Allocative Efficiency, X-Efficiency and the Measurement of Welfare Losses

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Allocative Efficiency, X-Efficiency and the Measurement of Welfare LossesAuthor(s): William S. Comanor and Harvey LeibensteinSource: Economica, New Series, Vol. 36, No. 143 (Aug., 1969), pp. 304-309Published by: Wiley on behalf of The London School of Economics and Political Science and TheSuntory and Toyota International Centres for Economics and Related DisciplinesStable URL: http://www.jstor.org/stable/2551810 .

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[AUGUST

Allocative Efficiency, X-Efficiency and the Measurement of Welfare Losses

By WILLIAM S. COMANOR and HARVEY LEIBENSTEIN

In estimating the loss from monopoly,' it has been common to assume that inputs are used as efficiently as in competitive markets. The presumed reason for this assumption is that firms have a clear interest in mini- mizing costs per unit of output. While the "carrot" of greater profits may well be a major determinant of firm behaviour, the competitive "stick" may be equally important, and to this extent, monopoly will affect costs as well as prices. In this context, the welfare loss from monopoly should include the reduction in what one of the authors has called "X-efficiency"2 as well as the extent of allocative inefficiency, and therefore the combined welfare loss from monopoly may be very much larger than the usually calculated loss.

Competition may have an important impact on costs because it serves as a major source of disciplinary pressure on firms in the market, which, to a greater or lesser degree, affects all firms in competitive industries. In the first place, the process of competition tends to eli- minate high-cost producers, while the existence of substantial market power often allows such firms to remain in business. This is due to the oft-noted fact that the high price-cost margins, which are established by firms with substantial market power, often serve as an umbrella which protects their high-cost rivals. Second, the process of competition, by mounting pressures on firm profits, tends to discipline managements and employees to utilize their inputs, and to put forth effort, more ener- getically and more effectively than is the case where this pressure is absent.3 Thus, a shift from monopoly to competition has two possible effects: (1) the elimination of monopoly rents, and (2) the reduction of unit costs.4

1 In this paper it is recognized that monopoly does not depend entirely on the size distribution of firms but rather rests on the entire set of factors which permits firms to behave differently from what would be enforced in purely competitive markets with similar cost and demand conditions.

2 Harvey Leibenstein, "Allocative Efficiency vs. 'X-Efficiency"', American Economic Review, vol. LVI (1966), pp. 392-415.

3 Cf. R. M. Cyert and J. G. March, A Behavioral Theory of the Firm, Englewood- Cliffs, N.J., 1963, where the related concept of "organizational slack" is used to describe the process whereby costs rise above minimum levels.

4 The hypothesized cost effect of competition is not original to this article but originated as long ago as 1897 in an article in the Atlantic Monthly of that year by A. T. Hadley. See Oliver E. Williamson, "A Dynamic Stochastic Theory of Managerial Behavior", in A. Phillips and 0. Williamson (eds.), Prices: Issues in Theory, Practice and Public Policy, p. 23. A more recent statement of this hypo- thesis was made by Tibor Scitovsky in "Economic Theory and the Measurement

304



1969] ALLOCATIVE EFFICIENCY, X-EFFICIENCY 305

Although both of these effects should be included in estimating the welfare losses which result from monopoly, in fact, frequently only the first has been examined. By assuming that actual costs equal minimum costs, Harbergerl and others have estimated the welfare loss which results from monopoly by calculating approximately the total consumer surplus which is lost. This is illustrated in Figure 1 by the triangle

P

Cm

Cc

FIGURE 1.

ABC where this area equals /ApAq, where Ap is the difference between price and actual unit costs and Aq is the corresponding difference in quantities. It is in these computations where actual costs are assumed to represent economic costs, for Ap is also considered to represent the difference in price between monopolistic and competitive equilibrium.

