Why economics must abandon its theory of the firm - · PDF filemarket price. Stigler’s...

Why economics must abandon its theory of the firm

Steve Keen, University of Western Sydney,John Legge, La Trobe University,Geoffrey Fishburn,University of New South Wales, &Michael Kelly, Illinois Institute of Technology1

Abstract: The standard neoclassical equilibrium arguments used to

justify the model perfect competition—and thereby the supply side of supply and

demand analysis—are erroneous. The textbook proposition that the individual firm’s

demand curve is horizontal was disproved by Stigler in 1957, Stigler’s elasticity

convergence equation is easily shown to be invalid if there is a minimum firm size,

and the mantra that a firm maximises profit by equating marginal cost and marginal

revenue is wrong in multi-firm industries. The only feasible defence for perfect

competition comes from game theory, and in this paper we give some tentative

reasons why this defence may also fail. We conclude with a plea that the economics

finally heed the empirical work on firms that shows that marginal cost and marginal

revenue are irrelevant to actual corporations, and start to model reality rather than

myth.

Keywords: Competition, monopoly, perfect competition, oligopoly,

profit maximization, Industrial Organization

JEL Classifications: A20, C71, D20, D21, D41, D42, D43, D46, D50,

D60, L11, L13, L21

Why economics must abandon its theory of the firm

Undergraduate instruction in economics puts the proposition that equilibrium price equals marginal

cost in competitive markets in the following way. Firstly, profit, total revenue and total cost for the

individual firm and the industry are defined as functions of quantity:

A. P(x ) = P(Q)x − TC(x ); x = Q,q (1)

Secondly, it is asserted that given the conditions that the derivative of demand is negative and of

total cost is positive, profit is maximised where the first derivative of profit is zero:

Pmax(x ) : P(Q) + xP ∏(x ) − TC ∏(x ) = 0; x = Q, q (2)

Thirdly, the assumption is made that the individual competitive firm is so small relative to the

entire industry that the derivative of market price with respect to the output of a single firm is zero.

Given this assumption, marginal revenue equals market price for the individual competitive firm.

Profit for the competitive firm is therefore maximised when its marginal cost equals price:

MC(q) = P(Q) = MR(q) (3)

It is not sufficiently well known that this argument is flawed. As Stigler showed in 1957, the slope

of the demand curve for the individual firm cannot be zero, but is instead identical to that for the

market (Stigler 1957: 8). His expression of this was succinct:

dPdqi

= dPdQ

dQdq i

= dPdQ

(4)

This is an unremarkable feature of continuous functions, but it can also be argued that Stigler was

implicitly applying the assumption of atomism. Stating this explicitly, define q as the output of a single

firm and QR as the output of all other firms in the industry. The assumption of atomism then gives us

that . Hence:dQR

dq i= 0

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dPdq i

= dPdQ

dQdq i

= dPdQ

ddq i

(q i + QR )

= dPdQ

ddq i

q i + ddqi

QR

= dPdQ

(1 + 0)

= dPdQ < 0

(5)

Thus , and the demand curve for the individual firm can only be horizontal if the marketdPdq i

= dPdQ

demand curve itself is horizontal.

Stigler proposed a reformulation of marginal revenue for the individual firm which he alleged

showed that the individual firm’s marginal revenue converged to price as the number of firms in an

industry increased. He began with and then worked with the simplification of identicaldPdq i

= dPdQ

output levels ( ) to derive:Q = nq

ddq i

(P % q i ) = P + q dPdQ

= P +Qn

PP

dPdQ

= P + Pn % E

(6)

where is the market elasticity of demand. Curiously writing this out in full English asE = PQ

dQdP

MarginalRevenue = Price + PriceNumberofSellers%MarketElasticity

(7)

he argued that “this last term goes to zero as the number of sellers increases indefinitely” (Stigler

1957: 8). If this were true, then for the very large number of firms that are necessary for the model

of perfect competition, “marginal revenue equals price” would be strictly false, but a reasonable

approximation to the truth.

Why economics must abandon its theory of the firm Keen et al 2002

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However, it should be obvious from the first line of (6) that the only conditions under which

Stigler’s supposition could be true are that , or that . If instead q remains greater thanq d 0dPdQ = 0

zero and , then will not go to zero as , because changes in E and P will exactlydPdQ < 0 P

n%E n d ∞

counterbalance changes in n. This can be made obvious by substituting into Stigler’s finaln = Q/q

line:

P + Pn % E = P + P

Qq % P

QdQdP

= P + PPq

dQdP

(8)

The final line of (8) is of course the same as the first line of (6). If there is a minimum firm size

, then the gap between market price and the individual firm’s marginal revenue isq = qmin > 0

completely independent of the term n. As an illustration, consider an industry with a linear demand

curve, with n identical firms each producing units of output:qmin

P = a − bQ

Q = n % qmin

E = PQ

dQdP =

a − bQQ % −1

b

P − MRi = Pn % E =

a − bQ

n % a−bQQ % b

=a − bQ

Qq min % a−bQ

Q % b= qminb

(9)

The difference between market price and own-output marginal revenue is thus a constant,

regardless of the number of firms in the industry, and is equal to the minimum feasible firm size times

b—the linear equivalent to Stigler’s more general first line in (6). Given that b>0 (and in general

), the only way that price can equal marginal revenue is if the representative firm in thedPdQ < 0

industry produces an infinitesimal output.


