The theory of the firm
Steve Keen
Price
In the beginning was…
Supply
• How to restore the
original result?
• “Perfect” competition!
Demand
Quantity
• Intersection of supply (marginal cost) and demand
(marginal benefit) means gap between total benefit &
total cost maximized
• But then along comes Harrod: profit maximizers
equate marginal revenue & marginal cost: welfare not
maximized!
Steve Keen 2006
2
Rescued by “perfect competition”
• “Perfect competition” and supply & demand…
Pe
Downward sloping
market demand curve
dP
 0 Supply
dQ
Horizontal demand
curve for single firm
Price
Price
“Price taking” atomistic firms
Pe
Marginal Cost
dP
 0, MR  P
dq
Demand
Qe
qe
Quantity
quantity
Supply curve is sum of marginal cost curves
Steve Keen 2006
3
Standard introductory supply & demand
• “Monopoly bad”:
– Monopoly maximizes profit by equating marginal
cost and marginal revenue
dP
MR Q   MC Q   P  Q
 MC Q 
dQ
• Price exceeds marginal cost with monopoly:
dP
P  MC Q   Q
0
dQ
• “Perfect Competition good”:
– Firms maximize profit by equating marginal cost
and marginal revenue BUT marginal revenue
equals price:
dP
MR qi   MC qi   P  qi 
 MC qi   P  MC qi   0
dqi
Steve Keen 2006
4
And that’s all bunkum!…
• Slope of demand curve for individual
firm can’t be zero
– Established in 1957 by George Stigler
• Equating marginal revenue and marginal
cost doesn’t maximise profits
– New result
• “Prisoners’ Dilemma” Game Theory has
a (or rather, yet another…) problem too:
– Rational firms won’t play games…
• New result
Steve Keen 2006
5
Horizontal demand curves: the 1st Fallacy
• If firms don’t react to each other then
• Demand curve for single firm cannot be horizontal
– Atomism incompatible with dP/dq=0
dP
dP dQ dP



0
dqi dQ dqi dQ
• Not a new result!
• First published in 1957!...
dP
dP dQ

dqi dQ dqi
dP

dQ
 n q j
 
 j 1 qi
dP

dQ
n q
 qi
j


 qi j i qi






n
 dP
dP
dP 

 1   0  
dqi dQ 
j i
 dQ
Steve Keen 2006
6
The 1st Fallacy…
• Stigler (1957). “Perfect competition historically
contemplated”, Journal of Political Economy, 65: 1-17
• Leading journal
– Lead article too!
• Leading neoclassical:
– Stigler main
opponent of
• Sweezy (“kinked
demand curve”)
• Means (“actual
administered
pricing policies
of real
companies”)
• See Freedman (1995,
1998)
Steve Keen 2006
7
The 1st Fallacy
dP
DP

d q DQ
P
dP
P-DP
• Acting “as if” demand
curve horizontal irrational:
P Q 
Price
Price
• The graphical intuition:
– If the market demand curve slopes down, then any
tiny part of it slopes down with the same slope:
P Q  qi   P Q 
•
May be small difference, but
“Infinitesimals ain’t zeros!”
q for ith firm
q
Q
dq Q+DQ
P Q  qi 
Quantity
Steve Keen 2006
qi
8
The 1st Fallacy
Price
• “Can’t we just assume
price-taking?”
– Firm assumes can sell
Irrational belief: P(Q+q)=P(Q)
as much as it likes at P(Q)
market price…
– Sure—but this is
irrational behavior,
not rational
– If the market
demand curve slopes
downwards, then any
increase in output, no
matter how small,
Q
Q+ q
must cause market
• Neoclassical result dependent
price to fall, however
upon irrational behavior…
infinitesimally.
The 1st Fallacy
• Summing up so far:
– Marginal revenue for individual firm less than
price…
– Demand curve for single atomistic firm can’t be
horizontal
– Introductory economics teaching a fallacy for over
40 years…
– Can standard tuition still be justified?
• Stigler 1957: Yes!
– reworked marginal revenue for the ith firm in
terms of the number of firms n and market
elasticity of demand E:
Steve Keen 2006
10
The 1st Fallacy
• Convergence to perfect competition argument
• Profit maximizers equate marginal cost & marginal
revenue:
d
d
P  qi  P  qi 
P
dqi
dQ
Q
n
Q P Q
1 Q
 
