ñòð. 10 |

AC

MC = AC

Po Po

x x

AC AR

AR

Pxo

MR MR

X X

Xo Xo

(a) (b)

X

Xo Figure 5.2 [A] + [C] + [D] implies not-[B]

Figure 5.1 Firm in long-run equilibrium

Models which drop assumption [B] usually resort to a claim that there is

Sometimes there is little difference between models which explain the some sort of unavoidable market failure or governmental interference

occurrence of a disequilibrium phenomenon and those which explain it preventing the firm from choosing the optimum amounts of inputs. Some

away. For example, models which drop assumption [D] usually explain imperfectly competitive firms are regulated to charge full-cost prices, that

away apparent disequilibrium phenomena as possible consequences re is, set price equal to average cost. Again, the apparent disequilibria may

Â© LAWRENCE A. BOLAND

78 Principles of economics Axiomatic analysis of disequilibrium states 79

still be the best that is possible. Since one cannot give a neoclassical expla- with zero profits and increasing returns may very well be the best we can

nation without assuming [B], one must resort to non-economic considera- do for society. Too often the transaction costs are invisible or imagined.

tions such as external politics or internal social structure to explain the The cleverest models are those which claim that the prices we see do not

constraints that inhibit the firm from using the optimum amounts of inputs. represent the true costs of purchase. The fact that people are willing to join

a queue and wait to be served when there are few producers is interpreted

as evidence that the price marked on the good is less than the price paid.

Model 3. Dropping assumption [A]

The full price includes that opportunity cost of waiting (i.e. lost income).

The most common disequilibrium model would involve the phenomenon of Thus, implicitly, the demand curve for the â€˜fullâ€™ price is horizontal and the

â€˜excess capacityâ€™. The typical model is shown in Figure 5.3. There is no resulting â€˜fullâ€™ cost curves if visible would look like Figure 5.1, thereby

literal long-run version since if all inputs were variable (the definition of denying [D] and allowing [A] to be re-established. I think such a model

the long run) then [A] would have to hold. Models which drop assumption may be too clever since it is difficult for me to understand what is being

[A] usually try either to explain why excess capacity may be an optimal explained with such a model.

social equilibrium or to explain [D] away so that [A] can be allowed to

$

$

hold. When [D] holds, competition can drive profits to zero without forcing

the firm to a point where it faces local linear homogeneity. To see this we

need only note that [B] combined with [C] is represented by equations

AR

Po Po

[5.2aâ€²], [5.2bâ€²] and [5.3]. And as we noted before these imply that the firm x x MC

AR

is facing a falling AC curve since it must be facing increasing returns. As I

AC

noted above, the common justification of [D] is to say there are transaction

MC = AC

costs which if recognized would explain that the situation represented by

Figure 5.3 is an optimum rather than a disequilibrium. It is the best possible MR MR

world.

X X

Xo Xo

$

(a) (b)

MC Figure 5.4 [A] + [B] + [D] implies not-[C]

AC

Pxo

Model 4. Dropping assumption [C]

AR

One obvious way to explain the existence of profits is to simply drop [C]

without dropping assumption [D]. The explanation in this case will be

MR direct since given assumptions [A] and [B] it is logically impossible for

profits to be zero or negative whenever [D] holds, hence the absence of

Xo X

zero profits is quite understandable. Consider Figures 5.4(a) and 5.4(b). In

Figure 5.3 Imperfectly competitive firm in long-run equilibrium

each figure we represent [D] by a falling demand curve (the AR curve) and

its resulting marginal revenue curve which is necessarily always below.

Some people wish to interpret excess capacity as evidence that

Assumption [B] is represented by the point where marginal revenue equals

imperfect competition leads to inefficiencies where it is clear that the firm

marginal cost. Assumption [A] is represented only at the point or points

is not maximizing its output for the resources used (i.e. AC not minimum).

where average cost equals marginal cost. Which of Figures 5.4(a) or 5.4(b)

It could equally be argued that the transaction costs needed to make

is the appropriate representation depends on why [C] does not hold.

decisions when there is the very large number of producers required to

Models which initially drop assumption [C] will usually be transformed

make everyone a perfect competitor are too high. A long-run equilibrium

Â© LAWRENCE A. BOLAND

80 Principles of economics Axiomatic analysis of disequilibrium states 81

into ones where [A] or [D] does not hold so that [C] can be allowed to hold. UNIFORMITIES IN EXPLANATIONS OF DISEQUILIBRIA

