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Profit maximization, industry structure & competition
Steve Keen (UWS)Russell Standish (UNSW)
From finance to economics?
• To date, econophysics has been the physics of finance– Attractions:
• Fantastic data sets• Market behavior clearly contrary to neoclassical beliefs• Relatively easy application of existing toolkit
• A plea: please consider a physics of economics too!– Attractions:
• Lousy data sets…• Market behavior clearly contrary to neoclassical beliefs• You have the toolkits that economists lack…
“In the beginning was Marshall…”
• Example: “theory of the firm”• “Baby” version of theory of firm “Marshallian”
– Firms are profit-maximizers– Diminishing marginal productivity—rising marginal
cost– Maximize profits by equating “marginal revenue”
(MR) to “marginal cost” (MC)– If industry “competitive”, constant MR=Market Price
• “Supply=Demand” optimal output level– Marginal Benefit to society (Price=MB) equals MC
– If monopoly, face falling marginal revenue• Sub-optimal output level• MB exceeds MC• Higher output would be socially beneficial…
“And Marshall said, ‘let there be competition’”
• Monopoly vs perfect competition distinction “atomism”– Individual firms so small that
• don’t react to what others do• are “price-takers”:
– can produce any amount without affecting price• So…
0
dP Q
dQ
0
i
dP Q
dq– for the individual firm
• Model forms base instruction of all economists– Believed true by 90% of more of them…
– Therefore… while for the market
0j
i
q
q
“A reading from the bible according to Gregory”
• This & next 4 slides from popular introductory economics textbook, Mankiw, Principles of Economics…– …
• Comparing Monopoly and Competition– For a competitive firm, price equals marginal cost.
P = MR = MC– For a monopoly firm, price exceeds marginal cost.
P > MR = MC
Quantity of Output
Demand
(a) A Competitive Firm’s Demand Curve
(b) A Monopolist’s Demand Curve
0
Price
0 Quantity of Output
Price
Demand
Demand Curves for Competitive and Monopoly Firms...
Price
0 Quantity
Marginal cost
Demand(value to buyers)
Efficientquantity
Cost to monopolist
Value to buyers
Value to
buyers
Cost to monopolist
Value to buyers is greater than cost to seller.
Value to buyers is less than cost to seller.
The Efficient Level of Output...
P = AR = MR
P=MR1
MC
Profit Maximization for the Competitive Firm...
Quantity0
Costsand
Revenue
ATC
AVC
QMAX
The firm maximizes profit by producing the quantity at which marginal cost equals marginal revenue.
MC1
Q1
MC2
Q2
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
The Inefficiency of Monopoly...
Quantity0
DemandMarginalrevenue
Marginal cost
Monopolyprice
Deadweightloss
Efficientquantity
Monopolyquantity
Price
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
“Then there was lousy mathematics…”
• “Marshallian” case mathematical nonsense– If atomism applies, then
i
dP dP
dq dQ
i i
dP dP dQ
dq dQ dq
• In the literature for 38 years, but ignored!:
nji
j ii i
qqdP
dQ q q
1 0n
j i
dP dP
dQ dQ
1
nj
j i
qdP
dQ q
“And Cournot said, ‘let there be strategy’”
• “Grown up” theory of firm is Cournot-Nash game theory• implicitly sets 0j
i
q
q
• Feasible that 0n
ji
j ii i
q q
• Standard CN analysis game theoretic
– Either “cooperate” or “defect”• In our terms, discrete values for j
i
q
q
• Our innovation: consider variable ,j
j ii
q
q
– Reaction of jth firm to output change by ith
• What is optimal value?
“And we said, ‘how much?’”
• Profit for ith firm is
0i i i
d dq P Q q TC q
dQ dQ
1 1
0n n
jj i i
j jj
dqP q q TC q
q dQ
, , , ,1 1 1 1 1
0n n n n n
j i k j i k j i j ij k j k j
dPP q MC q
dQ
i iP Q q TC q
• Optimal value is where total derivative is zero:
• Expanding, this is
• In terms of ij, for the ith firm, this is:
• Can now compare Marshallian & Cournot analysis– Marshallian: , 0,j i i j
– Substitute: formula reduces to 0i i
dPP nq MC q
dQ
“Verily, Marshall be bollocks then?”
• Neoclassical “profit-maximisation” rule false
1i i i
nMR q MC q P MC q
n
j
i
q
q i j 1i
i
1 i i
dPn P P nq MC q
dQ
0i i
dPP nq MC q
dQ can be rearranged to:
• 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 ?
