Skills, agglomeration and segmentation

This paper studies the role of skill heterogeneity in “new economic geography” models of location. In our setting, products are both horizontally and vertically differentiated, and producing higher quality goods requires workers with higher skills. Selling to customers based in a different location entails iceberg-type transport costs and additional “communication costs” consisting of a fixed quality loss. We show that the presence of pecuniary externalities creates a mechanism which always promotes spatial sorting of workers according to their skill levels. In particular, in all stable equilibria, workers with higher skill choose to stay in the location where aggregate skill and income is higher, while the less skilled stay in the other.     

Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion

This article analyzes the impact of transaction (search) costs and capacity constraints in an almost competitive market with homogeneous firms that compete on price. We characterize conditions under which Nash equilibria with price dispersion exist; in equilibrium, firms play pure strategies in prices and consumers adopt a symmetric mixed search strategy. Price dispersion is possible even though consumers all have the same search cost and valuation for the item and prices charged by all firms are common knowledge.     

A NONCOOPERATIVE SHIPPING COURNOT DUOPOLY WITH LINEAR‐QUADRATIC TRANSPORT COSTS AND CIRCULAR SPACE*

The mixed strategy equilibria in a location quantity duopoly model with circular markets are investigated. We find that a continuum of equilibria exists when the transport cost function is linear. However, if costs are strictly concave or convex, most strategies fail to qualify as equilibria. For any integer n, there are nondegenerate mixed strategy equilibria in which each firm locates at n possible locations with equal probability. This result explains possible outcomes in which firms’ on‐path locations are not minimally or maximally differentiated.     

Testing and the Composition of the Labor Pool

We consider a continuous‐time labor matching model with endogenous separation. Firms initially lack information about the quality of workers with whom they are matched. They acquire information both from pre‐employment testing and, in the case in which a labor relationship is established, on‐the‐job performance. Testing provides a signal of a worker's quality. A firm can pick the accuracy level of its test, but it pays a cost that increases in the accuracy. Workers who perform poorly on the test are not offered employment; those who perform poorly on the job are eventually fired (after some delay). Worker quality is not match‐specific; low‐quality workers are less productive with all firms. We show that, in equilibrium, there is an inverse and complementary relation between the level of testing that firms optimally perform and the overall quality of the workers in the matching pool. We consider the properties of a steady‐state, stable equilibrium in such an environment. The complementarity between testing and the composition of the unemployed pool introduces the possibility of multiple equilibria.     

Labor market structure and offshoring

We consider a two‐country, two‐sector model in which a firm’s offshoring decision depends on labor market rigidities that impose additional costs on the firm. Firms endogenously choose their organizational form considering their productivity level and organizational costs. The costs generated by labor market frictions play a key role in determining the benefits of each organizational structure, and thus helps determine the conditions under which a firm decides to offshore. There are three different types of equilibria depending on the relative levels of the domestic and foreign labor market costs and the price of the intermediate input. In all equilibria, a relative rise in the domestic labor market cost increases the share of firms that offshore, while decreasing domestic integration. Furthermore, an economy with offshoring has a higher welfare level and a lower unemployment rate than it would under autarky.     

Minimum wages and welfare in a Hotelling duopsony

Two firms choose locations (non-wage job characteristics) on the interval [0, 1] prior to announcing wages at which they employ workers who are uniformly distributed; the (constant) marginal revenue products of workers may differ. Subgame perfect equilibria of the two-stage location-wage game are studied under laissez-faire and under a minimum wage regime. Up to a restriction for the existence of pure strategy equilibria, the imposition of a minimum wage is always welfare-improving because of its effect on non-wage job characteristics.     

The design of voluntary agreements in oligopolistic markets

This paper analyses the conditions under which a group of firms have the incentive to sign a voluntary agreement (VA) to control polluting emissions even in the presence of free-riding by other firms in the industry. We consider a policy framework in which firms in a given industry decide whether or not to sign a VA proposed by an environmental regulator. We identify the features that a VA should possess in order to provide firms with an incentive to participate in the VA and to enhance its economic and environmental effectiveness. Under very general conditions on the shape of the demand schedule, we obtain the following results. First, a VA does not belong to the equilibrium of the coalition game when benefits from voluntary emission abatement are a pure public good, unless an industry emission target is set by the regulator. Second, in the presence of partial spillovers—i.e. when signatories obtain more benefits from the VA than non-signatories—a VA can belong to the equilibrium only if a minimum participation rule is guaranteed. Third, a VA with a minimum participation rule and a minimum mandatory emission abatement may improve welfare (and even industry profits) compared to a VA in which firms are free to set their own profit maximizing abatement level.     

