Knowledge that Transforms

Edward Lazear (1983) presents a model in which the number of unionized workers in an industry is endogenously determined by the utility-maximizing workers themselves. Hence in his model union firms and nonunion firms coexist. He assumes that the nonunion wage adjusts so that the labor market clears and full employment prevails. The purpose of this note is to examine the possibility of unemployment in Lazear's model. Of all the possible rigidities in the labor market that could lead to unemployment, the most natural one is the existence of minimum wage legislation.' It will be shown that the imposition of a minimum wage may induce the formation of a union. Furthermore, an increase in the minimum wage will result in a higher union wage, but decrease aggregate wage income. Finally, I investigate the influence of the elasticity of demand for labor on some indicators of union power. Henceforth it will be assumed that firms cannot pay a wage below some specified level W. This entails some modification of Lazear's model which is now briefly presented. The variables W, and WN are the union wage and the nonunion wage, respectively. Ci is the cost to firm i of blocking unionization of its workforce with Ci g(Ci) and G(C) the probability that firm i's blocking cost does not exceed C; apart from this disparity in blocking costs, all firms are identical. d(W) is the demand for labor by a firm faced with wage W and 11(W) is its profit outside of blocking costs. Define I *(W,, WN) --H1(WN)-11 (WU,) and firm i will block unionization when 1 *(W,, WN) > Ci, hence the probability that a firm will block is G[11*(Wi,, WN)]. The nunber of firms is S and R is the number of workers. The labor market equilibrium condition (1) of Lazear must be modified as

In his comment, Stanley Reynolds provides a very interesting application of subgame perfect equilibrium concept to my 1981 model.' Reynolds claims that contrary to my analysis, the Sylos Postulate and excess capital investment need not be inconsistent with Nash equilibrium (p. 896). It is not overly surprising if characteristics of equilibrium are altered by applying a different solution concept. However, conclusions arrived at in my earlier paper regarding Sylos Postulate and Excess Capacity Hypothesis are quite robust to changes in equilibrium. Reynold's assertion that behavior of incumbent at subgame perfect equilibrium is consistent with Sylos Postulate or Excess Capacity Hypothesis is based on a misunderstanding of these concepts. As Reynolds notes, two-period, openloop Nash equilibrium with capacity as an upper bound on output, which was examined in my earlier paper, is also a subgame perfect equilibrium. Thus, all of results for this case still hold. In particular, monopolist will deter only if capacity level without threat of exceeds entry-deterring level. This requires capacity to be relatively inexpensive as compared to discounted marginal profit evaluated at blocking output (Proposition 1 and equation (4) of my paper). Thus, the Sylos Postulate is only satisfied in this limited sense (p. 506). The established firm may choose, however, to permit entry. When occurs, established firm always operates at full capacity before entry, thus contradicting Excess Capacity Hypothesis. When capacity is relatively inexpensive, established firm lowers its output to accommodate entrant and holds excess capacity after entry, thus contradicting Sylos Postulate. For case where capacity investment affects production costs, entrant and incumbent firm behavior at subgame perfect equilibrium reinforces my conclusion that the Sylos Postulate ignores both strategic interaction between firms and dynamic aspects of entry (p. 503). The established firm at subgame perfect equilibrium will not deter whether or not it is profitable to do so. Rather, will be deterred only if

Two behavioral assumptions that are often made in the industrial organization literature are that an established firm (or group) may deter entry either through limit pricing (the Sylos Postulate) or by holding excess capacity (the Excess Capacity Hypothesis). In an interesting recent article in this Review (1981), Daniel Spulber examines these behavioral assumptions to see whether they are consistent with rational behavior by an established firm. Spulber's analysis is based on a two-firm, two-period game model in which the established firm is given a first-in advantage. By introducing this dynamic element into the model, Spulber is able to explicitly address the issue of the optimality of entry-deterring behavior. Spulber finds that the use of limit pricing and/or excess capacity to deter entry is rational only under a very limited set of circumstances.' In particular, when the second-period outcome is determined by a Cournot-Nash equilibrium, he derives the following results. 1) The first-period output of the established firm is always less than or equal to the first-period output produced by a firm not anticipating entry. The established firm essentially accommodates entry and limit pricing does not occur. 2) The established firm never holds more capital than the amount that would minimize its production costs, given its output choices in periods one and two. This comment takes issue with Spulber's conclusions about the Cournot-Nash case. It will be shown that the two results cited above may be reversed when the production technology is characterized by variable proportions. This reversal hinges on the particular type of Nash equilibrium employed in the analysis of the two-period model. Spulber implicitly uses a Nash equilibrium that is not subgame perfect.2 It is shown below that, when one requires the Nash equilibrium to be subgame perfect, both limit pricing and excess capital investment outcomes are possible for the variable proportions technology case. The subgame perfection property thus seems to capture an important strategic element in decision making for the established firm. In some cases, this type of strategic behavior leads to entry barriers that would not exist under innocent profit maximization by the established firm. Strategic entry barriers are discussed by Steven Salop (1979). Spulber's notation and assumptions about demand and costs are adopted below.