– Consider heuristic case • Then profit maximum is
• What is optimal value of ?• Occurs where 0i
dq
d
“Do not lead us into the valley of profitless”
• Optimal value is zero: 1i i i
d d dPq Q P nq MC q
d n d dQ
P Q a bQ
1 1
,1 2
n a cq n
nb n
2
max 2
1 1 1 1,
1 2 1 2
n a c a c n a cn k
nb n nb n
• Illustration:– Linear demand curve
• Constant marginal cost c, fixed cost k
• Profit-maximising output for ith firm as function of and n is
• Per firm profit is
• Maximum value at =0 – Example: a=800, b=1/10,000,000, k=1,000,000
c=100, 20 firm industry…
“Do not worship false cows before me”
• Cournot-Nash recommended level of strategic interaction generates 1/5th profit level of no interaction at all
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1 1010
2 1010
3 1010
4 1010
5 1010
6 1010
7 1010
8 1010
0
5 107
1 108
1.5 108
2 108
2.5 108
3 108
3.5 108
4 108
Maximum profit as function of thetaCournot ProfitProfit maximizing quantity as function of thetaCournot quantity
Maximum profit as function of thetaCournot ProfitProfit maximizing quantity as function of thetaCournot quantity
Profit (LHS) and quantity (RHS) as function of theta for 20 firm indust ry
Interaction parameter theta
Max
imum
Pro
fit
Pro
fit
max
imiz
ing
quan
tity
100 200 300 400 500 600 700 800 900 10000
50
100
150
200
250
300
0
0.2
0.4
0.6
0.8
Profit ratio (LHS)Theta value (RHS)Profit ratio (LHS)Theta value (RHS)
Ratio of maximum equilibrium firm profit
Number of firms in industry
Rat
io o
f K
een
to C
ourn
ot p
er f
irm
pro
fits
Cou
rnot
rec
omm
ende
d T
heta
val
ue
• 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?
From religion to evolution…
• Consider population of instrumental profit maximisers
F0 0 q.K 1 a b C D E( )
F1 0 q.K 1 a b C D E( )
Seed j 1( )
Q0
round runif i q.K i a b C D E( ) q.C i a b C D E( )
p0
P Q0 a b
dq 50000sign runif i 1 1( )( )
Qk
Qk 1 dq
pk
P Qk a b
dq sign pk
Qk
pk 1 Q
k 1 tc Qk
i C D E k tc Qk 1 i C D E k dq
k 1 runsfor
Q.endj
Qk Q
k 1 Qk 2 Q
k 3
4
j 0 rand 1for
Fi 0 mean Q.end
Fi 1 stdev Q.end
Q.end 0
i firms.min firms.min firms.steps firms.maxfor
F
– Change output +/-
– Choose initial output
– If profit rises, repeat
– If falls, change sign…
From reductionism to complexity
• Simple agent design generates striking behavioral complexity…
0 50 100 150 200 250 300 350 400 4502 10
7
3 107
4 107
5 107
6 107
7 107
8 107
CournotKeenMeanFirm 1Firm 2Firm 3
CournotKeenMeanFirm 1Firm 2Firm 3
Firm Outputs, 100 firms: 3 samples
Iterations
Zero interaction rules…
• Agents converge to Keen equilibrium, not Cournot…
50 100 150 200 250 300 350 400 450 5002.5 10
9
3 109
3.5 109
4 109
4.5 109
5 109
CournotKeenAverage of Simulations
+/- 2 St. Dev.
CournotKeenAverage of Simulations
+/- 2 St. Dev.
Market Output: Rising Marginal Cost
Number of Firms
Ave
rage
Fin
al M
arke
t Out
put
50 100 150 200 250 300 350 400 450 5003.45 10
9
3.5 109
3.55 109
3.6 109
KeenAverage of Simulations
+/- 2 St. Dev.
KeenAverage of Simulations
+/- 2 St. Dev.
Market Output: Constant Marginal Cost
Number of Firms
Ave
rage
Fin
al M
arke
t O
utpu
t
• But curious result applies when fixed step size replaced by normally distributed one…
dq round rnorm i 0q.C i a b C D E( )
10
Zero interaction rules … sort of
• Convergence to Keen equilibrium not as tight for fixed marginal cost…
50 100 150 200 250 300 350 400 450 5002 10
9
3 109
4 109
5 109
6 109
7 109
CournotKeenAverage of Simulations
+/- 2 St. Dev.
CournotKeenAverage of Simulations
+/- 2 St. Dev.
Market Output: Constant Marginal Cost
Number of Firms
Ave
rage
Fin
al M
arke
t Out
put
• But no effect of varying industry structure on result• However for rising marginal cost…
Cournot rises from the dead???
• Apparent trend for convergence to Cournot output level as n rises for normally distributed dq…
50 100 150 200 250 300 350 400 450 5002 10
9
3 109
4 109
5 109
6 109
CournotKeenAverage of Simulations
+/- 2 St. Dev.
CournotKeenAverage of Simulations
+/- 2 St. Dev.