Now let us suppose that a shift from monopoly to competition not only lowers price but also lowers costs (i.e., increases X-efficiency). What are the welfare losses under these circumstances which are due to monopoly? We show below that there is a simple mathematical relation, in the case of linear demand functions, which relates the full reduction in allocative efficiency to that estimated under the limiting assumption noted above. The important implication of our result is that the actual degree of allocative inefficiency may be very much larger than the level as heretofore calculated. Furthermore, to this larger sum must be added the volume of X-inefficiency for the monopolistically used inputs to obtain the total welfare loss from monopoly.

I.

In Figure 1, we assume that a shift from monopoly to competition will reduce the monopoly rent per unit of output by a units but that it will reduce unit costs by x units. On this basis, we can distinguish the

of Concentration", in NBER, Business Concentration and Price Policy, Princeton, 1955, pp. 106-8.

1 Arnold Harberger, "Monopoly and Resource Allocation", American Economic Review, Papers and Proceedings, vol. XLIV (1954), pp. 77-92.



306 ECONOMICA [AUGUST

various components of welfare loss which result from monopoly. Wa is the partial welfare loss which results from allocative inefficiency associated with monopoly, and is illustrated by the triangle ABC in Figure 1. This is the standard measure of the welfare loss which has been calculated in earlier studies. Wax, on the other hand, describes the full measure of allocative inefficiency which results from monopoly under the view that competition affects the level of costs as well as prices. It is measured by the triangle ADE. At the same time, Wx, is the welfare loss from X-inefficiency resulting from monopoly, and refers to the higher costs used to produce the restricted level of output. This loss has no allocative component since it is concerned with no change in output levels, and is the rectangle CmCcDB.

The quantity a is the price-cost margin which exists under monopoly, while the quantity x is the cost difference between monopoly and competition; q, is the difference in quantity which results from a shift from monopoly to competition exclusive of the cost effect, while q2 is the difference in quantity directly associated with the cost reduction. Now let X equal the cost difference in units of a, i.e., X is equal to x/a, which is the ratio of the cost difference to the price-cost margin under monopoly.

As indicated above, Wa=aq,/2, while

(1) Wax (a + Xa)(q1 +q2)/2.

We can then note that the total welfare loss which results from the allocative inefficiency due to monopoly is some multiple of the welfare loss as measured earlier, and this factor is indicated by

(2) Wax aq1 + aq2 + Xaq1 + Xaq2 Wa aq,

and hence'

(3) Wax Wx =(1 + X)2.

This relationship implies that where the cost difference due to monopoly is large relative to the price-cost margin, the loss in allocative inefficiency may be far greater than the allocative loss as usually measured. For example, in the diagram above, it is assumed that the monopoly rent and the cost effect are equal, and, as a consequence, Wax is four times the usual measure of welfare loss. If, on the other hand, the ratio of x to a were three, then we would need to multiply the conventional welfare loss by a factor of sixteen.

A numerical example may illustrate the implications of this relationship. Suppose that actual costs are 6 per cent. below the monopoly price, and that one-half of the total output of the economy is produced in monopolized sectors. If the price elasticity were equal to two, the welfare loss Wa would be approximately 0d18 per cent. of the net national

'We note that q2lql = x/a = X, by similar triangles. Therefore Waxl Wa =1 + 2X + X2.




product. Now, suppose that the cost-effect differential is 18 per cent., which does not appear to be an impossible figure. In that case, the full allocative welfare loss Wax is nearly 3 per cent. of the net national product-a not insubstantial sum.

The pure X-efficiency effect, apart from the allocative effect, is, of course, likely to be the largest of all. In the numerical illustration above, the welfare loss W, would be one-half of 18 per cent., i.e. 9 per cent., of the net national product. Furthermore, it should be noted that in fact W., is likely to be even larger relatively to Wax, since we have assumed a high price-elasticity of demand.

II.

