## Monopoly

The effects of shifts in product demand curves upon investment by unconditional monopolies can be studied by applying the modified cost curves. We will ignore the effects of changes in financing conditions. Modifications of the behavior of monopoly firms will be introduced in order to eliminate the postulate of continuous response. This analysis applies unconstrained profit maximizing behavior to a situation in which the negatively sloped demand curve for the product of a firm shifts.

For competitive markets we solved the problem of 'what does the firm really maximize?' by showing how the two maximization principles (that firms maximize the rate of return upon their own investment and that firms maximize the rate of return on total investment) are equivalent in equilibrium. This is not true in the same sense in monopoly markets. It is, of course, trivially true, that there exists an owners' equity such that maximization of the rate of return upon owners' equity and upon total investment are the same. However, in general, we cannot posit that a firm will be characterized by exactly this owners' equity, and as long as the 'freely' available rate of return is significantly lower than the rate which the monopolist can earn in his firm, there is no reason for the monopolist to shift his equity from his own firm to other firms.

Under the assumption that the monopolist is maximizing the rate of return upon the total investment in the firm, the optimum position is determined by the tangency of the demand curve and a long run average cost curve. In Figure 8.6, the LRACrj is tangent to the demand curve at the output qj. Obviously the long run marginal cost curve for rj and the marginal revenue curve intersect at this output. If we take another long run marginal cost curve, say LRMCr2[r2 < rj], we have that at the output where it intersects the marginal revenue curve the demand curve and the average cost curve have the same slope. But the average cost, earning r2 upon the total investment, is lower than the price; symmetrically, for a long run marginal cost curve based upon a rate of return r3 which is greater than rj. The standard monopoly argument, with the resultant monopoly profits, is based

upon the firm using a rate of return, such as r2, which is lower than the highest attainable rate of return, in its planning.15 The resultant difference between price and average costs, multiplied by output, is called monopoly profits. Without some basis for the firm using a planning curve such as LRMCrj, the usual argument is false. Such a basis can be the use of 'market financing' by the firm, and the relation between the freely available rate of return and the return which can be earned within the firm. The arguments which are necessary to determine the 'optimum' size of operations are relevant to the 'investment decision' problem.

If a monopolist maximizes the rate of return upon total investment then the firm will produce that quantity at which a long run average cost curve is just tangent to the demand curve. An upward shift in the demand curve raises the rate of return which the firm earns with the given plant. However, this plant does not yield the maximum possible rate of return upon total capital. This maximum available return is given by the plant determined by the long run average cost curve which is tangent to the shifted product demand curve.

There is no way of knowing whether the new optimum plant will be larger or smaller than the original plant. Therefore there is no way of knowing whether profit maximization in the sense used here will imply investment as the result of an upward shift in demand. If the upward shift in demand results in an increase in the elasticity of demand then the new optimum plant may be larger than the old plant. If the shifted demand curve is parallel to the original demand curve, then the plant which maximizes the rate of return with the new demand curve is smaller than the original plant.

It is obvious that an unconstrained monopolist can choose to transform a rise in demand into a 'Ricardian Rent' case. In this case the plant remains fixed - induced investment is zero. For both the 'rent' case and the maximization of the rate of return upon total investment case the accelerator phenomenon breaks down - a rise in demand may not induce investment. Therefore, to be able to use an accelerator, the economy must not be characterized either by monopolists who are 'lazy' and transform a rise in demand into a rent or by monopolists who maximize the rate of return upon total investment.

With a fixed equity base, a monopolist maximizing the rate of return earned upon its equity will have an invariant planning curve based upon the market financing terms and the evaluation of the risk of debt financing, for all plants greater than the largest plan which the owners' equity can finance. In this case an upward shift in the demand curve results in an increase in the volume of debt financing.16 This implies that investment takes place; therefore the accelerator can be used.