When the objective is to explain [D] away (e.g. with the recognition of

I will consider how many of the above models can be seen as variants

â€˜fullâ€™ costs), then [A] will be explained or explained away using one of the

which use the same mathematical property inherent in disequilibrium

strategies I noted in the discussion of Model 3 and this leads to the re-

states. In one sense I have already discussed the notion that increasing

establishment of Figure 5.1. Another strategy is to try to explain the

returns and imperfect competition are two ways of interpreting what is

appearance of profit as a return to an unrecognized input factor such that,

represented in Figure 5.3. And I showed that in this case the measure of

when accounted for as a cost, total profit is really zero. This latter strategy

distance from the perfect competition equilibrium is either a measure of

allows [D] to hold but puts [A] or [B] into question. However, if there is

closeness to constant returns or a measure of closeness to perfectly elastic

only one missing factor, its recognition begs the question as to whether it is

demand. The measures are equivalent.

being optimally used. Only if [D] is denied can it be argued that the

Can we do something similar for all disequilibrium models? That is, are

existence of profit implies that some of the factors are not being used

all explanations based on positing disequilibrium phenomena (inefficiency,

optimally.

exploitation, suboptimal resource allocations, profits, etc.) reducible to

Simply assuming [C] does not hold may provide the logic necessary to

statements about some measure from the perfectly competitive optimum

explain profits, but if the firm operates in a competitive industry something

equilibrium?

needs to be added to explain why profits are not zero. Figure 5.4(a) would

be appropriate if the reason given is that there has not been sufficient time

for competition to force profits down to zero. If there has been enough Interest rate as a measure of disequilibrium

time, then Figure 5.4(b) is appropriate since implicitly it is assumed that

Let us examine some models which are based on the presumption of a state

the firm is in the long run. If the firm is in the long run then there must

of disequilibrium. Many years ago, Oscar Lange [1935/36] presented an

exist exogenous barriers to inhibit entry or competition. One obvious way

elaborate model which in effect claimed that the interest rate (actually, the

to justify that [C] does not hold is to deny the existence of sincere

net internal rate of return) is implicit in a firmâ€™s or economyâ€™s misallo-

competition. Perhaps it is a matter of collusion. Perhaps it is a matter of

cation of resources between the production of final goods X (by firm x) and

high cost of entry. Perhaps it is a matter of government-imposed barriers to

intermediate goods K (which are machines produced by firm m). 17

entry such as we sometimes see in the case of utilities (e.g. power utilities,

telecommunications, transportation, broadcasting, etc.). Perhaps it is

because of the exercise of power granted in the social setting of a firm, so- Langeâ€™s Model

called exploitation of workers by the owners of the firm [see Robinson

Let the economy consist of two firms which are given the following

1933/69].

production function for final goods:

Whatever the reason given, least-cost production [A] combined with

X = F(Lx, Kx ) [L1]

maximization [B] means that the existence of a falling average revenue

precludes negative profits. In other words, we can never explain a and the following production function for machines which last only one

disequilibrium that involves negative profits with an imperfectly production period:

(Km + Kx ) = Ï†(Km, Lm )

competitive neoclassical model based on [A] and [B]. Moreover, we are [L2]

also limited to using such a model only to explain part of the economy where the subscript indicates which firm is using the machine. And we note

since it is impossible to have an economy where everyone is making that [L2] also indicates that it will be assumed that the supply of machines

profits.16 Aggregate profit for an entire (closed) economy must be zero, is exactly equal to the demand for machines (which are assumed to be used

hence if any firm is making profits, some other firm must be making losses. up in one production period). Similarly, it will be assumed that the market

Thus, the disequilibrium state of an entire economy cannot be explained for labour is cleared (i.e. there is full employment):

with an imperfect-competition-based neoclassical model.

L = Lx + Lm. [L3]

Let us now assume the economy is producing with an allocation of

labour between the two firms such that X is at its maximum. This assump

Â© LAWRENCE A. BOLAND

82 Principles of economics Axiomatic analysis of disequilibrium states 83

tion implies that there must be no surplus machine production on the or that

â€“ Î² = 1 â€“ (1 / i).

margin (i.e. the last machine produced is used to replace the last machine

used up):

(MPPK)m = 1 [L4]

Other measures of disequilibrium

and that there is an efficient resource allocation (i.e. MRTS x = MRTS m):

Let us now consider other, more familiar or more recent, models of

(MPPL )x / (MPPK)x = (MPPL )m / (MPPK)m . [L5â€²]

disequilibrium which claim to offer measures of the extent of

Note that when [L4] holds with [L5â€²] it gives:18 disequilibrium and see whether we can generalize the relationship between

those measures and either my Î² or equivalently the elasticity of demand.