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This is a commonplace assumption in the literature on the convergence of Cournot equilibrium to

the competitive equilibrium (Novshek & Sonnenschein 1983; Mas-Colell 1983; Novshek 1985;

and others). However, this assumption raises insurmountable logical problems for both the theory of

exchange and the theory of the firm.

With respect to the theory of exchange, if each firm produces an infinitesimal output, then a

consumer has to purchase all the output of a (lesser) infinity of producers in order to acquire one unit

of a commodity. The consumer must then integrate this infinity of infinitesimals of a commodity to

produce the single unit, thus making the consumer into a producer.

The consumer is clearly in a monopsony position with respect to the infinity of firms from which it

purchases, which raises further logical conundrums. Any attempt to counter this by presuming that

each consumer is in turn an infinitesimal part of demand for each firm rapidly reduces the theory to

the level of farce.

With respect to the theory of the firm, an essential aspect of this is the existence of fixed costs in

the short run. If there were no fixed costs then all inputs would be variable and diminishing marginal

productivity would not occur. Yet for the output of the representative firm to be infinitesimal, fixed

costs must in the limit be zero. The assumption of a limit of zero output for the individual firm is

inconsistent with fixed costs and the phenomenon of diminishing marginal productivity.

We therefore contend that any propositions derived from the condition of infinitesimal output

levels should be inadmissible in economics. There must be some minimum size for the firm qmin p 0

so that fixed costs exist, and so that the firm’s customers are not in a near-monopsony position with

respect to it.

Given the existence of a minimum firm size, does not converge to zero as , butPnE n d ∞

becomes a constant once this minimum size is reached. For a numerical example, consider an


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industry with a linear demand curve given by and technology such that theP = 100− 1100000000 Q

output of minimum size firm is . will fall as n rises, until such time as reachesqmin = 1000 PnE q = Q

n

this minimum scale: from that point on, . While is clearly small, it isPnE = qmin

dPdQ = − 1

100000 − 1100000

not zero, and therefore own-output marginal revenue for the individual firm must be less than the

market price.

Stigler’s argument therefore does not justify the propositions that price equals marginal revenue

for the individual competitive firm, or that price equals marginal cost is a profit maximising

equilibrium. However Stigler’s analysis is strongly related to a proposition first put by Cournot, that

the market equilibrium converges to the competitive equilibrium as the number of firms rises.

This proposition is true, but there is a fundamental problem with using it either to model

non-interactive behaviour in oligopolistic markets, or to underwrite the relevance of perfect

competition. Equating marginal cost to marginal revenue is not profit maximising in a multi-firm

industry.

1 Profit maximisation in a multi-firm industryIf every firm in an industry equates its own-output marginal revenue to its marginal cost, then indus-

try output will converge to the perfectly competitive level as the number of firms increases.

However, it is easily shown that this is profit maximising behaviour only for a monopoly, because

only then is the firm’s marginal revenue exclusuvely determined by its out output. In a multi-firm

industry, marginal revenue for the ith firm is:

dTR idq i

= dTRidq i

+ Sj!i

n dTRidq j

dq j

dq i(10)

As is well known, Cournot equilibrium is derived by assuming . However, a change indqj

dqi= 0

output by one firm will have an impact on the behaviour of others, indirectly, through the demand

function that makes them part of the same industry. The magnitude of this can be identified by


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working out the aggregate industry output level that results from all firms in the industry equating

marginal cost and marginal revenue. In this derivation we continue with , and also assumedPdq i

= dPdQ

constant identical marginal costs (this assumption is justified later in the paper, and the results

generalised to differing rising marginal costs):

Si=1

n ddqi

(P(Q) % qi − TCi(qi )) = Si=1

n

P(Q) + qid

dqiP(Q) − S

i=1

n ddqi

TCi(qi )

= nP(Q) + Si=1

nqi

ddQP(Q) − S

i=1

n(MCi(qi ))

= nP(Q) + ddQP(Q) S

i=1

n

qi − Si=1

n(MCi(Q))

= nP(Q) + Q ddQP(Q) − n % MC(Q)

= (n − 1)P(Q) + P(Q) + Q ddQP − n % MC(Q)

= (n − 1)P(Q) + MR(Q) − n % MC(Q)

= 0

(11)

This can be rearranged to yield

MR(Q) − MC(Q) = −(n − 1)(P(Q) − MC(Q)) (12)

Since price exceeds marginal cost in all industry structures (except, allegedly, perfect

competition), the second term on the LHS of (17) is clearly positive. Since -(n-1) is negative for

n>1, the Cournot strategy leads to an aggregate output level at which industry marginal cost

exceeds marginal revenue. Equating own-output marginal cost to marginal revenue is therefore a

profit maximising strategy only for a single firm industry. In multi-firm industries, setting own-output

marginal revenue equal to marginal cost ignores the fact that the firm's true marginal revenue is

affected not only by its own output, but also by the outputs of all other firms.