In allowing for the entry of new firms into a competitive industry we implicity allowed the equity base of the industry to increase. What is the optimum equity base for a firm that is a monopolist? With a given demand curve, the highest rate of return upon investment is earned by that plant that results in the tangency between the LRAC curve, the SRAC curve and the demand curve. Both larger and smaller plants result in a lower rate upon total investment. This can be represented by an average and marginal return upon investment curve. An upward shift in demand shifts these curves upward.

For a particular monopolist we define a rate of return which is freely available p. With a given demand curve, the maximum equity investment in a monopoly firm will be given by the condition that the marginal rate of return equals the freely available rate of return.

This means that the plant determined by the intersection of the long run marginal cost based upon p and the marginal revenue curve will be built. This plant will earn more than p upon the total investment. If the 'equity' base of the monopolist is smaller than that necessary to build this plant, the monopolist may either debt finance or build the plant which the equity will finance (this is equivalent to a completely inelastic 'risk' premium). For the debt financing firm, the long run marginal cost curve that determines the optimum plant is based upon the borrowing rate and risk premium of the firm.17

For a monopoly firm which borrows or which has an infinitely elastic supply of equity funds, a rise in the demand curve of the product implies

investment. The behavior of such a monopolist is consistent with the accelerator.

If a plant is continuously and instantaneously variable the short run marginal cost curves lose their significance. A firm would always be able to adjust its scale of plant to a shift in the demand curve. The relation between the quantity of investment induced and the change in the quantity of the product produced depends in these circumstances upon the nature of the firm's production function. Unless the production function is linear and homogeneous of the first degree, successive increases in output will involve, at constant factor prices, changing proportions of the factors of production. Therefore, the construction which we used for a competitive industry, which enabled us to derive a linear homogeneous production function for the industry, does not apply to monopolies.

For a monopoly that profit maximizes with relation to a fixed planning curve we can still write that

I = pAq but as price may change

The expenditure coefficient of induced investment is less than the output coefficient of induced investment, whereas in the competitive industry the relation was the same aside from a scale constant. This difference between competition and monopoly is significant for the efficacy of a rise in money income in inducing investment. In a competitive industry, none of the rise in income18 is absorbed by a rise in price, whereas in general a monopoly absorbs some of the rise in income as a price rise. Therefore the quantity of investment induced by a rise in money will be lower if the affected demands are for the outputs of monopoly industries than if the affected demands are for competitively produced products.19

Expansion of a monopoly is along a production function, whereas expansion of a competitive industry can take place by adding production functions. For those monopoly firms which have production functions that are not linear

However, v^ = รง(q). If the production function is one of increasing returns, dv^/dq^ < 0; if the production function is one of decreasing returns dv^/dq^ > 0. For a monopoly a change in output may result in changing proportions of investment to output due to the characteristics of the production function.

For a monopolist who is financing his expansion by debt, the relative price of the factors of production does not remain constant as the ratio of debt financing to equity financing changes. With a given equity base, the borrowing rate (including borrower's risk premium) rises with the upward shift in the demand curve. This is equivalent to raising the price of capital. This results in the firm's optimum plant for a given output being smaller than if the borrowing rate had not increased. To the extent that expansion is debt financed it will result in a less intensive utilization of capital. Therefore the amount of investment induced is less than if output had been expanded along the same 'expansion' path as the original plant was on. The resultant accelerator coefficient p became a function of the borrowing rate and risk premium: p = 9(r).20

In the case of a downward shift in the demand curve, the analysis for monopoly is symmetric with that for an upward shift in the demand curve. The effects of a downward shift in the demand curve are two: first the rate of return upon investment in a given plant is reduced, secondly a smaller plant yields the highest rate of return upon owners' equity. If depreciation transforms a large plant into a small plant, the rate of return upon owners' investment will rise if, as plant is being depreciated, with a stabilized demand for the product, the plant becomes that size determined by the intersection of the long run marginal cost curve based upon the financing rate and the marginal revenue curve. When this occurs, the firm will have the plant which yields the highest attainable rate of return. The relation between the amount of capital consumption and the change in the quantity produced depends upon the technical characteristics of the firm's production process. There is no reason inherent in the set-up for the unconstrained monopolist why there should be any time gap between the shift in the demand curve for a product and the resultant change in the capital used. Any time gap which occurs, any deviations from the long run production function, arise from the limitations due to the attainable time rate of change of capital.

