The theory of the firm

1
The theory of the firm

• Debunking

• Steve Keen

2
In the beginning was

• The

• Cross

• Marshallian

• How to restore the original result?
• Perfect competition!

• Lost welfare

Demand

• 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!

3
Rescued by perfect competition

• Perfect competition and supply demand

Price taking atomistic firms
Horizontal demand curve for single firm
Downward sloping market demand curve

• Welfare
• maximization
• restored...

Pe
Pe
Demand
qe
Qe
Supply curve is sum of marginal cost curves
4
Standard introductory supply demand

• Monopoly bad
• Monopoly maximizes profit by equating marginal
  cost and marginal revenue

• Negative

• Price exceeds marginal cost with monopoly

• Perfect Competition good
• Firms maximize profit by equating marginal cost
  and marginal revenue BUT marginal revenue equals
  price

• Zero

5
And thats all bunkum!

• Slope of demand curve for individual firm cant
  be zero
• Established in 1957 by George Stigler
• Equating marginal revenue and marginal cost
  doesnt maximise profits
• New result
• Prisoners Dilemma Game Theory hasa (or
  rather, yet another) problem too
• Rational firms wont play games
• New result

6
Horizontal demand curves the 1st Fallacy

• If firms dont react to each other then
• Demand curve for single firm cannot be horizontal
• Atomism incompatible with dP/dq0

• Not a new result!
• First published in 1957!...

7
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)

8
The 1st Fallacy

• The graphical intuition
• If the market demand curve slopes down, then any
  tiny part of it slopes down with the same slope

Price

• Acting as if demand curve horizontal irrational

P
dP
Price
P-DP

• May be small difference, but Infinitesimals
  aint zeros!

qi
q for ith firm
q
Q
QDQ
dq
Quantity
9
The 1st Fallacy

• Cant we just assume price-taking?
• Firm assumes can sell as much as it likes at
  market price
• Surebut this is irrational behavior, not
  rational
• If the market demand curve slopes downwards, then
  any increase in output, no matter how small, must
  cause market price to fall, however
  infinitesimally.

Price
Irrational belief P(Qq)P(Q)
P(Q)
Rational belief P(Qq)ltP(Q)
Q q
Q

• Neoclassical result dependent upon irrational
  behavior

10
The 1st Fallacy

• Summing up so far
• Marginal revenue for individual firm less than
  price
• Demand curve for single atomistic firm cant 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

11
The 1st Fallacy

• Convergence to perfect competition argument
• Profit maximizers equate marginal cost marginal
  revenue

So now we have
where
So that

• True!

• 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 isnt profit-maximizing behavior!

12
MCMR maximizes profits The 2nd Fallacy

• Aggregate effect of equating MC MR

n copies of P
n copies of MC
Replace with Q
Move a P
a MC
Rearranging this
This is MR(Q) (industry, not firm)
13
The 2nd Fallacy (first proof)

• 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

• This component ignored by conventional belief
• But firms can work out what it is

14
The 2nd Fallacy (first proof)

• Profit maximizing formula is not MRiMCi but

• Take earlier formula and rearrange so that
  industry MR-MC is on one side of equals sign

• Set this to zero to find maximum aggregate
  profit
• Take terms in P and MC inside summation

15
The 2nd Fallacy (first proof)

• Equating this expression to zero maximizes profit

• True single-firm profit-maximization rule is

• 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 cant control other firms, must take
  their existence into account

16
The 2nd Fallacy (second proof)

• But firms cant know that!
• Yes they can!
• Problem is

EconomistEasy! Equate MR MC!
Work out the output level that maximizes my
profits!
MathematicianHmm! Interesting problem set
total derivative of profit to zero
17
The 2nd Fallacy (second proof)

• The mathematicians logic
• What other firms do affects your profit
• Even if you cant control them
• Even if they dont react (game theory style) to
  what you do
• So profit maximized by zero of total differential
• So must solve

• Expanding

Equals 1 since with atomism

• Expanding

18
The 2nd Fallacy (second proof)

• Profit maximization rule for single firm is

• Second bit is marginal cost once zero n-1 times

• Equals 1 once when ij

• First bit is

• (n-1) times this is zero since firms independent

• This is

n times
19
MCMR The 2nd Fallacy

• So for profit maximization the firm sets qi so
  that

• 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 MRMC 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)

20
MCMR The 2nd Fallacy

• Standard false neoclassical advice
• equate MRi MC
• Output converges to PC result as number of firms
  increases (Stiglers result)

• Conditions

• Result

Monopoly
Competition
21
MCMR The 2nd Fallacy

• But profit maximizers solve

• Competitive industry produces monopoly level
  output at monopoly price
• Industry output independent of number of firms
• Similar result for other marginal cost functions
  competitive outcome same as monopoly

• Aggregating

• Same as for monopoly

22
MCMR The 2nd Fallacy

• Does it make much difference?
• It does if youre trying to maximize profits!
• Accepted formula

• Solving for profit

• Correct formula

• Solving for profit

• For ngt1

23
MCMR The 2nd Fallacy

• How much difference is that?
• Lots! And the more firms, the more it matters
• Try a800, b1/10,000,000, c100
• Conventional formula recommends up to twice true
  profit-maximizing output

24
MCMR The 2nd Fallacy

• And results in 96 less profit (with 100 firms)

• Mr Businessmans reaction to the advice?

Youre promoted!

• And...