A profit maximising firm facing constant marginal costs should therefore be able to

deduce that to maximise its profits, it should produce where its own-output marginal revenue


Page 6

exceeds its marginal cost. This conclusion, which generalises to any firm facing “well behaved”

demand and cost functions, of course contradicts a long-held belief in economics.

2 The equilibrium profit maximisation rule for a multi-firm industryWe use the aggregate relation under Cournot behaviour to work out the profit-maximising output

level for the individual firm. Since producing where own-output marginal revenue equals marginal

cost results in industry marginal cost exceeding marginal revenue by , a(n − 1)(P(Q) − MC(Q))

reasonable deduction by the ith firm would be that to maximise profits, it should produce an output

where the gap between its own-output marginal revenue and marginal cost equals times this1/n

aggregate excess of marginal cost over its marginal revenue:

MRi(qi)− MCi(qi) = n−1n (P(Q) −MCi(qi)) (13)

This formula obviously works for a monopoly, where it confirms that a monopoly maximises

profit by equating marginal cost and marginal revenue. We illustrate its relevance to multi-firm

industries by considering firstly the n-firm case with identical constant marginal costs and a linear

demand curve , secondly a duopoly with linear total cost functions , andP(Q) = a − bQ (k i + ciq i )

finally the general formula for firms with a well-behaved market demand function and differing

marginal cost functions.

Consider n identical firms each producing q units at a constant marginal cost of c. If every firm

follows the Cournot strategy, then

MRi − MC i = P − bq − c = 0

a − bQ − bq − c = 0

bnq + bq = a − c

q = a − cb(n + 1)

Q = nq = nn + 1

a − cb

(14)

If, on the other hand, every firm follows our strategy, then we have that in equilibrium:


Page 7

MRi − MC i = P − bq − c = n − 1n (P − c)

q = P − cbn

q =a − bnq − c

bn

q = 12

a − cnb ;and

Q = nq = 12

a − cb

(15)

The monopoly level of output thus applies, regardless of the number of firms in the industry.

In the duopoly case, the profit functions for the two firms are:

P1(q1 ) = (a − b(q1 + q2 ))q1 − (k 1 + c1q1 )

P2(q2) = (a − b(q1 + q2 ))q2 − (k 2 + c2q2 )(16)

As is well known, the Cournot equilibrium levels of output in this situation are:

q1

q2=

13

a−2c1+c2b

13

a+c1−2c2b

(17)

Total market output is , and if , this is , which isQ= q1 + q2 = 2a−(c1+c2)3b c1 = c2 = c 2

3a−cb

larger than the monopoly level of . According to our guidelines however, profit maximising12

a−cb

firms should set the derivatives of these profit functions to:

ddq1

(P1(q1 )) = 12

(P(q1 + q2 ) − c1 )

ddq2

(P2(q2 )) = 12

(P(q1 + q2 ) − c2 )

(18)

The solutions to these equations are:

q1

q2=

18

2a−3c1+c2b

18

2a+c1−3c2b

(19)

and the sum of these two amounts is

Q= q1 + q2 =a−

c1+c22

2b(20)


Page 8

This quantity is evidently less than the Cournot level, and equivalent to the output of a monopolist

(if ) with the attendant maximum level of profit. The difference between individual firmc1 = c2 = c

profitability at this level of output and that which results from Cournot behaviour is of course

substantial. This result scales to the n-firm case with differering constant marginal cost functions.

The formulae for an n-firm industry with any “well-behaved” demand and marginal cost

functions are:

qi = 1n

P − MCi(qi)− dP

dQ

Q =P − 1

n Si=1

nMCi(qi)

− dPdQ

(21)

We emphasise that these results are achieved not through collusion, but through rational

non-interactive profit maximising behaviour. The “monopoly” level of output is reached by

non-interacting firms independently working out the production level which yields them the highest

equilibrium level of profit (we consider interacting firms in the next section). In graphical terms, this

means that the point of profit maximisation for an individual firm in a multi-firm industry is no longer

given by the point of intersection of the marginal cost and marginal revenue curve, but by the

location at which the gap between marginal revenue and marginal cost equals times the gapn−1n

between price and marginal cost. Figure 1 illustrates this.


Page 9

Figure 1. Graphical illustration of true profit maximisation point.

P = AR > MR

MCMC

Quantity0Profit maximising q for n firm industry

MRMR-MC

( )1n P MCn− −

P = AR > MR

Costs&

Revenue

( )P MC−

Though derived with respect to a single market without entry, this profit-maximisation formula

also applies to multi-market models with entry, since it is obvious that the profit maximising condition

will apply in all industries. Free entry (NovshekMRi(qi)− MCi(qi) = n−1n (P(Q) −MCi(qi))

1980) will therefore not change the outcome that each industry will converge to the monopoly

solution, regardless of the number of firms, if the condition holds. WeSi=1

nMCi(qi) = n % MC(Q)

return to the interpretation of this shortly.

3 Game theory and competitive equilibriumThe previous sections consider firms that independently calculate their maximum level of profit

without considering the strategic actions of other firms. In all cases, it is established that the

non-interactive equilibrium level of output will be the monopoly level, regardless of the number of

firms in the industry.