If limitations as to the time rate of change of capital exist, then a cyclical movement in the level of income may be reversed prior to the achievement of the optimum plant. For example, if a cyclical downswing in the level of income is reversed prior to the achievement, through depreciation, of the optimum size plant for the lower level of demand, the initial upswing of the level of income may not induce investment. Similarly, the reversal of a cyclical upswing may not be effective in inducing disinvestment.

The assumption of a continuous response on the part of a profit maximizing monopolist to shifts in its demand curve is too stringent. It is true that to each demand curve confronting a monopolist there corresponds a unique plant size which will yield the highest returns. Ignoring the financial problems which arise in changing the size of plant, the firm may still choose not to alter the plant scale for each shift, however small, in its product demand curve. This is a relaxation of the unconstrained profit maximization assumption. For such firms the accelerator coefficient is zero for some range of changes in the demand curve. It also follows that shifts in the demand curve which are sufficient to trigger investment may result in responses which are out of proportion to the incremental shift.21

Let us assume a sequence of upward shifts in the product demand curve. With DD1 as the demand curve the plant indexed by SRMC1 is the optimum plant, that is, it is the plant which yields the highest attainable return on owners' investment. A shift of the demand curve DD2 may not be sufficient to induce a firm to build the plant SRMC2; rather the firm will continue to operate plant SRMC1. However, a further shift of the demand curve, say to DD3, will be sufficient to induce the firm to construct the optimum plant for the demand curve DD3. The amount of investment induced by the shift of demand from DD2 to DD3 is greater than this incremental shift in demand alone warrants.

If a profit maximizing firm expects a cyclical swing in its demand curve between DD1 and DD3, and if the time rate of change of capital is long

relative to the phases of the business cycle, then the firm will have to choose a plant somewhere between SRMCj and SRMC3. Once such an unconstrained monopolist makes his choice, the usual cyclical swings of the demand curve will not induce any investment. For firms of this sort where the cyclical accelerator is zero, only shifts in demand which are greater than the cyclical pattern will induce investment.

Monopolized industries exhibit a number of investment characteristics different from competitive industries. One is that 'profit maximization' in the sense of a maximum rate of return on total investment may induce disinvestment as the result of an upward shift in demand, so that the coefficient of induced investment is negative. For monopoly firms which finance debt, and for monopoly firms which are characterized by owners who 'distribute' their portfolios, an expansion involves a rise in the effective planning rate. Therefore independent of changes in the market rates of interest, the expansion is taking place on the basis of more expensive financing which lowers the accelerator coefficient. In addition, as a monopolist firm expands, the laws of return to scale of the production function affect the amount of investment which takes place. For decreasing returns monopolists, this increases the ratio of investment to output.

In addition, for a monopolist, we can expect that a rise in market price will take place as the demand curve shifts independently of changes in factor prices. As a result, a portion of a change in money income is transformed into a change in price, making the quantity of investment induced by a rise in expenditures smaller than if the industry had been competitive.

A monopoly industry is similar to a competitive industry in that, from the trough of the business cycle, we can expect that the initial increases in demand will not be effective in inducing investment. In fact, for monopoly firms which expect cycles, the cyclical accelerator may be zero. Investment will be induced only by increases in demand beyond previous peak demands.

Monopoly firms also have the alternative of remaining passive when demand changes: not varying their plant with a change in market demand. The passive behavior filters out the effect of small changes in demand. Such firms would be characterized by spurts of induced investment. Induced investment will be zero for small changes in demand and a disproportionate increase in investment will take place for large changes in demand. Whereas in a competitive industry a strong boom tends to increase induced investment somewhat, for a monopoly a strong boom may be a necessary condition for investment to be induced.

The workings of the accelerator coefficient seems much more certain in competitive industries than in unconstrained monopoly. Therefore the cyclical behavior of an economy should be affected by the proportion of industries characterized by these market structures.

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