Asymmetry, stability and growth in a step-by-step R&D-race

We define a notion of stability of equilibrium in an infinitely repeated step-by-step R&D race. The unique symmetric equilibrium is shown to be unstable, and stable asymmetric equilibria arise, if product market competition is intense, firms are patient, imitation is difficult and innovations are large. Some predictions based on symmetric equilibria, e.g. that less patient firms always invest less in research, or that more intensive competition leads to higher economic growth, are reversed for “realistic” values of the underlying parameters.     

Endogenous Comparative Advantage*

We develop a model of trade between identical countries. Workers endogenously acquire skills that are imperfectly observed by firms; therefore, firms use aggregate country investment as the prior when evaluating workers. This creates an informational externality interacting with general equilibrium effects on each country's skill premium. Asymmetric equilibria with comparative advantages exist even when there is a unique equilibrium under autarky. Symmetric, no‐trade equilibria can be unstable under free trade. Welfare effects are ambiguous: trade can be Pareto‐improving even if it leads to an equilibrium between rich and poor countries, with no special advantage regarding country size.     

On-the-job search and strategic bargaining

This paper studies wage bargaining in a simple economy in which both employed and unemployed workers search for better jobs. The axiomatic Nash bargaining solution and standard strategic bargaining solutions are inapplicable because the set of feasible payoffs is nonconvex. I instead develop a strategic model of wage bargaining between a single worker and firm that is applicable to such an environment. I show that if workers and firms are homogeneous, there are market equilibria with a continuous wage distribution in which identical firms bargain to different wages, each of which is a subgame perfect equilibrium of the bargaining game. If firms are heterogeneous, I characterize market equilibria in which more productive firms pay higher wages. I compare the quantitative predictions of this model with Burdett and Mortensen's [1998. Wage differentials, employer size and unemployment. International Economic Review 39, 257-273.] wage posting model and argue that the bargaining model is theoretically more appealing along important dimensions.     

Welfare, home market effects, and horizontal foreign direct investment

Abstract.  We investigate the spatial distribution and organization of an imperfectly competitive industry when firms may choose to operate more than a single production unit. Focusing on a short-run setting with a fixed mass of firms, we first fully characterize the spatial equilibria analytically. Comparing the equilibrium and the first-best, we secondly show that both organizational and spatial inefficiencies may arise. In particular, when fixed costs are low, when transport costs are high, and when products are close substitutes, the market outcome may well have to too many multinationals operating from a social point of view ('over-investment'). As a by-product, under-agglomeration of exporters in the larger market may arise.     

Absenteeism: A comparison of incentives in alternative organizations

This paper uses a game-theoretic model to analyze the incentives workers may have to play “hookey” from work given that there is an outwardly unobservable probability of being sick and thus being unable to work. We compare incentives and equilibria in labor-managed firms (LMFs) and in profit-maximizing firms (PMFs), both in single-period and repeated games. We show, among other things, that in an egalitarian LMF there are circumstances under which members will not work when it is optimal to work, while the PMF suffers from the opposite problem; daily paid workers will work even when it would be better if they did not.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Bertrand-Edgeworth duopoly with unit cost asymmetry

Summary This paper characterizes the set of Nash equilibria in a price setting duopoly in which firms have limited capacity, and in which unit costs of production up to capacity may differ. Assuming concave revenue and efficient rationing, we show that the case of different unit costs involves a tractable generalization of the methods used to analyze the case of identical costs. However, the supports of the two firms' equilibrium price distributions need no longer be connected and need not coincide. In addition, the supports of the equilibrium price distributions need no longer be continuous in the underlying parameters of the model.As an application of our characterization, we examine the Kreps-Scheinkman model of capacity choice followed by Bertrand-Edgeworth price competition and show that, unlike in the case of identical costs, Cournot equilibrium capacity levels need not arise as subgame-perfect equilibria. The low-cost firm has greater incentive to price its rival out of the market than exists under Cournot behavior.We are grateful to Joseph Harrington, Marie Thursby, Casper de Vries and, especially, William Novshek for helpful discussions and comments. Thomas Faith and Ioannis Tournas provided valuable research assistance. This paper was presented at the Winter Meetings of the Econometric Society in December 1988, the Midwest Mathematical Economics Conference in April 1989, the Sixteenth Annual Congress of the European Association for Research in Industrial Economics in August 1989, the European Meetings of the Econometric Society in September 1989, and in seminars at the Ecole Nationale des Ponts et Chaussées, Erasmus University Rotterdam, Indiana University, INSEAD, Texas A&M University, Tilburg University, the University of Bonn and the University of Florida. Deneckere acknowledges financial support through National Science Foundation Grant SES-8619012 and the Kellogg Graduate School of Management's Beatrice/Esmark Research Chair. Kovenock acknowledges financial support through Erasmus University Rotterdam, the Purdue Research Foundation, the Ford Motor Company Fund, and an Ameritech Foundation Summer Faculty Research Grant.     