P  
n P Q
n P
Introduce
Introduce qi 
Q d
where P  dQ P 
P 
PQ
PQ
Q P Q d
  
P
n P Q dQ
So now we have
1
 P  qi 
 1
E
P Q d
 
P
P Q dQ
Rearrange P 's & Q 's
d
1 Q d
P  qi  P  P   
P
dqi
n P dQ
So that
d
P
P  qi  P 
dqi
n E
P dQ

Q dP
• And… “this last term goes to zero as the number of sellers
increases indefinitely” (Stigler 1957: 8)
• Just one problem: equating marginal cost & marginal
revenue isn’t profit-maximizing behavior!
Steve Keen 2006
11
MC=MR maximizes profits… The 2nd Fallacy
• Aggregate effect of equating 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  n copies of MC
dQ
i 1
i 1
n
 n P Q 
d
P  n  MC Q 
dQ
& a MC…


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 2006
12
The 2nd Fallacy (first proof)
MR  MC   n  1  P  MC   0
• “Profit maximizing” 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
• But firms can work out what it is…
Steve Keen 2006
13
The 2nd Fallacy (first proof)
• Profit maximizing 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 2006
14
The 2nd Fallacy (first proof)
• Equating this expression to zero maximizes profit:
n
n 1


mr

mc


P

MC

  0

i 
 i
n

i 1 
• True single-firm profit-maximization rule is:
n 1
mri  mci 
  P  MC 
n
• Standard rule wrong in
multi-firm industry
• “Maximize profits with
respect to own output only”
a bit like “row across river
and ignore the current”…
• Even if you can’t control
other firms, must take their
existence into account…
Steve Keen 2006
15
The 2nd Fallacy (second proof)
• “But firms can’t know that!”
– Yes they can!
• Problem is…
Economist:
“Easy! Equate
MR & MC! ”
“Work out the
output level
that maximizes
my profits!”
Mathematician:
“Hmm! Interesting
problem: set total
derivative of profit to
zero…”
Steve Keen 2006
16
The 2nd Fallacy (second proof)
• The mathematician’s logic:
• What other firms do affects your profit
– Even if you can’t control them;
– Even if they don’t react (game theory style) to
what you do…
• So profit maximized by zero of total differential
• So must solve: d  qi    0 Impact of j th firm on i th s profit
dQ
Sum over j firms
n 
d qj
d
d
 qi     
 qi  


dQ
dQ
j 1  d q j

• Expanding:
0


Equals 1 since
d qj
dQ

1

1
with “atomism” dQ
d qj
n 
 n  d

d
d
 qi     
P Q   qi  
TC qi  

• Expanding:  



d qj
j 1  d q j
1  d q j
 jSteve

Keen 2006
17
The 2nd Fallacy (second proof)
• Profit maximization rule for single firm is:
n 

d
d
P Q   qi  
TC qi    0





d qj
j 1  d q j

• Second bit is marginal cost once & zero n-1 times
d
d
1
TC qi   n  1 
TC qi   MC qi   n  1  0
d qi
d qj
• Equals 1 once
• First bit is:
when i=j
 d
 n 

d
d
P Q   qi      P Q  
qi   qi 
P Q   






 j 1 

d qj
d qj
j 1  d q j



n
• (n-1) times this is zero
since firms independent
• This is
Steve Keen 2006
dP
dP

dq j dQ
n times
18
MC=MR… The 2nd Fallacy
• So for profit maximization the firm sets qi so that:
 d

d
P Q   qi  
TC qi  





d qj
j 1  d q j

n  qi  Q
 P Q   n  qi  P ` Q   MC qi   0
n
• Conventional economic formula leaves out the n:
• Since P`(Q) negative, with rising (?) marginal cost &
falling price, true profit maximizing qi a lot less than
“MR=MC” level
• Real “MR” for firm same as industry MR
• Conventional formula only right for monopoly…
• “Competitive” profit maximizers produce same output
level as monopoly (given comparable costs…)
• An example (with constant MC; rising considered later)
Steve Keen 2006
19
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 2006
20
MC=MR… The 2nd Fallacy
• But profit maximizers 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 2006
21
MC=MR… The 2nd Fallacy
• Does it make much difference?
– It does if you’re trying to maximize profits!
1 a c
• Accepted formula: qc 
•
•
•
•
n 1 b
n a c  1 a c
1 a c
 qc    a  b 


