On monopolistic competition and optimal product diversity: workers' rents also matter

Abstract .  In the Dixit-Stiglitz model of monopolistic competition, entry of firms is socially too small. Other authors have shown that excess entry is also a possibility with other preferences for diversity. We show that workers' rents also contribute to explain excess entry through a general equilibrium mechanism. Larger wages indeed raises the aggregate earnings and firms sales and profits, which entices too many firms to enter. We discuss the possibility of over-provision of varieties by comparing the equilibrium to unconstrained and constrained social optima and to other regulatory frameworks where wages are not controlled.     

Cartels in the unidirectional Hotelling model

We study the impact of space on perfect collusion sustainability within the unidirectional Hotelling model where the firms are constrained to move to the left. We obtain that when the firm that located to the left of the Hotelling segment has the greater incentive to deviate, the distance between the firms has a negative impact on the capability of the firms to sustain the collusion in equilibrium. On the other hand, when the firm that located to the right has the greater incentive to deviate, greater spatial distance makes the collusion easier to sustain in equilibrium. These results substantially differ from the bidirectional Hotelling model.     

Does Poaching Distort Training?

We analyse the efficiency of the labour market outcome in a competitive search equilibrium model with endogenous turnover and endogenous general human capital formation. We show that search frictions do not distort training decisions if firms and their employees are able to coordinate efficiently, for instance, by using long-term contracts. In the absence of efficient coordination devices there is too much turnover and too little investment in general training. Nonetheless, the number of training firms and the amount of training provided are constrained optimal, and training subsidies therefore reduce welfare.     

Strategic tariffs, tariff jumping, and heterogeneous firms

The majority of research to date investigating strategic tariffs in the presence of multinationals finds a knife-edge result where, in equilibrium, all foreign firms are either multinationals or exporters. Utilizing a model of heterogeneous firms, we find equilibria in which both pure exporters and multinationals coexist. We utilize this model to study the case of endogenously chosen tariffs. As is standard, Nash equilibrium tariffs are higher than the socially optimal tariffs. Unlike existing models with homogeneous firms, we find that non-cooperative tariffs promote the existence of low-productivity firms relative to the socially optimal tariffs. This highlights a new source of inefficiency from tariff competition not found in models of homogeneous firms. In addition, we find that in many cases the Nash equilibrium tariff when FDI is a potential firm structure is lower than when it is not. As a result, FDI improves welfare by mitigating tariff competition.     

Financial Markets and Wages

We study a labour market equilibrium model in which firms sign optimal long-term contracts with workers. Firms that are financially constrained offer an increasing wage profile: they pay lower wages today in exchange for higher future wages once they become unconstrained. Because constrained firms grow faster, the model predicts a positive correlation between the growth of wages and the growth of the firm. Under some conditions, the model also generates a positive relation between firm size and wages. Using matched employer–employee data from Finland and the National Longitudinal Survey of Youth for the U.S., we show that the key dynamic properties of the model are supported by the data.     

TAX COMPETITION IN A SIMPLE MODEL WITH HETEROGENEOUS FIRMS: HOW LARGER MARKETS REDUCE PROFIT TAXES*

We set up a simple two‐country model of tax competition where firms with different productivity decide in which location to produce and sell output. In this model, a unique, asymmetric Nash equilibrium is shown to exist, provided that countries are sufficiently different with respect to their exogenous market size. Sorting of firms occurs in equilibrium, as the smaller country levies the lower tax rate and attracts the low‐cost firms. A simultaneous expansion of both markets that raises the profitability of firms intensifies tax competition and causes both countries to reduce their tax rates, despite higher corporate tax bases.     

An Observable Delay Game with Unionised Managerial Firms

The endogenous order of moves is analysed in a unionised Cournot duopoly with managerial delegation and firm‐specific unions, where firms choose whether to set quantities sequentially or simultaneously. It is shown that, in contrast to the standard duopoly with profit‐maximising firms where both firms prefer to be the leader and thus simultaneously chosen quantities emerge as an endogenous equilibrium, a rich set of equilibrium outcomes may occur. In particular, the result of sequential choices, which reverses the conventional wisdom in regard to Cournot duopolies, emerges as the endogenous equilibrium when the union's wage orientation is sufficiently high.     

QUALITY COMPETITION WITH STOCHASTIC DEMAND AND COSTLY SEARCH: THEORY AND EVIDENCE FROM THE VIDEO RENTAL MARKET

A theoretical model is developed to predict optimal service rates in markets where firms compete in availability. We show that firms are more likely to stock-out of popular products as the cost of consumer search increases. Carlton (1978) showed that, in a zero-profit competitive environment, firms balance the risk of not being able to serve a particular customer against the cost of holding excess capacity and that this balancing act will result in an equilibrium in which not all customers are served. The model was later adapted to oligopolistic competition by Peters (1984) and Deneckere and Peck (1995) . This paper extends this literature on competition under stochastic demand by developing a model that incorporates 1) the possibility that customers may be able to purchase from another firm in the case of a stock-out and 2) the option for firms to offer an imperfect substitute in order to persuade some customers to make a purchase when the first choice product is out of stock. Empirical evidence is presented in support of the theoretical model using data collected from video rental outlets in a midsize southeastern US city.     

Endogenous rationing,price dispersion and collusion in capacity constrained supergames

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price–quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price–quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with optimal collusion, it may be a requirement of optimal collusion.     

