Number Of Firms In Equilibrium Research Articles

Endogenous Entry and Growth of Firms with Heterogeneous Firms

We analyze the impact of persistent cost heterogeneity of potential firms on free entry equilibria under a Cournot setting. We show that firm heterogeneity always reduces the number of firms in equilibrium, and that vertical and horizontal market growth have different effects on industry population and firm dynamics. Vertical market growth always promotes entry and growth of new firms, but heterogeneity weakens this effect. For horizontal market growth, we identify two growth regimes: incumbents dominate in large markets with significant heterogeneity, while new entrants grow faster in smaller markets with low heterogeneity. In contrast to existing research, we show that higher degrees of heterogeneity among potential firms reduces entry rates in both cases.

Free and second‐best entry in oligopolies with network effects

AbstractWe compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second‐best entry. Under free entry, the firms decide whether to enter the market or not; in the second‐best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business‐stealing competition), free entry may lead to more or less firms than the second‐best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business‐stealing competition, free entry leads to an excessive number of firms compared with the second‐best solution.

Endogenous number of firms, horizontal concentration and heterogeneity of firms—A note

We re-examine implications of heterogeneity of firms under a Cournot setting on free entry equilibria concerning the number of firms. Heterogeneity reduces the number of firms in equilibrium—the larger the cost asymmetries, the smaller the free entry equilibrium number of firms in an industry.

Bertrand and Cournot Competition Under Asymmetric Costs: Number of Active Firms in Equilibrium

We compare the number of active firms, i.e. the number of firms producing a positive quantity, in equilibrium across four different models of oligopoly. The two main models are Cournot where quantity is the strategic variable and prices are determined by the market, and Bertrand where price is the strategic variable and demands are determined by the market. Within each of these models, we also have two types of goods: homogeneous and differentiated. We concentrate on the linear demand structure with constant marginal costs. We find that within a fixed class of good, either homogeneous or differentiated, Cournot always results in more active firms in equilibrium than Bertrand. Moreover, we find that within a fixed type of market, Cournot or Bertrand, differentiated goods result in more active firms in equilibrium than homogeneous goods. These results depend crucially on cost asymmetries between the firms, as with symmetric costs the results trivialize to all firms active or all firms inactive. Many studies have shown that consumer welfare is generally higher under Bertrand than Cournot. Our result can be seen as explaining this as consumers have more choice in Cournot markets at the expense of lower welfare, whereas they have less choice in Bertrand markets (as the number of firms in equilibrium is less) but they are compensated for this fact by reduced prices and therefore higher welfare.

Input Constraints and the Efficiency of Entry: Lessons from Cardiac Surgery

Prior studies suggest that with elastically supplied inputs free entry may lead to an inefficiently high number of firms in equilibrium. Under input scarcity, however, the welfare loss from free entry is reduced. Further, free entry may increase use of high-quality inputs, as oligopolistic firms underuse these inputs when entry is constrained. We assess these predictions by examining how the 1996 repeal of certificate-of-need (CON ) legislation in Pennsylvania affected the market for cardiac surgery in the state. We show that entry led to a redistribution of surgeries to higher quality surgeons, and that this entry was approximately welfare neutral. (JEL I11, L13)

Input Constraints and the Efficiency of Entry: Lessons from Cardiac Surgery

Prior studies suggest that, with elastically supplied inputs, free entry may lead to an inefficiently high number of firms in equilibrium. Under input scarcity, however, the welfare loss from free entry is reduced. Further, free entry may increase use of high-quality inputs, as oligopolistic firms underuse these inputs when entry is constrained. We assess these predictions by examining how the 1996 repeal of certificate-of-need (CON) legislation in Pennsylvania affected the market for cardiac surgery in the state. We show that entry led to a redistribution of surgeries to higher-quality surgeons and that this entry was approximately welfare neutral.

Welfare Losses in Oligopoly and Monopolistic Competition

ESTIMATES OF the magnitudes of monopoly welfare losses (MWL) appearing in the economics literature have tended to differ quite widely. At one end of the spectrum we find figures of the order of o. I % of GNP quoted by Harberger [I 954] in his pioneering study, while at the other extreme Cowling and Mueller [ I 978] have derived estimates of around I O % of gross corporate product from some of their measures. Two of the major sources of such differences lie in the treatment of (a) the general equilibrium aspects of deviations between prices and marginal costs, and (b) the impact of market power on the cost levels of firms; but, unfortunately, the tendency of writers to adopt rather different analytical frameworks often makes it difficult to accurately assign the variations in the estimates to specific factors. In the present paper the issue of monopoly welfare loss is considered in the context of a differentiated goods model based upon work on monopolistic competition by Spence [I976] and by Dixit and Stiglitz [I977]. Within a set of common assumptions about demand, the effects of varying cost conditions and differing equilibria on the level of MWL are examined. On this basis, four major factors connected with suboptimal resource allocation can be identified: (a) supernormal profits, (b) product differentiation, (c) suboptimal scale, and (d) factor bias. The first of these needs little explanation: its association with welfare loss has been well explored in structure-conduct-performance theory and is used extensively in applied anti-trust economics. Attention will therefore be focused upon the remaining three, all of which can produce MWL in zeroprofit equilibria. The paper is organised as follows. Section II sets out and discusses the differentiated goods framework which will be used throughout the rest of the analysis. It is also shown how a simple transformation of variables reduces the model to the homogeneous goods case and thereby makes immediately available a number of familiar results from the structure-conduct-performance literature. In Section III the focus is on welfare analysis of monopolistic competition. The results here are essentially restatements of earlier work, although the transformation of variables helps to clarify their foundations. Section IV extends the analysis to incorporate additional decision variables such as advertising, research and development, etc., while section V considers the case where market conditions will not sustain a large number of firms in equilibrium and suboptimal scale effects become important. Factor bias is analysed in