(MPPL )x = (MPPK)x Â· (MPPL )m . [L5]

We will look at Robinsonâ€™s [1933/69] measure of exploitation due to

If X is not maximum, either [L4] or [L5â€²] does not hold (or neither holds).

monopoly power, John Roemerâ€™s [1988] more general measure of

If we assume [L5â€²] holds because the two firms have somehow achieved

exploitation, Abba Lernerâ€™s [1934] index of monopoly power, Michal

an efficient allocation of labour between them, that is, they have achieved a

Kaleckiâ€™s [1938] degree of monopoly, and Sidney Weintraubâ€™s [1949]

Pareto optimum for the given amount of labour, L, then failure to maximize

index of less-than-optimum output.

X must imply that equation [L4] does not hold. If the failure to maximize X

Robinsonâ€™s measure of exploitation due to monopoly power is the

is the result of misallocating too much labour to the production of X, then

difference between the marginal product of labour and the price paid for

we can measure the extent to which [L4] does not hold by a scalar i as

the labour services. This index can be derived straight from equation [5.2aâ€²]

follows:

above. In effect her measure is merely 1/Îµ since this fraction is the measure

(MPPK)m = 1 + i. [L17]

of the difference.

This i is equivalent to what Lange calls a net â€˜rate of real interestâ€™. Note

Roemerâ€™s measure of exploitation is the ratio of profit to variable costs.

that whenever this two-firm economy is not maximizing X but has reached

Roemerâ€™s measure does not assume [C] holds. If we assume that his

a Pareto-optimal equilibrium in the sense that neither firm can increase its

disequilibrium model has only one input, then his measure is just

output without the other firm decreasing its output, i cannot be zero. 19 In

(price â€“ AC)/AC.

other words, i is a measure of the distance the Pareto-optimal point is from

the global optimum of a maximum X for the given amount of labour being If we also assume Roemer is presuming maximization in the sense that

price equals MC then his measure of exploitation is just 1/Î². 21

allocated between these two firms.

We can look at Langeâ€™s real interest rate as a measure of increasing Kaleckiâ€™s degree of monopoly is based on an assumption that [A] and

returns if we assume the machine producing firm is a profit maximizer. In [B] hold but [C] does not. Thus his measure is the difference between AR

effect equation [L17] can be the equivalent of my equation [5.2bâ€²] once we and MR which again is 1/Îµ.

recognize that the real price of capital in the production of machines is Lernerâ€™s index of monopoly power is defined as the ratio of difference

Pk /Pk thus [L17] is really: between the price and MC as a proportion of the price, or since AR is price:

(MPPK)m = (Pk /Pk )Â·(1 + i). [L17â€²] (AR â€“ MC) / AR.

Thus we can say that If we assume zero profit then his index is my 1/Î² and if instead we assume

(1 + i) = 1 / [1 + (1/Îµ)]. profit maximization (MR = MC), then his index is the negative of 1/Îµ. If we

Since Îµ is in general a measure of the difference between the marginal and assume both conditions hold (i.e. an imperfect competition equilibrium)

the average20 (and thus equal to â€“ Î²), we can determine the one-to-one then his index is equivalent to both my 1/Î² and 1/Îµ (as I explained earlier).

Weintraubâ€™s index of less-than-optimum output is the ratio of less-than-

correspondence between i and my measure of closeness to local linear

optimum output to optimum output where the optimum is the one where

homogeneity as follows:

[A] holds or, equivalently, where MC = AC. Thus his index is dependent on

(1 + i) = 1 / [1 â€“ (1/Î²)]

the specific form of the production function or, equivalently, of the cost

or, equivalently, we can say either that

function. To illustrate, let us assume the total cost (TC) of producing X is as

â€“ i = 1 / (1 â€“ Î²) follows:

Â© LAWRENCE A. BOLAND

84 Principles of economics Axiomatic analysis of disequilibrium states 85

TC = 200 + 10X + 2X2 the social institutions that are needed yet taken for granted in neoclassical

explanations. The critics complain that until these two exogenous elements

AC = (200 + 10X + 2X2) / X

then

are made endogenous, neoclassical theories will always be incomplete.