c


n 1 b  n 1 b
n 1 b

2
a  c 
Solving for profit:  qc   b  n  1 2


1 a c
q

Correct formula:
k
2 n b
1 a c  1 a c
1 a c

 qk    a  b  n 
c 

2
n

b
2
n

b
2 n b


2
1 a  c 
Solving for profit:  qk   4 n  b
2
2
1 a  c 
a  c 
For n>1  qk   4 n  b   qc  
2
b  n  1
Steve Keen 2006
22
MC=MR… The 2nd Fallacy
• How much difference is that?
– Lots! And the more firms, the more it matters
– Try a=800, b=1/10,000,000, c=100
• Conventional formula recommends up to twice true
profit-maximizing output…
Output Level
3 10
2 10
Recommended output level
Conventional formula
Keen formula
9
Ratio
2
1.8
1.6
9
1.4
1 10
9
1.2
0
20
40
60
80
Number of firms in industry
Steve Keen 2006
Ratio Conventional to Keen
4 10
9
1
100
23
• And results in 96% less profit (with 100 firms)
Resulting profit level
• Mr Businessman’s
10
4 10
30
reaction to the
Conventional formula
25
Keen formula
10
advice?
3 10
Ratio
20
2 10
1 10
10
15
10
10
5
0
20
40
60
80
Ratio Keen to Conventional
Output Level
MC=MR… The 2nd Fallacy
You’re
promoted!
0
100
Number of firms in industry
Steve Keen 2006
24
Costs & Revenue
MC=MR… The 2nd Fallacy
Profit maximizing output level
for ith firm in n-firm industry
MC
MR  MC 
n 1
P  MC
n
True profit
maximizing
rule
(Generalized rising
marginal cost
formulae are)
P Q   MCi qi 
qi  
n  P ` Q 