25
MCMR The 2nd Fallacy
Profit maximizing output levelfor ith firm in
n-firm industry
(Generalized rising marginal cost formulae are)
MC
Costs Revenue
P AR gt MR
True profit maximizing rule
MR
Conventional economic belief
Quantity
Equilibrium where curves dont intersect
26
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
• Cant achieve welfare ideal of Marginal
  CostPrice if firms profit-maximize
• Welfare results of theory turned on head

27
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 (MRMC), lower costs via economies
  of scale
• Theory is a shambles
• Deadweight loss of monopoly actually
  deadweight loss of profit maximization

28
Summing up Marshall
The aggregate picture (correcting Mankiw)
29
Summing up Marshall

• Monopoly better than perfect competition if costs
  lower (as is likely)

30
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 MRMC the best response
  strategy
• As shown above, MRMC converges to PMC as number
  of firms rises
• An example shortly
• But before more theory, a reality check

31
Theory versus reality?

• In real sciences, laws are explanations/codificati
  ons 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 its a joke between 89 95 per cent of
  firms report constant or falling marginal cost

32
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

33
Economic facts of the firm

• Does marginal cost rise?
• Blinders 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)

34
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 dont function as economists
  expect
• Maybe prices dont 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 doesnt make
  products less profitable to produce

35
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 whats 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 dont
  matter

36
Lets assume the opposite of reality

• Literature on actual behavior of firms was real
  target of Friedmans 1953 assumptions dont
  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?
• Shouldnt we instead be modelling what they do?
• Back to theory
• Standard response of neoclassical economists to
  my demolition of Marshallian theory has been

37
What about game theory?

• Ah! But that doesnt 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

38
What about game theory?

• Linear demand curve P(Q)a-bQ
• Two firms with identical costs tc(q)kcq ½dq2
• Payoff matrix shows output combinations if
• Both firms produce profit-maximizing amount

• Or Both firms produce where MRMC

• Or combination of strategies

• MCMR output clearly higher
• What about profit levels?

39
What about game theory?

• Defector clearly gains, Cooperator clearly
  loses
• But both lose with twin Defect strategies vs
  twin Cooperate

• Note no longer accurate to describe strategies
  as cooperate vs defect since firms can work
  out profit-maximising output level without
  collusion
• However

40
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)

41
Repeated Games

• Quoting Varian The prisoners 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? Lets check out the
  equilibrium

42
Local instability

• Defect/Cooperate interpretation of Prisoners
  Dilemma implies Cooperate (Keen) strategy
  unstable
• Defector increases profit by producing where
  MRMC
• 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

43
Local instability

• Assume firms start at Cournot output level
• What happens to profits of both if Column Firm
  (C) increases output by 1 unit?
• How is Row firm (R) likely to react?
• Table shows changes in profit for /- 3 units

Cs output change
Cs profit change
Rs output change
Rs profit change
44
Local instability

• Firm getting negative result from output change
  will change its strategy

• 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

45
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 ones move counters others, so dynamics
  oscillates around Keen equilibrium level

46
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

47
Virtual market

• The program

Seed random number generator
Initial outputs randomly allocated between Keen
Cournot levels
Arguments
Initial price based on initial aggregate output
No. of firms
Randomly allocated fixed amount by which each
firm alters its output each iteration mean 0,
st. dev. 1 of Cournot output level
Iterations
Repeat this loop for r iterations
Random seed
Each firm alters its output by its dq amount
Demand parameters
Calculate new price
Each firm works out whether its profit has risen
if so, no change if profit has fallen, each firm
changes sign of its dq
Cost parameters
Return matrix of each iteration for each firm

• The results

48
Virtual market

• Market output converges towards Keen prediction

49
Virtual market

• 1,000 firm industry produces aggregate amount
  very close to neoclassical monopoly prediction

• Must be some deep problem with Cournot-Nash
  model
• Lets look more closely

• "Experimental
• Result"

• "Monopoly"

• "PC"

50
Best response is MRMC the 3rd fallacy

• Cournot-Nash game theory mathematically OK
  (unlike Marshallian) since sets

• Feasible therefore that

• So effectively horizontal demand curve for each
  firm

• But still problem of repeated instability. Why?
• Standard CN analysis game theoretic
• Either cooperate or defect
• Discrete values for

• Our innovation consider variable

• Reaction of ith firm to output change by jth
• What is optimal value for profit maximizer?

51
The 3rd fallacy

• Profit for ith firm is

• Optimal value is where total derivative is zero

• Expanding, this is

• In terms of qij, for the ith firm, this is

• True general profit
• maximization formulae

• Can now compare Marshallian Cournot analysis
• Marshallian

• Substitute formula reduces to

52
The 3rd fallacy

• As before, Neoclassical profit-maximization
  rule false

• can be rearranged to

• Neoclassical rule only maximises profit for n1
• Multi-firm industry, profit maximisation is MRgtMC
• What about when qij non-zero?
• What is optimal value of qij ?
• Consider heuristic case

• Then profit maximum is

• Optimal value of q where

53
The 3rd fallacy

• Optimal q value is zero

• Illustration
• Linear demand curve

• Constant marginal cost c, fixed cost k

• Profit-maximising output for ith firm as function
  of q and n is

• Per firm profit

• Maximum value at q0
• Example a800, b1/10,000,000, k1,000,000
  c100, 20 firm industry

54
The 3rd fallacy

• Cournot-Nash recommended level of strategic
  interaction generates 1/5th profit level of no
  interaction at all

• "A strange game.
• The only winning strategy
• is not to play..."

• 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?

55
From Fallacies to Reality

• As empirical literature shows, set price well
  above marginal cost!
• Research ignored because incompatible with
  theory
• Target of Friedmans (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

56
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)
  thats consistent with observed macro (finance
  demand constrained)

57
And before we have one?

• 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

58

• www.debunking-economics.com

59
References

• Blinder, A.S., Canetti, E., Lebow, D., Rudd,
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  to Understanding Price Stickiness, Russell Sage
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• 'The least cost point, capacity and marginal
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60
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