However, the modern game theory approach provides one more argument that supports the

proposition that the Cournot equilibrium will prevail in the marketplace—and therefore that market

output will converge to the perfectly competitive equilibrium value as the number of firms increases.

As is well known, the Cournot and “collusive” monopoly equilibrium levels of output can be put into


Page 10

a Prisoner’s Dilemma strategic game. Using the numerical example given in equations 26 and 27, the

following table of strategic interactions can be devised for a duopoly:

Table 1: Cournot and Monopoly output levels as a “Prisoner’s Dilemma”

31,250,000,00026,040,000,000

31,250,000,00034,720,000,000Keen

34,720,000,00027,780,000,000

26,040,000,00027,780,000,000Cournot

MonopolyCournot

Firm2

Firm 1PayoffMatrix

From this perspective, the interactive outcome will be the Cournot equilibrium, since both firms

have an incentive to defect from the Monopoly to the Cournot solution. With an n-firm game, the

Cournot solution will converge to the perfectly competitive output level as . Graphing thisn d ∞

process, we get the prediction shown in Figure 2 for the relationship between output, price and the

number of firms in the industry:

Figure 2. Cournot equilibrium converges to perfect competition as n d ∞

20 40 60 80 1000

1 .109

2 .109

3 .109 Cournot quantity per firm for n firms

Number of Firms

Qua

ntity

20 40 60 80 1002 .109

3 .109

4 .109

5 .109 Cournot market quantity for n firms

Number of Firms

Qua

ntity

10 20 30 40 50 60 70 80 90 10050

60

70

80Cournot price for n firms

Number of Firms

Qua

ntity

However, as is well-known, this strong conclusion is weakened in the case of repeated games

(Aumann 1987: 469, 478), when the Monopoly outcome can be shown to prevail, and it is also

weakened in the case of the realistic assumption that each firm does not know the cost functions of


Page 11

other firms, nor the market demand curve: it simply knows the profit level resulting from whatever

output level it chooses, and the unknown output levels chosen by other firms. There are thus

problems with the stability of the Cournot equlibrium as the game theory model of interactive

behaviour is made more realistic.

In this section we provide further evidence of this problem, and provide a topological conjecture

as to why this is so. While we of course agree with Aumann that “economic agents must take the

interactive nature of economics into account when making their decisions” (Aumann, 1987: 462),

we feel that the attempt to capture the process of interaction using game theory is flawed.

In modelling how firms interact, we take our lead from Friedman 1953, who argued that

economic agents do not necessarily consciously solve the optimising formulae taught to

students—nor do they necessarily behave like players in a game—but that any agent who did not

behave “as if” it was doing this would fail. Giving the example of expert billiard players, Friedman

argued that:

“Excellent predictions would be yielded by the hypothesis that the billiard

player made his shots as if he knew the complicated mathematical formulas …,

could make lightning calculations from the formulas, and could then make the balls

travel in the direction indicated by the formulas. Our confidence in this hypothesis is

not based on the belief that billiard players, even expert ones, can or do go through

the process described; it derives rather from the belief that, unless in some way or

other they were capable of reaching essentially the same result, they would not in

fact be expert billiard players.” (Friedman 1953: 21)

We now pose the question: if a firm simply “groped” for a level of output on the basis of whether

its profit rose or fell, would its output level converge to where game theory predicts (in which case


Page 12

its own-output marginal revenue would equal its marginal cost), and therefore industry output

converge to where price equals marginal cost as the number of firms increases? Or would output

converge to where industry marginal revenue equals aggregate marginal cost, with each firm

producing where its own-output marginal revenue exceeds its marginal cost?

The following program (Figure 3) provides our simplest rendition of this “blind groping”

algorithm. Firms begin with a specified level of output initial, and a specified amount stepsize by

which they all alter this output level in a search for the output level that returns the maximum profit

level. The search procedure followed independently by each firm is to change output by stepsize in

an initially randomly determined positive or negative direction. If this change in output increases

profit, then the firm continues altering its output in this direction; if it reduces profit, then the firm

alters direction. The algorithm is repeated independently a large number of times by each firm.


Page 13

Figure 3. Program One: fixed step size from specified initial output levelMkt n initial, stepsize,( ) F matrix n 1, M,( ) initial⋅←

Q ini F∑←

P ini P F∑

←

Profit ini P F∑

F⋅ tc F( )−←

dq ran sign rnorm n 0, 1,( )( ) stepsize⋅←

F F dq ran+←

Profit ran P F∑

F⋅ tc F( )−←

dq sign Profit ran Profit ini−( ) dq ran⋅( )→

←

Profit pre P F∑

F⋅ tc F( )−

→←

F F dq+←

Profit post P F∑

F⋅ tc F( )−

→←

dq sign Profit post Profit pre−( ) dq⋅( )→

←

Quantity i F∑←

Pricei P F∑

←

i 0 2 roundq CO n( )

stepsize

⋅..∈for

augment Price Quantity,( )

:=

Our hypothetical industry has the following linear demand curve:

P(Q) = 100− 1100000000 Q (22)


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Figure 4. Convergence to Monopoly equilibrium from Cournot “equilibrium”

