      


            
               
            
                 
            
              
   
         
     
            
              

 
                 
                
 
         
     

               
  



         

       




            
                     
                   


        
               
 


            
          
       
              
               
          
            
              


 
             
                
             
                 
      
                 
              
 
          
    

              
                

            
  

              
          




  

             
         
             
           



 
 
       
     


   
           
    
            


   
       
    

   
       


  
           
              
            
             
      

     
              
               
 
               


               

      
        

            
               
            
           
      


                

               
          
                 
                 
              


       
      



               
     
                

         
   
       
                   

    
    

 
                 
            
               
                  
       
         
           
 