MR  MC
1 n
P    MCi qi 
P = AR > MR
n i 1
Q 
P ` Q 
MR
Conventional economic belief
Quantity
Equilibrium where curves don’t intersect…
Steve Keen 2006
25
Summing up “Marshall”
• “Marshallian” theory of the firm incoherent
– Monopoly/perfect competition distinction based on
mathematical fallacy
– “Atomistic competition” leads to same output as
monopoly (if costs comparable… another problematic
issue!)
– Rational profit-maximizing incompatible with
welfare maximization
• Can’t achieve welfare ideal of Marginal
Cost=Price if firms profit-maximize
• Welfare results of theory turned on head
Steve Keen 2006
26
Summing up “Marshall”
• “PC” prices at same level as monopoly
• Profit maximization incompatible with welfare
maximization
• General equilibrium analysis invalidated
• Monopoly better than competition according to
corrected neoclassical theory: same aggregate pricing
policy (MR=MC), lower costs via economies of scale…
• Theory is a shambles…
– “Deadweight loss of monopoly” actually “deadweight
loss of profit maximization”
Steve Keen 2006
27
Summing up “Marshall”
The aggregate picture (correcting Mankiw)
Price
Profitmaximizing
price
Deadweight loss
due to profit maximization
Marginal
revenue
0
ProfitWelfare
maximizing Efficient
quantity quantity
Steve Keen 2006
Demand
Quantity
28
Summing up “Marshall”
• Monopoly better than perfect competition if costs
lower (as is likely):
Price
Welfare gain
due to monopoly
Competitive
price
Monopoly
price
Marginal
revenue
Competitive Monopoly
quantity
quantity
0
Demand
Quantity
Steve Keen 2006
29
But what about Cournot?
• Game theory as alternative defence of perfect
competition
– Assumes firms are profit maximizers, and
• Sees profit-maximizing behavior as constrained
by strategic interactions with other firms
• Firms set output level based on expected
strategic reactions of other firms
– Interactions make “MR=MC” the “best response”
strategy
– As shown above, MR=MC converges to P=MC as
number of firms rises
• An example shortly…
– But before more theory, a reality check…
Steve Keen 2006
30
Theory versus reality?
• In real sciences, laws are explanations/codifications
of empirical regularities
– Law of Conservation of Energy
– Second Law of Thermodynamics (rising entropy)
• Derived from empirical observation
• Never violated in real world
• Economics also has “Laws”
– “Law” of Diminishing Marginal Productivity
• Basis of rising marginal cost
• Any violations in reality?…
– So many it’s a joke: between 89 & 95 per
cent of firms report constant or falling
marginal cost
Steve Keen 2006
31
Theory versus reality?
• Over 100 survey studies have shown marginal costs
fall or are constant for between 89% & 95% of firms
& products
• Most recent survey work Blinder et al. 1998: Asking
About Prices
• Neoclassical theory ignores this research
– Never acknowledged in textbooks
– Rarely cited in (neoclassical) research papers
– Why? Empirical literature ignored because
incompatible with accepted theory
Economic facts of the firm
• Does marginal cost rise?
– Blinder’s results: only minority have rising marginal
cost
• 41% of firms have falling marginal costs
• 48% of firms have constant marginal costs
• Only 11% of firms have rising marginal costs
• “The overwhelmingly bad news here (for
economic theory) is that, apparently, only 11
percent of GDP is produced under conditions of
rising marginal cost.” (102)
Steve Keen 2006
33
Economic facts of the firm
• Why are falling marginal costs “bad for theory”?
– Because theory sees price as reflecting relative scarcity
– If demand rises, relative scarcity rises  price should
rise
• With falling marginal costs, rise in demand  fall in price
– “price signals” don’t function as economists expect
• Maybe prices don’t reflect relative scarcity
• Maybe other factors (e.g., rate of growth of demand) play
role economists assume played by prices
– Think computer, MP3 players
• Rising demand & falling price
• Falling relative price obviously doesn’t make products
less profitable to produce
Steve Keen 2006
34
Economic facts of the firm
• Economic facts of the firm conflict
strongly with assumptions of
(neoclassical) economics
– Infrequent price adjustments
– Fixed price contracts common
– Most sales to other businesses,
not “utility maximizing” consumers
– Fixed costs very important, large
percentage of product costs
– Marginal costs fall for most
businesses, not rise
• So what’s gone wrong with theory?
• Ignores reality in order to maintain a
priori beliefs in supply and demand
• Economic methodology encourages
counter-factual theory on false basis
of “assumptions don’t matter”…
Steve Keen
Summary of Selected Factual Results
Price Policy
Median number of price changes in a year
Mean lag before adjusting price months following
Demand Increase
Demand Decrease
Cost Increase
Cost Decrease
Percent of firms which
Report annual price reviews
Change prices all at once
Change prices in small steps
Have nontrivial costs of adjusting prices of
which related primarily to
the frequency of price changes
the size of price changes
Sales
Estimated percent of GDP sold under contracts
which fix prices
Percent of firms which report implicit contracts
Percent of sales which are made to
Consumers
Businesses
Other (principally government)
Regular customers
Percent of firms whose sales are
Relatively sensitive to the state of the economy
Relatively Insensitive to the state of the economy
Costs
Percent of firms which can estimate costs at least
moderately well
Mean percentage of costs which are fixed
Percentage of firms for which marginal costs are
Increasing
Constant
2006
Decreasing
1.4
2.9
2.9
2.8
3.3
45
74
16
43
69
14
28
65
21
70
9
85
43
39
87
44
11
3548
41
“Let’s assume the opposite of reality…”
• Literature on actual behavior of firms was real target of
Friedman’s 1953 “assumptions don’t matter” methodology
paper:
– “the businessman may well say that he prices at average
cost, with of course some minor deviations when the
market makes it necessary. The ... statement is [not] a
relevant test of the associated hypothesis.” (Friedman
1953)
– Ignore what businesses say they do?
– Shouldn’t we instead be modelling what they do?
• Back to theory…
– Standard response of neoclassical economists to my
demolition of Marshallian “theory” has been…
What about “game theory”?
• “Ah! But that doesn’t matter!
– Cournot-Nash game theory reaches same result
• (Marshallian theory just a ‘parable’ we teach
undergrads…)”
• The argument goes
– Real firms interact with each other strategically
– “Best response” in strategic interaction converges
to perfect competition as number of firms
• Unlike Marshallian theory, Cournot game theory
mathematically correct
– But there are problems…
– First, an example:
Steve Keen 2006
37
What about “game theory”?
• Linear demand curve P(Q)=a-bQ
• Two firms with identical costs tc(q)=k+cq+ ½dq2
• “Payoff matrix” shows output combinations if:
– Both firms produce profit-maximizing amount
n 1
MR  MC 
P  MC
n
– Or Both firms produce where MR=MC
– Or combination of strategies…
Outputs
Firm 1
Firm 2
MR MC
MR
MC
Firm 1
MR
MC
1 2 P MC
q1
q2
q1
a c
3b d
q2
a c
3b d
Firm 2
MR MC 1 2 P MC
2ab 2bc ad cd
5 b2 5 b d d2
q1
ab bc ad cd
5 b2 5 b d d2
q2
ab bc ad cd
5 b2 5 b d d2
q1
a c
4b d
2ab 2bc ad cd
5 b2 5 b d d2
q2
a c
4b d
• MC=MR output
clearly higher
• What about profit
levels?
Steve Keen 2006
38