0 1 .104 2 .104 3 .104 4 .104 5 .104 6 .104 7 .10465

70

75

802 firms starting at Cournot equilibrium

Iterations

Pric

e

0 1 .104 2 .104 3 .104 4 .104 5 .104 6 .104 7 .104 8 .104 9 .104 1 .10550

60

70

8010 firms from Cournot equilibrium

Iterations

Pric

e

0 2000 4000 6000 8000 1 .10450

60

70

80100 firms from Cournot equilibrium

Iterations

Pric

e

0 2000 4000 6000 8000 1 .10450

60

70

801,000 firms from Cournot equilibrium

Iterations

Pric

e

Our example uses a constant cost production function, with of course the same function for all scales

of firm:

TC(q) = 50q (23)


Page 15

With these parameters, the profit maximising level of output for a monopoly is 2,500 million units

at a price of 75, while the alleged level for a competitive industry is 5,000 million units at a price of

50. In the simulations shown in Figure 5, all firms begin with the output level predicted for the

specified number of firms by the Cournot formula. Each firm then varies its output by stepsize

(50,000 for the duopoly, 10,000 for the ten and hundred firm case, and 1,000 for the thousand firm

simulation).

If the Cournot equilibrium was truly an equilibrium in this iterated adjustment process, then the

simulations should all fluctuate around the Cournot equilibrium. Instead, as Figure 4 shows, in all

cases the aggregate output and price converge to the Monopoly solution from the Cournot.

Our second program (not shown here) takes as its argument the number of firms in an industry,

and then assigns a random initial production level to each firm (bounds are set to avoid aggregate

output levels that could result in an initially negative market price). Each firm works out its profit, and

makes a random change in its output level. If this change in output decreases its profit, the firm

changes its output in the opposite direction, but by a randomly decided smaller amount. The same

process is repeated on subsequent iterations. If standard Industrial Organisation theory is correct,

the point of convergence should be a function of the number of firms, with a single firm converging to

the monopoly values and a many-firm industry converging towards perfect competition. 50 runs are

done, and the initial and final aggregate quantities and prices calculated. As Figure 4 shows, output

and price converge to the monopoly level no matter how many firms are in the industry.


Page 16

Figure 5. Initial and final output for different numbers of firms with constant marginal cost

0 10 20 30 40 500

2 .109

4 .109

6 .109

8 .109

1 firm2 firms10 firms100 firms1,000 firms

Initial quantity & number of firms

Iterations

Qua

ntity

0 10 20 30 40 502 .109

4 .109

6 .109

8 .109

1 .1010

1 firm2 firms10 firms100 firms1,000 firms

Final quantity & number of firms

Iterations

Qua

ntity

Table 2 shows the mean and standard deviations for final prices and quantities. While the

numti-firm output levels were higher than those for the monopoly, there was no tendency for the

number of firms to be positively correlated with the market level of output, and in all cases the price

and output levels were much closer to those predicted for a monopoly than even those predicted for

a duopoly—let alone the perfectly competitive levels.


Page 17

Table 2: Mean and standard deviations of price and quantity

91,467,1802,793,353,3920.9172.11000 firms112,474,5692,823,338,3311.1271.8100 firms267,519,7602,810,743,9772.6871.910 firms956,017,2862,755,783,1299.5672.42 firms141,788,9912,524,265,6311.42751 firmStdevMeanStdevMean

QuantityPrice

4 Why the Cournot instability?We suggest that a topological conjecture may explain why these results differ so clearly from those

predicted by a Prisoners’ Dilemma comparison of the Cournot and Monopoly equilibria. In a

topological sense, each firm can be regarded as a mountaineer trying to climb the highest visible

“profit peak”. The landscape itself is a function both of each firm’s actions, and those of the other

firms in the industry. Considering for simplicity a duopoly, if both firms begin at the Monopoly

position, then a Prisoners’ Dilemma analysis would predict that both firms would decide to move in

the direction of the Cournot equilibrium. However, if both firms do this, then both will experience a

fall in profits: the dynamic topology of their profit functions makes movement from Monopoly to

Cournot a downward movement.

If one firm moves in the Cournot direction (increasing output) while the other decreases output,

then it is feasible that the former will increase profits while the latter will decrease. But on the next

step, both firms will then increase output—which will result in them both experiencing a fall in profits.

They will then both change direction, reducing output and returning to the Monopoly equilibrium.

The same arguments apply in reverse for commencing at the Cournot equilibrium, as our simulations

indicate. If both firms move in the direction of the Monopoly equilibrium from the Cournot, then they

will experience rising profits. Competitive and interactive behaviour will thus lead to the behaviour of

a multi-firm industry converging to the behaviour of a single firm. This argument can be illustrated by


Page 18

considering the linear example given above and seeing what the change in profit table is for each firm

in a duopoly from the Cournot position.

