Heterogeneous Discount Factor, Education Subsidy, and Inequality























           
            



           
          
           
        
        
         
          




          
            

      



          
          
           















 































               
        


           

         



              
           



      


        

           
           
             
          


          
             
          


           
              
           


              
            
           

            







           
              

              


























































            
          
            
            

       
         
        
               
            
          






            
            
              
           
             
         
           

           



            


            

  
              

             



          



   
   
   
   
 
 
 
   

 
          
        



             
             


 
 


 


   

  
 
 
            

         
            



 





  
  

  









 
  
 

             
            



             


   



                  



          

   
 



            



             




                  


 


 






  

 





 















     

  
 



  









           



   
    
 
 









     

  
 




 







                



 
 


 

   
   

 

 


 

    
 



 











            

         


          









   

 



   
 



  
  
 

 
              







 

           


   





   

  
 
              






 
  

 
 
              


 


 


 



 





 

 





 


 


 

             

         


             




 




 


  
   



  










  


         
            





            
         
 

          

             


            



  
 
 
 



 


 
 
 

 
 









             
 

              

              


              
   
             
                  
  

        
             

           
             





 


           




   


  





             



           

           




           
            
         



 





























































 

 


  

            

       
  
      

          
  
 





 



             






             

            

           

              
            
           

            
             
               
            





             


             
             



































   



             




            











 






















           

             
             
             



             
           
             
            
            
            
              























            

       
 




              


     

            

 
            
          

           









































       






            
             



































       
           



              





       
           
             




















         
           
          

 



               
           
 



 

              

            
            
             





            





         
             
            
            
           

          
         

         

           

           

        
          
             


 
               
             

   



 





 

  
  









 






 

  


 



 






  
 









  











 


 


 
  






















               


 

   

 


 
 

  

 

  




 
  


   

 



 













   
  
  


 
  






   

 









 

  














               
              




               
             





 
  

 
 

  

  



   


 
  
              
 



            
 

              
             
 

   


   





 



 




 




 
  


  


 




            

          

       


            


             














       


           
              


              

























           
            
            


 
 

           

 
       

 

 
           

            

 
        

            

          

 


 
     

 

            
          

 
         

 

          

           

        

          