The usual estimates of Wa ignore the problems associated with the theory of the second best, for they indicate only the welfare gain associated with a single change from monopolistic to competitive equilibrium. On this account, they have few policy implications where policy necessarily demands piecemeal and partial measures. A shift, for example, from monopoly to competition in some industries may not improve welfare if the resources allocated to the newly-competitive industry are drawn from uses where they are currently in insufficient supply. In some circumstances, the value of the additional resources used in a newly-competitive industry may conceivably have been higher in the industries where they had been previously allocated. Thus, second- best considerations may make it difficult to determine whether a shift to a greater degree of competition in a particular industry represents a true improvement in allocative efficiency. In the case, however, where there is a reduction in costs as well, and thereby an improvement in X-efficiency, it becomes far easier to conclude that a shift from monopoly to competition in a single industry represents a welfare gain.

Returning to the numerical example of the previous section, we determined that W, was 9 per cent. of net national product. Such gains represent a clear improvement in welfare since they do not depend on a re-allocation of resources. More units of output for particular goods can be produced without reducing the output of other goods in the economy. Furthermore, even if the allocative effect of a single industry shift from monopoly to competition were negative, this gain would represent a positive counter-weight.

Second-best results depend on the structure of inter-relationships among sectors in the economy and focus on the traditional general equilibrium conclusion that "everything depends on everything else". While this conclusion is qualitatively correct, it ignores quantitative considerations. The magnitude of the second-best problem for specific sectors depends on the degree of interdependence among industries, the degree of monopoly in sectors related to the one at issue, as well as the structure of input-output relationships. Quantitatively important second-best considerations may depend on a small set of related



308 ECONOMICA [AUGUST

industries rather than all others, and thereby policy judgments may demand a specific rather than a general theory of the second best. In such circumstances, it might be possible to estimate the gain or loss in allocative efficiency from a shift from monopoly to competition, and if the latter, to compare it with the clear gain in X-efficiency. In any event, since the X-efficiency improvement may be large and represents a clear gain, we should have confidence that changes which represent both allocative and cost-differential effects are far more likely to represent positive welfare gains as compared to those where only the re- allocation of resources is concerned.

One further point should be noted. Because of the higher costs which are assumed to exist under monopoly, the increase in output with competition demands only a partial re-allocation of resources. In Figure 1, xqo denotes the volume of redundant inputs under monopoly which could be used to produce xq0/C, additional units of output. At the same time, the percentage increase in output, due to a shift from monopoly to competition, is (q1 +q2)/qO, which equals

(4) (a + x)e/M,

where e is the absolute value of the elasticity of demand.' Then, the increase in output from re-allocated inputs, expressed as a proportion of original output, is

(5) (a+x)e x (5) M cc,

which equals2

(6) ae + x(e-1) x(a + x) M MCC

The extent to which inputs have to be re-allocated depends on the degree to which e is close to unity, and the ratio of x to a (i.e., the value of X). This can be seen by considering the proportion of the total increase in output which must be produced from re-allocated inputs. Dividing both terms in (6) by (4) gives the following expression:

(7) X X 1(a+x)e Cce

In industries where demand is relatively inelastic, no increase in inputs may be required, and it may even be the case that output is increased while the total volume of imports is reduced. In the latter situation,

This elasticity represents the average value between points A and E such that

eAj, Aq p q

2 This can be seen by expanding the second term of expression (5): x xM x(Cc+a+x) x x(a+x) Cc MC0 - MCI M MCI




expression (7) will be negative. And here no second-best problem will arise.

From this analysis it appears that there may be many cases where the clear welfare gain associated with the cost effect of competition is a significant counteracting element to the possible loss on "second best" grounds from the re-allocation of inputs. The likelihood of an improved welfare position resulting from a single industry shift from monopoly to competition would seem thereby to be greatly enhanced.

Stanford University, Stanford, California. Harvard University, Cambridge, Massachusetts.



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Allocative Efficiency, X-Efficiency and the Measurement of Welfare Losses