Table 3: Change in profit for a change in output from Cournot levels

-16.6667-16.6667-16.6667

-16.6667-1.0E-0816.6667Increase by 1

-1.0E-080-1.0E-08

-16.6667016.6667Stay the same16.666716.666716.6667

-16.6667-1.0E-0816.6667Decrease by 1Firm 2Increase by 1Stay the sameDecrease by 1

Firm 1Cournot “Equilibrium” and change in output

As can be seen from the table, Firm 1 will increase its profit by 16.6667 units if it reduces its

output by one unit, regardless of what Firm 2 does. Similarly, Firm 2 will increase its profit by the

same amount if it reduces its output by one unit, regardless of what firm 1 does. Both firms will

therefore reduce their output, and this process continues until they arrive at the Monopoly level. The

Cournot equilibrium is therefore not a true dynamic equilibrium in an iterated game where firms do

not have knowledge of the behaviour of other firms.

5 Rising marginal cost and aggregationThese results may be thought to be an artifact of the assumption of constant costs that we have used

so far in this paper. Simulations with rising marginal costs do indeed give results where competitive

industries produce a greater output at a lower cost, but this apparent confirmation of the theory is

due to a condition that must be fulfilled for marginal cost curves to be aggregated. The results differ,

not because the monopoly produces where marginal cost equals marginal revenue while a competi-

tive industry produces where marginal cost equals price, but because given diminishing marginal

productivity, the cost function for the monopoly necessarily differs from the sum of cost curves in an

industry with more than one producer.

Figure 6 compares the total cost and profit curves for a single firm industry and a ten firm industry

where each firm has the same rising total cost function . ItTC(q) = 10,000,000 + 50q + 5 % 10−9q2


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is apparent that, given the same functional form for the total cost curve, the sum of the total cost

curves for the ten firm industry is lower than the total cost curve for the single firm industry. The

higher level of output of the multi-firm industry occurs, not because of a difference in profit

maximisation principles, but because of lower costs for the many firm instance than for the

monopoly. This returns us to the interpretation of the aggregation condition given earlier, on marginal

costs, that where , the output levels of n competitive firms will equal thatSi=1

nMCi(qi) = n % MC(Q)

of a monopoly.

Figure 6. Total revenue and aggregate total cost functions for different numbers of firmswith rising marginal cost

0 5 .108 1 .109 1.5 .109 2 .109 2.5 .109 3 .109 3.5 .109 4 .109 4.5 .109 5 .1092 .1011

1 .1011

0

1 .1011

2 .1011

3 .1011

4 .1011

RevenueCostProfitSum of Costs for 10 firmsSum of profits for 10 firms

Output

Rev

enue

/Cos

t/Pro

fit

3.75 1011×

1.25− 1011×

P x( ) x⋅

tc x( )

P x( ) x⋅ tc x( )−

10 tcx

10

⋅

P x( ) x⋅ 10 tcx

10

⋅−

50000000000 x

In order to make a definitive comparison between monopoly and a competitive market, the

marginal cost curve for the monopoly must be identical to the sum of the marginal cost curves for the

competitive market. If the cost curves differ, then it is quite possible for a monopoly to produce a

larger quantity at a lower price than a competitive industry because of lower costs (Schumpeter

1942: 81-83). It is easily shown that this condition of identical marginal cost functions is only

possible where all firms have the same constant marginal cost.


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The condition that the marginal cost curve of a single plant and the sum of marginal cost curves

for two or more plants must be identical is simultaneously the condition that their marginal products

must be identical—since differences in marginal product are the only allowable source of differences

in per unit cost. If the marginal product curves are identical, then total product curves can only differ

by a constant. If we take labour as our variable factor of production, then output is zero at zero

input, and the constant can be set to zero.

We can put this condition into the following form: given the same number of variable inputs, the

output of the single plant must be identical to the sum of the outputs of the other plants. If we

consider (without loss of generality) a multiple firm industry with n firms each with one plant

employing x workers, then for the aggregate cost curve to be identical to that of the monopoly, the

output of these n firms must be equal to the output of the single plant firm employing nx workers.

Using f for the production function of the competitive firms, and g for the production function of the

monopoly, this condition is Euler's Equation with a constant of zero:

n % f(x ) = g(n % x ) (25)

As can easily be shown, the only production function that satisfies this is one that yields identical

constant marginal product, and therefore identical constant marginal cost. Thus only in the case of

constant identical marginal costs will the marginal cost curve of a single firm be identical to the sum

of the marginal cost curves of two or more firms. As soon as diminishing marginal productivity is

introduced, the comparison of monopoly and any other industry structure can no longer be

definitive, since their cost functions must differ.

Given this, then if diminishing marginal costs are assumed, no definitive output, price or welfare

comparisons can be made between monopoly and any other industry structure. In fact, given

economies of scale, and our result that the equilibrium output for each firm will be where


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regardless of the number of firms, it is highly likely thatMRi(q i ) − MC i(q i ) = n−1n (P(Q) − MC i(q i ))

monopolistic or oligopolistic markets will have a lower cost structure than more competitive

markets, and therefore lower prices and higher output levels. This conjecture about the real world

depends, of course, on the conventional neoclassical image of firms facing rising marginal costs being

an accurate depiction of reality.

6 The real worldNumerous researchers (Eiteman 1947 et seq., Haines 1948, Means 1972, Blinder et al.

1998—see Lee 1998 and Downward & Lee 2001 for surveys) have shown that the majority of

actual firms have enormous fixed costs and constant or falling marginal costs. This cost structure,

which is described as “natural monopoly” in economic literature and portrayed as an exception to

the rule of rising marginal cost, actually appears to be the case for 95 per cent or more of real firms

and products.