MC = 10 + 4X.

While some critics argue that such a completion is impossible, some

Now let us calculate the ratio of MC to AC using the given cost function: friends of neoclassical theory willingly accept the challenge. In the next

MC / AC = XÂ·(10 + 4X) / (200 + 10X + 2X2) three chapters I will examine these disputes to determine the extent to

which they represent serious challenges to neoclassical economics.

MC / AC = (5X + 2X2) / (100 + 5X + X2).

or

Note that MC = AC when X = 10 and thus Weintraubâ€™s index (WI) will be

(X/10) for the given cost function. Since MC = ACÂ·[1 â€“ (1/Î²)], we can NOTES

calculate Î² for the given cost function if we are given an X: 1 There have been some analyses of the stability of equilibrium models which

Î² = (6 + WI + 2WI2) / (2WI2 â€“ 6). recognize the need to deal with conceivable disequilibrium states [e.g. Hahn

1970; Fisher 1981, 1983]. Also, in macroeconomics we find models which try

So, again, we see that the measure of distance from a perfectly competitive to deal with the disequilibria caused by â€˜distortionsâ€™ such as sticky prices or

equilibrium can be seen as a variant of Î² or Îµ. wage rates [e.g. Clower 1965; Barro and Grossman 1971]. Little of this

literature approaches the way equilibrium models have been axiomatized.

Besides, it is not clear what consistency and completeness mean when one sees

A GENERAL THEORY OF DISEQUILIBRIA disequilibrium as a distorted equilibrium.

2 It might appear that by assuming all consumers are maximizing we are always

In general terms, each of the models of disequilibrium I have discussed assuming that the only possible disequilibrium is one of excess supply, that is,

here are combinations of the axioms I have presented in this chapter. for disequilibrium prices above the equilibrium level. This does not have to be

Which of the four axioms ([A] to [D]) is denied will be the basis for a the case if one adopts the Marshallian view of the producer where the given

price is a demand price and marginal cost represents the supply price. In this

clearly defined measure of disequilibriumness. The opportunities for

way, prices on both sides of the equilibrium level can be considered.

criticism are limited to examining the reasons why the particular axiom

3 Here â€˜capitalâ€™ always refers to physically real capital (e.g. machines and

was denied. And since any measure of disequilibrium will be determined computers, etc.).

by the denied axiom, not much will be learned by arguing over the nature 4 If all inputs are unrestricted then it is possible to double output either through

of the measure presented. In general, unless the same axioms are used to internal expansion (viz. by doubling all inputs) or through external expansion

(viz. by building a duplicate plant next door). It should not matter which way. If

build alternative models of disequilibrium, arguing over which is a better

it does matter then it follows that not all inputs are variable. By definition, a

measure would seem to be fruitless. Whether the disequilibriumness is the

linear-homogeneous function is one where it does not matter which way output

result of assuming [D] or [A] in combination with either [B] or [C] will is expanded. Some of my colleagues argue that, even in the long run, some

determine which is the appropriate index. And as we saw in the case of production functions cannot be linear-homogeneous. They give as an example

imperfectly competitive equilibria, either index will do. With the one the production of iron pipe. One can double the capacity of the pipe without

doubling the amount of iron used â€“ the perimeter of the pipe does not double

exception of Kaleckiâ€™s degree of monopoly which neutralized the role of

when we double the area of the pipeâ€™s cross-section. Unfortunately, this

the production function by assuming linear homogeneity [A], all of the

example does not represent a counter-example as claimed. To test linear

other measures can be seen to depend on the extent to which the production homogeneity one would have to restrict consideration to producing more of the

function is not linear-homogeneous (as measured by my Î²). same product and 20-inch pipe is not the same product as 10-inch pipe.

The questions of the pervasiveness of equilibrium and maximization are 5 It should be noted that equations [5.1], [5.2a], [5.2b] and [5.3] are formaliza-

tions of the statements (b) to (d) used to discuss Marshallâ€™s method (see above,

fundamental and thus little of neoclassical literature seems willing or able

pp. 32â€“5).

to critically examine these fundamental ideas. Outside of neoclassical lit-

ñòð. 10 |