What about “game theory”?
• “Defector” clearly gains, “Cooperator” clearly loses:
• But both lose with twin “Defect” strategies vs twin
“Cooperate”
Profit Change
Firm 1
Firm 2
MR MC
MR
MC
Firm 1
MR
MC
1 2 P MC
Firm 2
MR MC 1 2 P MC
b2 a c 2
2 3b d 2 4b d
b2 a c 2 7 b2 6 b d d2
2 4 b d 5 b2 5 b d d2 2
b2 a c 2
2 3b d 2 4b d
b2 a c 2 9 b2 10 b d 2 d2
2 4 b d 5 b2 5 b d d2 2
b2 a c 2 9 b2 10 b d 2 d2
2 4 b d 5 b2 5 b d d2 2
0
b2 a c 2 7 b2 6 b d d2
2 4 b d 5 b2 5 b d d2 2
0
• Note: no longer accurate to describe strategies as
“cooperate” vs “defect” since firms can work out profitmaximising output level without collusion…
• However…
Steve Keen 2006
39
What about “game theory”?
• At first glance, looks clearcut…
– “Cooperate” (“Keen strategy”) yields highest shared
profit; but
– “Defector” gains from defection
– Both “defect” (“Cournot strategy”); higher output,
lower profit from strategic interaction…
– Limit of process (as number of firms rises) is
“perfect competition”
• But as usual, problems on deeper examination:
– Problem of repeated games (old result); and…
– Cournot strategy locally unstable (new result)
Steve Keen 2006
40
Repeated Games
• Quoting Varian: “The prisoner’s dilemma has provoked a lot
of controversy as to … what is a reasonable way to play
the game. The answer seems to depend on ... whether the
game is to be repeated an indefinite number of times. If
… just one time, the strategy of defecting … seems …
reasonable… However, … In a repeated game, each player
has the opportunity to establish a reputation for
cooperation, and thereby encourage the other player to do
the same.” (2003: 503)
– Game theory “unstable” proof of competitive outcome.
Given repeated games, “monopoly” outcome likely
• Competition in real world has to be seen as repeated
game
• Why the instability? Let’s check out the “equilibrium”
Steve Keen 2006
41
Local instability
• “Defect/Cooperate” interpretation of Prisoner’s Dilemma
implies “Cooperate” (“Keen”) strategy unstable
– Defector increases profit by producing where MR=MC
• Much higher output, slightly lower market price
– Cooperator suffers
• Lower output, slightly lower market price
• However, this interpretation implies
– (a) One firm will not react when other changes output
– (b) Each firm “knows everything” about what other firm
might do
• “Real world” closer to
– (a) One firm will react when other changes output
– (b) Each firm “knows nothing” about what other firm
might do
Steve Keen 2006
42
Local instability
• Assume firms start at Cournot output level
– What happens to profits of both if “Column” Firm
C’s output change
(C) increases output by 1 unit?
– How is “Row firm” (R) likely to react?C’s profit change
• Table shows changes in profit for +/- 3 units:
3
2
1
3
99.9567
99.9567
66.6378
99.9567
33.3189
99.9567
2
99.9567
66.6378
66.6378
66.6378
33.3189
66.6378
1
99.9567
33.3189
66.6378
33.3189
33.3189
33.3189
0
99.9567
18009
20000000000
66.6378
2001
5000000000
33.3189
2001
20000000000
1
99.9567
33.3189
66.6378
33.3189
33.3189
33.3189
2
99.9567
66.6378
66.6378
66.6378
33.3189
66.6378
3
99.9567
99.9567
66.6378
99.9567
33.3189
99.9567
R’s output change
1
2
3
18009
20000000000
0
33.3189
99.9567
66.6378
99.9567
99.9567
99.9567
2001
5000000000
33.3189
66.6378
66.6378
66.6378
99.9567
66.6378
2001
20000000000
33.3189
33.3189
66.6378
33.3189
99.9567
33.3189
33.3189
66.6378
99.9567
99.9567
66.6378
33.3189
0