Market Output: Rising Marginal Cost
Number of Firms
Ave
rage
Fin
al M
arke
t Out
put
• But looking more closely, consider:– output for fixed industry structure (value of n)– rising divergence of dq around mean of zero
Testing divergence
• Program iterates over standard deviation of dq from 1% to dispersal % of Cournot firm output level
F0 0 q.K 1 a b C D E( )
F1 0 q.K 1 a b C D E( )
Seed j 1( )
Q0
round runif firms q.K firms a b C D E( ) q.C firms a b C D E( )
p0
P Q0 a b
dq round rnorm firms 01 i100
q.C firms a b C D E( )
Qk
Qk 1 dq
pk
P Qk a b
dq sign pk
Qk
pk 1 Q
k 1 tc Qk
firms C D E k tc Qk 1 firms C D E k dq
k 1 runsfor
Q.end j
Qk Q
k 1 Qk 2 Q
k 3
4
j 0 rand 1for
Fi 0 mean Q.end
Fi 1 stdev Q.end
Q.end 0
i 0 dispersal .steps dispersal 1for
F
“Nope, he’s still dead!”
• Convergence to Cournot a function not of number of firms, but of dispersal of dq!
0 2 4 6 8 10 12 14 16 18 202 10
9
3 109
4 109
5 109
6 109
CournotKeenAverage of Simulations
+/- 2 St. Dev.
CournotKeenAverage of Simulations
+/- 2 St. Dev.
Market Output vs Dispersal (Rising Marginal Cost)
Per cent of qC
Ave
rage
Fin
al M
arke
t Out
put
• Conjecture: result due to stochastic differential effects
– ij a stochastic variable…
Goodbye to the ‘totem of the econ’
• Neoclassical religion teaches “perfect competition good, monopoly bad”– But Marshallian
theory bollocks– Cournot results
depend on dispersal, not n…
0 2 109
4 109
6 109
8 109
1 1010
0
200
400
600
800
1000
1200
Price FunctionMarginal RevenueMarginal CostCournot 50 FirmsKeen1% dispersal10% dispersal20% dispersal
Price FunctionMarginal RevenueMarginal CostCournot 50 FirmsKeen1% dispersal10% dispersal20% dispersal
Market Functions, Predictions, Outcomes: 50 firms
Market Quantity
Dem
and,
Mar
gina
l Rev
enue
, Mar
gina
l Cos
t
• Worse still, neoclassical assumptions counter-factual• Not simplifications of reality, but contradictions of it…
“Just the facts, Ma’am”
• Diminishing marginal productivity/Rising marginal cost?
– “The overwhelmingly bad news here (for economic theory) is that, apparently, only 11 percent
of GDP is produced under conditions of rising marginal cost. Almost half is produced under constant MC… But that leaves a stunning 40 percent of GDP in firms that report declining MC functions” (Blinder 1998: 102)
• “Applied” economic concepts like Elasticity of demand?– “Can it really be true that firms that sell 40
percent of GDP believe that their demand is totally insensitive to price, and that only about one-sixth of GDP is sold under conditions of elastic demand?” ([Blinder]: 101)
Blinder’s economic facts of the firm• Economic facts of the firm conflict
strongly with assumptions of (neoclassical) economics– Infrequent price adjustments
Summary of Selected Factual ResultsPrice Policy
Median number of price changes in a year 1.4Mean lag before adjusting price months followingDemand Increase 2.9Demand Decrease 2.9Cost Increase 2.8Cost Decrease 3.3Percent of firms whichReport annual price reviews 45Change prices all at once 74Change prices in small steps 16Have nontrivial costs of adjusting prices of 43which related primarily tothe frequency of price changes 69the size of price changes 14
SalesEstimated percent of GDP sold under contractswhich fix prices 28Percent of firms which report implicit contracts 65Percent of sales which are made toConsumers 21Businesses 70Other (principally government) 9Regular customers 85Percent of firms whose sales areRelatively sensitive to the state of the economy 43Relatively Insensitive to the state of the economy 39
CostsPercent of firms which can estimate costs at leastmoderately well 87Mean percentage of costs which are fixed 44Percentage of firms for which marginal costs areIncreasing 11Constant 48Decreasing 41
– 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
• Neoclassical theory irredeemably bad
• Internally flawed• Factually irrelevant• We need a new “theory of the
firm”
Econophysicists to the rescue?
• Neoclassical economics a dead end
• Alternative evolutionary theory of firm needed– Schumpeter’s “creative destruction” best verbal
model– Economists not up to the task of formalising it
• ‘great expectations … have only become substantiated slowly and partially… First, … there are significant there are significant barriers to entrybarriers to entry for students and researchers who want to explore and extend evolutionary models by simulation; you simply have to master a great many you simply have to master a great many skills to be able to combine evolutionary theorising and skills to be able to combine evolutionary theorising and simulation in a fruitful waysimulation in a fruitful way. Second, there is a lack of cumulativeness … many entrants to the field seem to build their efforts from scratch.’ (Anderson & Valente: 44)
Econophysicists to the rescue?
• Physics skill set much more up to the job than economics• Please… having reinvented finance…
• And help move economics– from a religion– to a science…
