Subsidies in oligopoly markets: a welfare comparison between symmetric and asymmetric costs

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Date: November-December 1997
From: Public Finance Review(Vol. 25, Issue 6)
Publisher: Sage Publications, Inc.
Document Type: Article
Length: 2,486 words

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Oligopolistic industries generally produce less than is socially desirable. As a result, the use of production subsidies is often suggested as a means of raising production toward the efficient level in imperfectly competitive markets. In cases where firms are equally efficient in producing the good, the common prescription is a policy of uniform subsidization, as suggested by Besley (1989).(1) When firms in an industry differ in cost efficiency, however, uniform subsidization involves subsidizing inefficient firms in the same manner as efficient firms. Consequently, uniform policy may be undesirable from a social perspective, particularly when the price-cost margins of inefficient firms are small.

In an oligopolistic industry comprising firms that differ in cost effectiveness, one might ideally like to subsidize only the most efficient firm(s) and perhaps tax or even exclude inefficient firms from the market. Yet, in many situations, treating rival firms in an industry differently is politically infeasible. It is therefore important to understand how the welfare implications of uniform policy in an asymmetric-cost industry diverge from the case of equal cost efficiency. Different welfare implications are likely to arise because changes in regulatory structure can affect market structure in an asymmetric-cost industry (see Dierickx, Matutes, and Neven 1988; Kimmel 1992).

Several papers in the public finance literature have addressed the issue of tax incidence on the rivalry and profitability of firms in oligopoly markets. Katz and Rosen (1985) show, in a conjectural variations model with symmetric firms, that a uniform tax on production can lead to an outcome with larger after-tax profits for firms. This result is also supported by Dierickx, Matutes, and Neven (1988); Kimmel (1992); and Seade (1985) for the case when the cost efficiency of firms differs. However, these papers do not directly analyze the industry profit and social welfare effects of a change in the tax or subsidy program.

This article identifies relevant implications for tax policy by comparing welfare changes in the asymmetric-cost case to a benchmark case of symmetric costs. It is shown that, relative to the symmetric-cost case, the welfare effect is smaller when demand is nonconvex in the asymmetric-cost case, while the opposite is true for the case of convex demand. The greater the cost asymmetry in the industry and the more collusive firm behavior, the greater is this difference in welfare impact.


Consider a traditional conjectural variation model with two firms producing a homogeneous good.(2) We assume full information and profit-maximizing behavior for both firms. Letting l and h denote the low- and high-cost firm, respectively, the profit expression for firm i is


where P(Q) is the inverse demand function, Q = [q.sub.l] + [q.sub.h], [c.sub.i]([q.sub.i]) is the cost function of firm i, and t is a unit production subsidy (t [greater than] 0).(3) The cost function is quadratic and has the form

[c.sub.i]([q.sub.i]) = [[Alpha].sub.i][q.sub.i] + [Theta]/2 [([q.sub.i]).sup.2], i = l, h(2)

where the parameter [Theta] is identical for both types of firm, which means the difference in cost efficiency between firms is characterized entirely by...

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Gale Document Number: GALE|A20463265