These firms in general determine their prices by a markup on variable costs, with the size of the

markup reflecting partly by the degree of competition (so that there is still some sense in which a

more competitive industry is preferable to a less competitive one), the need to cover their fixed costs

at a levels of output well within the current production capacity of the firm, and the desire to finance

some investment and/or repay debt with retained earnings, and the impact of the trade cycle. Price is

set by the firm prior to the market, and the firm attempts to sell as much of its output as it can at this

price. Firms produce competing but heterogeneous products, and the main form of competition

between firms is not price but product differentiation (by both marketing and R&D).

Means coined the term “the administered price thesis” for this perspective on the behaviour of

the firm (Means 1972). Since that model accurately describes how actual firms behave, and since

that behaviour cannot be reduced to profit maximisation via the equating of marginal cost and


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marginal revenue, economics should abandon its theory of the firm and instead develop a

microeconomics that is consonant with this empirical reality.

7 ConclusionOur paper calls into question much of supply and demand analysis, to the extent that it is based

upon the presumption of non-interactive profit-maximising behaviour. The proposition that the

individual firm maximises profit by equating its marginal revenue and marginal cost is true only for a

monopoly. For multi-firm industries, setting own-output marginal revenue to be greater than marginal

cost is the proper rule for profit maximisation, and the generally believed formula is a special case

relevant only when . Output is not determined by the intersection point of marginal revenue andn = 1

marginal cost, but by the locus at which the gap between these two curves equals times the gapn−1n

between price and marginal cost (where n is the number of firms).

At the partial equilibrium level, since price cannot equal marginal cost unless firms produce

substantially more than the profit maximising level, the well-known result that a supply curve cannot

be derived for a monopoly generalises to any industry structure. It can no longer be argued that

price is set by the intersection of supply and demand, but at best that output is determined by the

intersection of industry marginal revenue and marginal cost, and the market price is set by the

demand curve at this quantity.

At the general equilibrium level, the incompatibility of the assumption that price equals marginal

cost with profit maximising behaviour means that any model that makes this assumption must now

justify it on the basis of interactions between agents which results in them producing more than the

profit maximising level. Welfare theorems that rely upon both profit maximising behaviour and the

equality of marginal cost and price are also prima facie false—as are those that rely upon individual

firms equating marginal cost and marginal revenue in a multi-firm industry. The conventional theory


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of the firm is therefore, to borrow a phrase from Kirman, an “empty citadel”. What then should

replace it?

Marshall once famously remarked that an economist should “(1) Use mathematics as a shorthand

language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into

English. (4) Then illustrate by examples that are important to real life. (5) Burn the mathematics. (6)

If you can’t succeed in 4, burn 3. This last I did often” (Marshall, cited in Pigou 1925: 427). Few

economists have followed this advice, and in fact the profession has a history of ignoring empirical

research—something akin to Marshall's step 4—which contradicts its model of the firm. We surmise

that this failure to appreciate empirical data that did not conform to the accepted model was in part

due to the belief that the mathematics behind the theory of the firm was incontrovertible (but see also

Moss 1984). We hope we have demonstrated that this is not so. In this situation, the only sensible

approach is to develop a theory of the firm which conforms to the substantial but neglected literature

on the pricing and output behaviour of actual corporations. It is high time that economists began to

model reality rather than myth.

References

Arrow, K.J., (1959). “Towards a theory of price adjustments”, in Abramovitz, M. et al., (eds.), The Allocation ofEconomic Resources, Stanford University Press, Stanford.

Aslambeigui, N, & Naples, M.I., (1997). “Scissors or horizon: Neoclassical debates about returns to scale, costs,and long run supply, 1926-1942”, Southern Economic Journal, vol. 64: 517-530.

Aumann, R.J., (1964). “Markets with a continuum of traders”, Econometrica, vol. 32: 39-50.Aumann, R.J., (1966). “Existence of competitive equilibria in markets with a continuum of traders”, Econometrica,

vol. 34: 1-17.Aumann, R.J., (1987). “Game theory”, in Eatwell, J, Milgate, M. & Newman, P., (eds.), The New Palgrave,

Macmillan, London.Bishop, R.L., (1948). “Cost discontinuities, declining costs and marginal analysis”, American Economic Review,

vol. 38: 607-617.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.Conkling, R.L., (1999). “Marginal cost pricing for utilities: a digest of the California experience”, Contemporary

Economic Policy, vol. 17: 20-32.Cournot, A. (1838[1988]) “Of the competition of producers”, Chapter 7 of Researches into the Mathematical

Principles of the Theory of Wealth, L. Hachette, Paris, reprinted in Daughety, A.F., (ed.), 1988. CournotOligopoly, Cambridge University Press, Cambridge.

Downward, P. & Lee, F., (2001). “Post Keynesian pricing theory reconfirmed? A critical review of Asking AboutPrices”, Journal of Post Keynesian Economics, vol. 23: 465-483.