0
2001
20000000000
2001
5000000000
18009
20000000000
2001
20000000000
33.3189
33.3189
66.6378
33.3189
99.9567
33.3189
2001
5000000000
33.3189
66.6378
66.6378
66.6378
99.9567
66.6378
18009
20000000000
33.3189
99.9567
66.6378
99.9567
99.9567
99.9567
33.3189
66.6378
99.9567
R’s profit change
Steve Keen 2006
43
Local instability
• Firm getting negative result from output change will
change its strategy…
3.0
3.0
99.9567
99.9567
2.0
66.6378
99.9567
1.0
33.3189
99.9567
2.0
99.9567
66.6378
66.6378
66.6378
33.3189
66.6378
1.0
1.0
99.9567
33.3189
99.9567
9. 10 7
99.9567
33.3189
66.6378
33.3189
66.6378
4.0 10 7
66.6378
33.3189
33.3189
33.3189
33.3189
1.0 10 7
33.3189
33.3189
2.0
99.9567
66.6378
66.6378
66.6378
33.3189
66.6378
3.0
99.9567
99.9567
66.6378
99.9567
33.3189
99.9567
0
0
9. 10 7
99.9567
4.0 10 7
66.6378
1.0 10 7
33.3189
0
0
1.0 10 7
33.3189
4.0 10 7
66.6378
9. 10 7
99.9567
1.0
33.3189
99.9567
2.0
66.6378
99.9567
3.0
99.9567
99.9567
33.3189
66.6378
66.6378
66.6378
99.9567
66.6378
33.3189
33.3189
33.3189
1.0 10 7
33.3189
33.3189
66.6378
33.3189
66.6378
4.0 10 7
66.6378
33.3189
99.9567
33.3189
99.9567
9. 10 7
99.9567
33.3189
33.3189
66.6378
66.6378
66.6378
99.9567
66.6378
33.3189
99.9567
66.6378
99.9567
99.9567
99.9567
• C increases output by 1 & R does nothing, both lose…
• R increases by 1, both lose…
• R decreases by 1, R loses & C gains…
• But if C reduces output & so does R, both win:
reinforcing result applies…
Steve Keen 2006
44
Local instability
• Interaction between competitors in vicinity of Cournot
output level causes movement away from it by
reducing output
– Position is locally unstable: not a true equilibrium
• On the other hand, Keen output level locally stable:
– No combination of moves that cause both parties
to gain; one’s move counters others, so dynamics
oscillates around Keen equilibrium level…
3
6
2
1
0
1
2
3
24.9913
24.9913
49.9825
49.9825
74.9738
74.9738
99.965
99.965
124.956
124.956
149.948
149.948
0.
0.
24.9913
24.9913
49.9825
49.9825
74.9738
74.9738
99.965
99.965
124.956
124.956
24.9913
24.9913
49.9825
49.9825
74.9738
74.9738
99.965
99.965
0
0
24.9913
24.9913
49.9825
49.9825
74.9738
74.9738
24.9913
24.9913
49.9825
49.9825
0.
0.
24.9913
24.9913
24.9913
24.9913
1.90735 10
1.90735 10
2
3.8147 10
3.8147 10
24.9913
24.9913
1
49.9825
49.9825
24.9913
24.9913
0
74.9738
74.9738
49.9825
49.9825
1.90735 10
1.90735 10
24.9913
24.9913
1
99.965
99.965
74.9738
74.9738
49.9825
49.9825
24.9913
24.9913
2
124.956
124.956
99.965
99.965
74.9738
74.9738
49.9825
49.9825
3
149.948
149.948
124.956
124.956
99.965
99.965
74.9738
74.9738
3
6
6
6
1.90735 10
1.90735 10
24.9913
24.9913
Steve Keen 2006
49.9825
49.9825
6
6
45
6
6
Local instability
• Implies profit-maximising firms will “grope” way
towards Keen equilibrium.
• Checking this out experimentally: define
“instrumentally rational profit maximizer” (IRPM):
– Changes output (either increase or decrease);
– If profit rises, continues to change output in same
direction
– If profit falls, changes direction
• Test outcome of virtual market with defined demand
curve P(Q)=a-bQ and population of IRPMs
Steve Keen 2006
46
Virtual market
• The program:
Sim( f  r  s  a  b  C D  E k) 
Arguments:
No. of firms
Iterations
Random seed
Seed random number generator
Seed ( s )
Q  round
 q K( f  a  b  Callocated
 D  E)  q C( f between
a  b  C D  EKeen
) 
runif frandomly
Initial
outputs
& Cournot levels
0
Q  a  b 