Wage–vacancy contracts and multiplicity of equilibria in a directed search model of the labour market

This paper studies a directed search model of the labour market, which is standard in all aspects except two. First, we allow firms to post wage–vacancy contracts advertising the number of workers they would pay as well as the payment all will receive. Second, we consider two cases: one where workers are risk neutral and one where workers are risk averse, both in finite and large economies. Our paper shows that when firms post wage–vacancy contracts, whether workers are modelled as risk neutral or risk averse matters: the types of symmetric equilibria and the nature of multiplicity of equilibria are different. Somewhat surprisingly, when there are finite numbers of risk‐neutral workers and firms, we obtain a finite number of symmetric equilibria, but when workers are risk averse, we obtain a continuum of equilibria. Furthermore, our paper sounds a cautionary note on using large economies as an approximation of finite economies: when workers are risk neutral, the nature of equilibrium is preserved going from a finite to a large economy, but the nature of equilibrium is different when workers are risk averse.     

Wage/tenure contracts with heterogeneous firms

This paper investigates equilibria where firms post wage/tenure contracts and risk averse workers search for new job opportunities whether employed or unemployed. We generalize previous work by assuming firms have different productivities. Equilibrium implies more productive firms always offer more desirable contracts. Thus workers never quit from more productive firms for less productive firms. Nevertheless turnover is inefficient as employees with long tenures at low productivity firms may reject outside job offers from more productive firms. A worker who quits to a more productive firm may accept a wage cut. Such wage cuts are compensated by faster “promotion” rates to higher wage levels in the future. We also generalize previous arguments by showing equilibria exist where the distribution of offers contains interior mass points and find equilibrium wage/tenure contracts need not be smooth.     

Strategic choice of financing systems in regulated and interconnected industries

The growing importance of inter-network exchanges in infrastructure-based utilities influences regulatory choices and access pricing for downstream services using the networks. We analyze this problem in a setting where the infrastructure managers of two bordering countries are in charge of pricing the access to their networks for downstream transport firms that provide international services. Network costs can be financed through public funds and user charges.In this context, access prices are affected by the incomplete internalization of consumers' surplus and infrastructure costs; we analyze how this distortion at the access pricing level generates a distortion in the levels of public funds dedicated to infrastructure financing.Because of these distortions, it turns out that in a non-cooperative setting the second-best outcome might consist in the simultaneous adoption of a no-subsidy system. However, multiple equilibria typically exist and the second-best outcome is never a stable equilibrium. Other properties of the different possible equilibria are studied, as well as the impact of supra-national policies aimed at encouraging the development of international services. Finally, we show that the coordination problems deriving from the existence of multiple equilibria can, sometimes, be solved by separating the choice of a regulatory mode from the access pricing stage, thereby allowing the infrastructure managers to commit to use a specific financing system before setting the access price.     

Crime and punishment in the “American Dream”

We observe that countries where belief in the “American dream”(i.e., effort pays) prevails also set harsher punishment for criminals. We know that beliefs are also correlated with several features of the economic system (taxation, social insurance, etc). Our objective is to study the joint determination of these three features (beliefs, punitiveness and economic system) in a way that replicates the observed empirical patterns. We present a model where beliefs determine the types of contracts that firms offer and whether workers exert effort. Some workers become criminals, depending on their luck in the labor market, the expected punishment, and an individual shock that we call “meanness”. It is this meanness level that a penal system based on “retribution” tries to detect when deciding the severity of the punishment. We find that when initial beliefs differ, two equilibria can emerge out of identical fundamentals. In the “American” (as opposed to the “French”) equilibrium, belief in the “American dream” is commonplace, workers exert effort, there are high powered contracts (and income is unequally distributed) and punishments are harsh. Economists who believe that deterrence (rather than retribution) shapes punishment can interpret the meanness parameter as pessimism about future economic opportunities and verify that two similar equilibria emerge.     

An elasticity approach to equilibrium and preference concentration in the Hotelling game

We consider the standard Hotelling price-and-location game with two firms, and show how equilibrium is affected by the shape of the consumers’ density. By describing the latter in terms of elasticity (Esteban in Int Econ Rev 27:439–444, 1986), we develop a framework which enables us to prove a sufficient condition for the existence of multiple asymmetric equilibria when the density is symmetric, in terms of a lower bound on the Gini coefficient of the distribution of preferences.