Page 24

Eiteman, W.J., (1947). “Factors determining the location of the least cost point”, American Economic Review,vol. 37: 910-918.

Eiteman, W.J., (1948). “The least cost point, capacity and marginal analysis: a rejoinder”, American EconomicReview, vol. 38: 899-904.

Eiteman, W.J. & Guthrie, G.E., (1952). “The shape of the average cost curve”, American Economic Review, vol.42: 832-838.

Friedman, J., (1983). Oligopoly Theory, Cambridge University Press, Cambridge.Friedman, M., (1953). “The methodology of positive economics”, in Essays in Positive Economics, University of

Chicago Press, Chicago.Groenewegen, P., (1995). A soaring eagle: Alfred Marshall 1842-1924, Edward Elgar, Cheltenham.Haines, W.W., (1948). “Capacity production and the least cost point”, American Economic Review, vol. 38:

617-624.Harrod, R.F., (1934). “Doctrines of Imperfect Competition”, The Quarterly Journal of Economics, vol. 48: 442-470Keen, S., (2001). Debunking Economics, Pluto Press & Zed Books, Sydney.Kuenne, R.E., (1998). Price and Nonprice Rivalry in Oligopoly, Macmillan, London.Langlois, C., (1989). “Markup pricing versus marginalism: a controversy revisited”, Journal of Post Keynesian

Economics, vol. 12: 127-151.Lee, F., (1996). “Pricing and the business enterprise”, in C.W. Whalen (ed.), Political Economy for the 21st

century, ME Sharpe, Armonk.Lee, F., (1998). Post Keynesian Price Theory, Cambridge University Press, Cambridge.Lipsey, R. G., & Chrystal, K. A., (1999). Principles of Economics: 9e, Oxford University Press, Oxford.Mankiw, N.G., (2001). Principles of Microeconomics, Harcourt, New York.Marshall, A., (1907 [1961]). Principles of Economics, Macmillan, London.Marshall, A. “Correspondence with Professor A. L. Bowley”, in Pigou, A.C., (ed.), (1925). Memorials of Alfred

Marshall, Macmillan Publishing Company, London.Martin, S., (2001). Advanced Industrial Economics, Blackwell, Cambridge.Mas-Colell,, A. (1983). “Walrasian Equilibria as Limits of Noncooperative Equilibria. Part I: Mixed Strategies”,

Journal of Economic Theory, vol. 30: 153-70.Means, G.C, (1972). “The administered-price thesis reconsidered”, American Economic Review, vol. 62: 292-306.Nash,J., (1951 [1997]). “Non-cooperative games”, Annals of Mathematics, vol. 54: 286-295; reprinted in Kuhn,

H.W., (ed.), (1997), Classics in Game Theory, Princeton University Press, Princeton.Novshek, W. (1980). “Cournot Equilibrium with Free Entry”, Review of Economic Studies, vol. 47: 473-86.Novshek, W. (1985). “Perfectly Competitive Markets as the Limits of Cournot Markets”, Journal of Economic

Theory, vol. 35: 72-82.Novshek, W. & Sonnenschein, H., (1983). “Walrasian Equilibria as Limits of Noncooperative Equilibria. Part II:

Pure Strategies”, Journal of Economic Theory, vol. 30: 171-87.Pigou, A.C., (1922). “Empty economic boxes - a reply”, Economic Journal, vol. 36: 459-465.Pigou, A.C., (1927). “The law of diminishing and increasing cost”, Economic Journal, vol. 41: 188-197Pigou, A.C., (1928). “An analysis of supply”, Economic Journal, vol. 42: 238-257.Robertson D.H., (1924). “Those empty boxes”, Economic Journal, vol. 34: 16-31.Robertson D.H., (1930). “The trees of the forest”, Economic Journal, vol. 44: 80-89.Robbins, L. (1928). “The representative firm”, Economic Journal, vol. 42: 387-404.Sato, K., (1979). “A note on capital and output aggregation in a general equilibrium model of production”,

Econometrica, vol. 47: 1559-1568.Schumpeter, J. A., (1942 [1976]). Capitalism, Socialism and Democracy, George Allen and Unwin, London.Shepherd, W.G., (1984). “'Contestability' vs. competition”, American Economic Review, vol. 74: 572-587.Shove, G.F., (1930). “The representative firm and increasing returns”, Economic Journal, vol. 44: 93-116.Simon, J.L., Puig, C.M., & Aschoff, J., (1973). “A duopoly simulation and richer theory: an end to Cournot”,

Review of Economic Studies, vol. 40: 353-366.Sraffa, P. (1926). “The Law of returns under competitive conditions”, Economic Journal, vol. 40: 538-550.Sraffa, P. (1930). “The trees of the forest—a criticism”, Economic Journal, vol. 44: 89-92.Stigler, G.J. (1957). “Perfect competition, historically considered”, Journal of Political Economy , vol. 65: 1-17.

1 The authors would like to thank Mike Honeychurch (University of Melbourne), Trond Andresen(Norwegian Institute of Technology), Joanna Goard (University of Wollongong), Greg Ransom (UCLARiverside) and members of the HAYEK-L internet discussion list for useful insights and comments on earlierdrafts.


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