Horizontal demand curves: the 1st Fallacy
• Demand curve for single firm cannot be horizontal:
• Stigler (1957). “Perfect
competition historically
considered”, Journal of Political
Economy, 65: 1-17
dQ
• Leading journal

dqi
• Lead article too!

• Leading neoclassical: main
d  n

  q j 
opponent of Sweezy (“kinked
dqi  j 1 
demand curve”) and Means
d
(“actual administered pricing

q1  q2  ...  qi  ...  qn 
dqi
policies of real companies”);
See Freedman (1995, 1998)
  0  0  ...  1  ...  0 
dP
dP dQ dP



0
dqi dQ dqi dQ
dP
dP

dqi dQ

dP
dQ
dP
dQ
dP

dQ
dP

0
dQ

Steve Keen 2004
1
MC=MR… The 2nd Fallacy
• What matters to profit-maximising firm is total
revenue – total costs
• Total costs under its control
• Total revenue depends on
– Own actions (a bit)
– Actions of other firms (a lot, especially for
“competitive” industries)
• So real profit-maximisation occurs where total
derivative of revenue = total derivative of costs
(assuming rising marginal cost…)
n 
 q  Equals 1 since
d

j
 qi     
 qi  
0


dQ
Q 
j 1   q j
Steve Keen 2004
 qj

Q
1
Q  1
 qj
2
MC=MR… The 2nd Fallacy
• So profit maximisation rule for single firm is:
n 



P Q   qi  
TC qi    0





 qj
j 1   q j

• Second bit is marginal cost once & zero n-1 times


1
TC qi   n  1 
TC qi   MC qi   n  1  0
 qi
 qj
• Equals 1 once
• First bit is:
when i=j
 
 n 



P Q   qi      P Q  
qi   qi 
P Q   






 j 1 

 qj
 qj
j 1   q j



n
• (n-1) times this is zero
since firms independent
• This is
Steve Keen 2004
dP
dP

dq j dQ
n times
3
MC=MR… The 2nd Fallacy
• So for profit maximisation the firm sets
 


P Q   qi  
TC qi  





 qj
j 1   q j

 P Q   n  qi  P ` Q   MC qi   0
n
• Rearranging to show “marginal revenue”:
P Q   n  qi  P ` Q   MC qi 


 P Q   qi  P ` Q   n  1   qi  P ` Q   MC qi 
 MR qi   n  1   qi  P ` Q   MC qi   0
• So true profit maximisation formula is:
MR qi   MC qi    n  1  qi  P ` Q 
Steve Keen 2004
4
MC=MR… The 2nd Fallacy
• Can replace RHS with something more meaningful
• Since n 



P Q   qi  
TC qi  





 qj
j 1   q j

 P Q   n  qi  P ` Q   MC qi   0
1
`
• We know that qi  P Q     P Q   MC qi  
n
• Substituting this into
MR qi   MC qi    n  1  qi  P Q 
`
• We get the true profit maximisation rule:
n 1
MR qi   MC qi  
P Q   MC qi  

n
• There’s also an easier way to prove this…
Steve Keen 2004
5
MC=MR… The 2nd Fallacy
• Assume firms equate MC & MR:
Substitute
dP
dP

dqi dQ

 n
d
mri  mc qi    0   P  qi dq P Q    mc qi 

i 1
i 1 
i
 i 1
n
n
n copies of P
Replace with Q
Move a P…
Substitute mc q   MC Q 
n
d
 n  P   qi
P   MC Q  Move to front
dQ
i 1
i 1
n
n copies of MC
d
 n P Q 
P  n  MC Q 
& a MC…
dQ


d
 n  1   P   P  Q
P   n  1   MC Q   MC Q   0
dQ 

This is MR(Q) (industry, not firm) Rearranging this:
Steve Keen 2004
6
MC=MR… The 2nd Fallacy
MR  MC   n  1  P  MC   0
• “Profit maximising” strategy of each firm maximising
profit w.r.t. its own-output results in aggregate
output level where marginal cost exceeds marginal
revenue
• Why? Own-output marginal revenue is not total
marginal revenue:
dTRi QR , qi  


P
Q

q
dQ

P Q   qi dqi
  i R


QR
qi
• This component ignored by conventional belief (and
unknowable by firms)…
Steve Keen 2004
7
MC=MR… The 2nd Fallacy
• Profit maximising formula is not MRi=MCi but:
mr qi   mc qi

n 1

  P Q   MC qi
n
  0
• Take earlier formula and rearrange so that industry
MR-MC is on one side of equals sign:
n
 mr
i 1
i
 mci  n  1   P  n  1   MC  MR  MC
 n
  mri  mci
 i 1

  n  1  P  n  1  MC  MR  MC

• Set this to zero to find maximum aggregate profit;
• Take terms in P and MC inside summation:
Steve Keen 2004
8
MC=MR… The 2nd Fallacy
• Equating this expression to zero maximizes profit:
n 1


mr

mc


P

MC

  0

i 
 i
n

i 1 
n
• True single-firm profit-maximization rule:
n 1
mri  mci 
  P  MC   0
n
• Example:
– n firm industry with constant identical marginal
cost = c
– Linear demand curve P(Q)=a - bQ
Steve Keen 2004
9
MC=MR… The 2nd Fallacy
• Standard false neoclassical advice:
– equate MRi & MC
– Output converges to PC result as number of firms
increases (Stigler’s result):
• Conditions:
P Q   a  b  Q
dP
 b
dQ
MRi  P  q 
MC  c
dP
 P  b q
dQ
• Result:
MRi  P  b  q  MC  c
a  b Q  b  q  c
a  b n  q  b  q  c
b  n  1  q  a  c
1 a c
1 a c
Q

Monopoly:
n 1 b
2 b
n a c
a c

as n  
Competition: Q  n  q 
n 1 b
b
q 
Steve Keen 2004
10
MC=MR… The 2nd Fallacy
• But profit maximisers solve:
n 1
P  b q c 
P  c 
n
n 1
MR  MC 
P  MC
n

• Competitive industry
produces “monopoly” level
n

1

b q  P c  
P  c   output at “monopoly” price
 n

P c
• Industry output independent
q 
of number of firms
n b
a  b  n  q  c a  c • Similar result for other
q 

q
marginal cost functions:
n b
n b
1 a c
“competitive” outcome same
q 
2 n b
as monopoly
• Aggregating:
1 a c
Q  n q 
• Same as for monopoly
2 b
Steve Keen 2004
11