0


p  P
0
Initial price based on initial aggregate output
Randomly allocated fixed amount by which each firm alters its
q C( f  a  b  C D  E)  
 each
 iteration;
mean 0,
dq  output
round  rnorm
 f  0
  st. dev. 1% of Cournot output
level
100



for i  1  r
Q Q
i
i 1
Each firm alters its output by its dq amount
 dq
Demand parameters pi  P Qi  a  b 
Cost parameters
Repeat this loop
for r iterations
Calculate
new price




Each
firm works out whether its profit has risen; if so, no
dqchange;
 sign if
p  Q  tc Qhas
 f  Cfallen,
 D  E k each
  p firm
Q
 tc Q  fsign
 C D of
E kits
dq
 dq
i
i
i 1 i 1 changes
i 1
  i profit

Return matrix of each iteration for each firm
Q
• The results:
Steve Keen 2006
47
Virtual market
• Market output converges towards Keen prediction:
Virtual Market of IRPMs
Market Output
8
9 10
8 10
8
7 10
8
6 10
8
5 10
8
4 10
8
Model outcome 1000 firms
Neoclassical Prediction
Keen Prediction
0
100
200
300
400
500
600
700
800
900
1000
Iterations
Steve Keen 2006
48
Price & Cost
Virtual market
• 1,000 firm industry produces aggregate amount very
close to neoclassical “monopoly” prediction:
Aggregate market outcome
• Must be
100
Demand curve
some
Marginal revenue
Aggregate marginal cost
“deep”
80
Market equilibrium
problem
with
60
CournotNash
40
model…
• Let’s look
20
more
closely…
0
0
1 10
8
2 10
8
3 10
8
4 10
8
5 10
8
6 10
8
7 10
8
8 10
8
9 10
8
1 10
9
Quantity
Steve Keen 2006
49
Best response is MR=MC: the 3rd fallacy
• Cournot-Nash game theory mathematically OK (unlike
Marshallian) since sets qi  0
• Feasible therefore that
q j
n
qi
q
 i 0
qi j  i q j
• So effectively horizontal demand curve for each firm
• But still “problem” of repeated instability. Why?
– Standard CN analysis game theoretic
• Either “cooperate” or “defect”
q i
– Discrete values for q
j
• Our innovation: consider variable
qi
 i , j
qj
– Reaction of ith firm to output change by jth
• What is optimal value for profit maximizer?
Steve Keen 2006
50
The 3rd fallacy
• Profit for ith firm is
P Q  qi  TC qi 
• Optimal value is where total derivative is zero:
d
d
  qi  
P Q  qi  TC qi   0
dQ
n 




j 1  q j
dQ
  n 
 dq j 
0
 P  q j  qi  TC  qi  

  j 1 
 dQ 
• Expanding, this
is
• In terms of ij, for the ith firm, this is:
n
n


dP n n
P    i , j  j , k   qi
 j , k  MC  qi   i , j  0

dQ j 1 k 1
j 1 
k 1
j 1

n
• Can now compare Marshallian & Cournot analysis
– Marshallian: i , j  0, i  j
dP
 MC  qi   0
– Substitute: formula reduces to P  nqi
Steve Keen 2006
dQ
51
The 3rd fallacy
• As before, Neoclassical “profit-maximization” rule false
dP
 MC  qi   0 can be rearranged to:
dQ
n 1
MR  qi   MC  qi  
P  MC qi  
n
P  nqi
• Neoclassical “rule” only maximises profit for n=1
• Multi-firm industry, profit maximisation is MR>MC
• What about when ij non-zero?
– What is optimal value of ij ?
q
qi
– Consider heuristic case i  j : q j   ; qii  1
dP
• Then profit maximum is  n  1 P  P  nqi dQ  MC qi 
• Optimal value of  where
d
  qi   0
d
Steve Keen 2006
52
The 3rd fallacy
• Optimal  value is zero:
d
1 d 
dP

  qi  
Q  P  nqi
 MC  qi  
d
n d 
dQ

• Illustration:
P Q   a  bQ
– Linear demand curve
• Constant marginal cost c, fixed cost k
• Profit-maximising output for ith firm as function
of  and n is q  , n     n  1  1 a  c
nb   n  1   2 
• Per firm profit:



