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Duopoly Models with Consistent Conjectures

American Economic Review 1981
The theory of oligopoly price is very sensitive to behavioral assumptions. Even given identical assumptions about costs and demand, different models can predict every price between marginal cost and monopoly. This paper selects a single oligopoly model, and thus predicts a single oligopoly price. The selection criterion is consistency of conjectures; each firm's conjectures about the way other firms react to it will be correct. The two classical oligopoly theories, Bertrand and Cournot, make identical assumptions about costs and demand, but different assumptions about firm behavior. In Cournot equilibrium, each firm maximizes profit given the quantity of output other firms produce. In Bertrand equilibrium, each firm maximizes given the prices other firms charge. This difference in behavioral assumptions leads to a large divergence in predicted prices. Cournot predicts positive markups that decline as the number of firms increases, while Bertrand predicts marginal cost pricing even in duopoly. Clearly both models cannot be correct. Is their truth an empirical question, as recent work suggests?' This paper attempts to decide on theoretical grounds. No attempt to decide among Bertrand, Cournot, and their more modern competitors can be based on mathematical correctness. Economic criteria must guide the decision. Oligopoly models are examples of what game theorists call Nash equilibrium. In them, every firm maximizes profits given the of all other firms. The mathematics does not care whether actions are defined to be prices (Bertrand), quantities (Cournot), or any other variables. Yet these distinctions are crucial to the economics of the situation. The notion of Nash equilibrium already entails one economic condition-individual rationality. This paper will determine the correct definition of by imposing a further economic conditionconsistency of conjectures.2 The precise sense in which conjectures are to be consistent is this; the conjectural variation and the reaction function will be equated. The conjectural variation is the firm's conjecture about other firms' behavior. In Cournot, for example, each firm conjectures that all other firms' quantities are constant. The reaction function is the firm's actual behavior. It is the solution to the profit-maximizing problem, and tells what the firm will do as a function of all other firms' actions. Clearly, what the firm conjectures affects how it reacts. This paper will search for cases where conjectures and reactions are the samewhere each firm's conjectures about other firms' reactions are perfectly correct, locally.3 Every notion of Nash equilibrium has the feature that, in equilibrium, each firm's beliefs about the level of all other firms' are confirmed. For example, in Cournot duopoly, each firm's equilibrium quantity is that one which induces the other firm to produce its equilibrium quantity. The firms are right in their beliefs, in Fellner's famous remark, but right for the wrong reason. That is, it is not actually true, as conjectured by the firm, that the other firm's quantity is a constant. The other firm's quantity depends nontrivially on ours-the reaction function does not have zero slope, although the conjecture does. This paper will find Nash equilibrium notions in which firms are right for

SEGMENT SHIFTS AND CAPACITY UTILIZATION IN THE U.S. AUTOMOBILE INDUSTRY.

American Economic Review 1993
An important school of thought argues that shifts may account for a substantial portion of aggregate fluctuations (e.g., David Lilien, 1982; Fischer Black, 1987; Steven Davis, 1987). Events such as the oil shocks of the 1970's, exchange-rate fluctuations, and shifts in government spending have their direct effect on the composition of economic activity. The sectoral-shift literature argues that they may affect the level and the dynamics of output and employment as well. The typical story is of a slowly functioning labor market. After a shock, search behavior, matching problems, and a time cost of switching slow the reallocation of workers across sectors. This focus, however, misses important elements of the reallocation problem. As Black (1987) has argued, not only sector-specific human capital, but also complementary physical and managerial (engineering, organization, etc.) capital must be reallocated or recreated in response to shocks. If jobs are linked to capital, then the slow adjustment of labor may be attributable in part to the sluggishness in the adjustment of capital. This paper presents an empirical study of the impact of oil-shock shifts within the U.S. automobile industry. From an analytical perspective, a sectoral shift is any event that raises desired output and employment in some sectors and lowers them in others. For our purposes, a sector is a size class of automobiles. Within the automobile industry, we will be able to study two distinct questions. First, did the oil-priceinduced shocks to the composition of demand interact with short-run rigidities in supply to limit industry-wide capacity utilization? We will quantify the extent to which the changing composition of demand was reflected in a lower aggregate output level, with obvious consequences for the employment of capital and of labor and for the return to firms' knowledge capital. Our second question concerns the pace of the intermediate-run adjustment to shocks. How rapidly could capital and labor be reallocated to new demand conditions? Such considerations determine the impact of shocks on employment and capacity-utilization dynamics.

Localized Competition and the Aggregation of Plant-Level Increasing Returns: Blast Furnaces, 1929-1935

Journal of Political Economy 1996 104(2), 241-266
A recent empirical literature has shaken economists' confidence in the value of aggregate (industry-level) data to illuminate production relationships. But the statistical finding "you cannot aggregate," however well documented, is not an economic explanation. Plant-level relationships do aggregate in Depression-era blast furnace operations despite the presence of very substantial interplant heterogeneity, the most common economic cause of nonaggregability. The economic explanation of this lies in poor short-run substitutability of one plant's output for another's. Substitutability determines the importance of composition effects in understanding aggregate time series, constrains the potential cleansing effects of recessions, and therefore influences industry evolution quite broadly.

Localized Competition and the Aggregation of Plant-Level Increasing Returns: Blast Furnaces, 1929-1935

Journal of Political Economy 1996 104(2), 241-266
A recent empirical literature has shaken economists' confidence in the value of aggregate (industry-level) data to illuminate production relationships. But the statistical finding "you cannot aggregate," however well documented, is not an economic explanation. Plant-level relationships do aggregate in Depression-era blast furnace operations despite the presence of very substantial interplant heterogeneity, the most common economic cause of nonaggregability. The economic explanation of this lies in poor short-run substitutability of one plant's output for another's. Substitutability determines the importance of composition effects in understanding aggregate time series, constrains the potential cleansing effects of recessions, and therefore influences industry evolution quite broadly.

Entry in Monopoly Markets

Review of Economic Studies 1990 57(4), 531
This paper develops new empirical models of market concentration from game-theoretic models of entry. We construct our models from inequality conditions that describe entrants' equilibrium strategies in simultaneous-move and sequential-move games, and use them to study the effects of entry in isolated monopoly markets for new automobiles. From estimates of the market size necessary to support one and two dealers, we conclude that monopoly dealers do not block the entry of a second dealer. We also find that entry does not cause price-cost margins to fall by much.

Entry and Competition in Concentrated Markets

Journal of Political Economy 1991 99(5), 977-1009
This paper proposes an empirical framework for measuring the effects of entry in concentrated markets. Building on models of entry in atomistically competitive markets, the authors show how the number of producers in an oligopolistic market varies with changes in demand and market competition. These analytical results structure the authors' empirical analysis of competition in five retail and professional industries. Using data on geographically isolated monopolies, duopolies, and oligopolies, they study the relationship between the number of firms in a market, market size, and competition. The authors' empirical results suggest that competitive conduct changes quickly as the number of incumbents increases.