Directed search with multiple job applications

We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. Our main theoretical contribution is to integrate the portfolio choice problem faced by workers into an equilibrium framework. All equilibria of our model exhibit wage dispersion. Consistent with stylized facts, the density of wages is decreasing and higher wage firms receive more applications per vacancy. Unlike most models of directed search, the equilibria are not constrained efficient.     

Firm size distributions in an industry with constrained resources

We propose an equilibrium model for firm size distribution in an industry with a constrained essential input. The model applies when the population of firms is small and homogeneous and the supply of the necessary input factor is perfectly inelastic. We argue that although the Gibrat assumption obtains, this does not result in the lognormal distribution because of the entries, exits and mergers of firms competing for the inelastic essential resource. Using our own 32-year database of firms, we test the broken-stick, or random-ordered-interval, model that we call the Whitworth distribution, successfully applied by others to a number of data sets, including the abundances of bird species. We propose the Whitworth as the basic model of the equilibrium distribution of firm sizes for such supply-constrained industries, and find it fits our 31-year database best.     

COMPETITIVE SEARCH,EFFICIENCY, AND MULTIWORKER FIRMS*

I study competitive search equilibrium in an environment where firms operate a decreasing‐returns production technology and hire multiple workers simultaneously. Firms post wages, possibly several of them. The equilibrium can feature wage dispersion even though all firms and workers are ex ante identical. Unlike the benchmark where firms hire a single worker, hiring is constrained inefficient. Efficiency requires that firms commit to the number of hires, pay all applicants, or pay wages that depend on the number of applicants. Under wage‐posting, the inefficiency is highest at intermediate levels of labor market tightness.     

Vertical Product Differentiation When Quality is Scarce: The Case of n > 2 Firms

This paper describes a model of vertical product differentiation in which more than two firms compete in quality and price. Quality is of fixed supply, so firms participate in an auction to attain it. Firms then simultaneously choose prices. The paper determines equilibrium bids in the quality auction and the Bertrand equilibrium prices. In equilibrium one firm attains all the units of quality, but pays a price such that it, like the minimum-quality firms, earns zero profits. Aggregate welfare is computed, and is shown to decrease as competition increases.     

Location equilibrium with asymmetric firms: the role of licensing

It is known that if exogenous cost heterogeneities between the firms in a spatial duopoly model are large, then the model does not have a pure-strategy equilibrium in location choices. It is also known that when these heterogeneities are stochastically determined after firms choose their locations, spatial agglomeration can appear. To tackle these issues, the current paper modifies the spatial framework by allowing firms to exchange the cost-efficient production technology via royalties. It is shown that technology transfer guarantees the existence of a location equilibrium in pure strategies and that maximum differentiation appears in the market.     

Limited knowledge of demand and oligopoly equilibria

In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.     

Standards Migration and Peripheral Competition

The impact of competition from peripheral firms on the standards migration efforts by integrated systems firms with de facto standards control is investigated. When systems firms try to migrate their customers to a new standard, they can lose some control over their installed base because they are constrained in their product offerings. Peripherals firms do not face such constraints. Their product offerings allow the emergence of hybrid systems which systems firms are unwilling to match. Improved peripherals from independent firms make these hybrid systems possible. Such hybrid systems lengthen the economic life of the products that make up the existing standard. Historical and empirical evidence from the mainframe computer industry in the 1960s and 1970s illustrates the competition from peripheral firms and their impact on IBM's standards migration efforts. IBM pursued the establishment of a new de facto standard, while independent disk drive manufacturers supplied peripherals that enabled hybrid systems. For the computer mainframe industry, it was shown that those hybrid systems increased the economic life of IBM's older computers, although IBM was able to migrate its customers to the new standard in this case.     

Standards Migration and Peripheral Competition

The impact of competition from peripheral firms on the standards migration efforts by integrated systems firms with de facto standards control is investigated. When systems firms try to migrate their customers to a new standard, they can lose some control over their installed base because they are constrained in their product offerings. Peripherals firms do not face such constraints. Their product offerings allow the emergence of hybrid systems which systems firms are unwilling to match. Improved peripherals from independent firms make these hybrid systems possible. Such hybrid systems lengthen the economic life of the products that make up the existing standard. Historical and empirical evidence from the mainframe computer industry in the 1960s and 1970s illustrates the competition from peripheral firms and their impact on IBM's standards migration efforts. IBM pursued the establishment of a new de facto standard, while independent disk drive manufacturers supplied peripherals that enabled hybrid systems. For the computer mainframe industry, it was shown that those hybrid systems increased the economic life of IBM's older computers, although IBM was able to migrate its customers to the new standard in this case.     

Perfect competition and optimal product differentiation

This paper considers whether a competitive economy will achieve an optimal allocation when firms produce differentiated products.In the model studied, firms market those products which maximize profit given the demand curves facing them. Markets are assumed to be open only for goods actually traded. Competitive conditions are achieved by replicating the consumer sector. It is shown that market equilibrium may be suboptimal if those products not being produced are highly complementary in consumption. Sufficient conditions on preferences and production sets for the market equilibrium to be optimal are given.     

International Capital Mobility in the Presence of Unemployment Insurance

The paper develops a general–equilibrium model with layoff unemployment to examine the effect of different unemployment insurance policies on international capital mobility. Conditions are derived under which capital will flow to the high–benefit country. Incentives for international capital movements are unaffected by how the burden of financing unemployment benefits is distributed between workers and firms. It is shown that capital outflows might have positive welfare effects for workers. This contrasts with results from standard models of international factor movements.