  n  1  1 a  c  a  c     n  1  1 a  c
 max  , n  

 nb  n  1   2 2
nb   n  1  2 




2

k


• Maximum value at =0
– Example: a=800, b=1/10,000,000, k=1,000,000
c=100, 20 firm industry…
Steve Keen 2006
53
The 3rd fallacy
• Cournot-Nash recommended level of strategic interaction
generates 1/5th profit level of no interaction at all
Profit (LHS) and quantit y (RHS) as function of theta for 20 firm indust ry
300
10
3 10
5 10
10
2.5 10
4 10
10
2 10
3 10
10
1.5 10
8
8
10
2 10
1 10
8
1 10
5 10
7
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
8
8
250
0.8
200
0.6
150
0.4
100
0.2
50
Interaction parameter theta
Maximum profit as function of theta
Cournot Profit
Profit maximizing quantity as function of theta
Cournot quantity
0
100
200
300
400
500
600
700
800
900
0
1000
Number of firms in industry
• Cost of strategic interaction rises with n:
• No interaction 300 times as profitable as Cournot
interaction for 1,000 firms…
• What are real firms likely to do?
Steve Keen 2006
54
Cournot recommended Theta value
6 10
Profit ratio (LHS)
Theta value (RHS)
8
Ratio of Keen to Cournot per firm profits
3.5 10
10
7 10
Maximum Profit
Ratio of maximum equilibrium firm profit
8
Profit maximizing quantity
8 10
4 10
10
From Fallacies to Reality
• As empirical literature shows, set price well above marginal
cost!
– Research ignored because incompatible with “theory”
– Target of Friedman’s (in)famous 1953 methodology paper
• “the businessman may well say that he prices at
average cost…
• The … statement is [not] a relevant test of the
associated hypothesis.”
• Ignore what businesses say they do?
• Can no longer ignore what businesses actually do when
“associated hypothesis” is gibberish
– What should a real “theory of the firm” be?
• A model that explains & interprets actual data
Steve Keen 2006
55
A real theory of the firm?
• Output constrained not by supply (rising costs) but by
demand & finance factors:
• Heterogeneous goods & consumers
• Financial limitations on expansion
– Generates “Power law” distribution of firm sizes
within industries
– Has competition on innovation/marketing rather
than price
– Evolutionary rather than static modelling
• Overall, a micro (finance & demand constrained) that’s
consistent with observed macro (finance & demand
constrained)
Steve Keen 2006
56
And before we have one?
Price
• Teach empirical record of firms’ behaviour: Downie,
Means, Guthrie, Eiteman, Lee, Blinder literature
• Teach Schumpeter on creative destruction,
evolutionary perspective on firm competition
– And teach neoclassical economics the way chemists
teach phlogiston: as an example of an outdated and
erroneous theory
Supply
Pe
Demand
Qe
Quantity
Steve Keen 2006
57
Steve Keen 2006
58
References
•
•
•
•
•
•
•
•
•
•
Blinder, A.S., Canetti, E., Lebow, D., & Rudd, J., (1998). Asking About Prices: a New
Approach to Understanding Price Stickiness, Russell Sage Foundation, New York.
Eiteman, W.J., (1947). 'Factors determining the location of the least cost point',
American Economic Review 37: 910-918.
– 'The least cost point, capacity and marginal analysis: a rejoinder', American
Economic Review 38: 899-904.
Eiteman, W.J. And Guthrie, G.E., (1952). 'The shape of the average cost curve',
American Economic Review 42: 832-838.
Freedman, Craig (1998). “No End to Means: George Stigler's Profit Motive”, Journal
of Post Keynesian Economics, vol. 20, no. 4, Summer, pp. 621-48
Freedman, Craig (1995). “The Economist as Mythmaker--Stigler's Kinky
Transformation ” Journal of Economic Issues, vol. 29, no. 1, March, pp. 175-209
Friedman, M., (1953). "The methodology of positive economics", in Essays in Positive
Economics, University of Chicago Press, Chicago.
Steve Keen, (2001). Debunking Economics: the naked emperor of the social sciences,
Pluto Press & Zed Books, Sydney & London.
Steve Keen, (2004). “Deregulator: Judgment Day for Microeconomics”, Utilities
Policy, 12: 109 –125.
Steve Keen & Russell Standish(2006). “Profit Maximization, Industry Structure, and
Competition: A critique of neoclassical theory”, Physica A 370: 81-85.
Lee, F.S., (1998). Post Keynesian Price Theory, Cambridge University Press, New York.
Steve Keen 2006
59
References
• Lipsey, R. G., & Chrystal, K. A., (1999). Principles of Economics: 9e,
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