Equilibrium Search with Continuous Productivity Dispersion: Theory and Nonparametric Estimation

In this article we develop an equilibrium search model with a continuous distribution of firm productivity types within a given labor market. We characterize equilibrium, derive expressions for the endogenous equilibrium wage distributions, and characterize the set of wage distributions that can be generated by the model. We develop a structural nonparametric estimation method for the productivity distribution. We estimate the model using French longitudinal survey data on labor supply, and we compare the results with those from a French panel data set of firms. The results are informative on the degree to which firms exploit search frictions.     

Average-cost pricing: Some evidence and implications

We present new survey evidence on pricing behavior for more than 14,000 European firms, and study its macroeconomic implications. Among firms that are price setters, roughly 75% respond that their prices are set as a markup on total costs, a business practice termed “full cost pricing”. Only 25% set prices as markups over variable or marginal costs. Moreover, using industry data for the U.S., we find that the correlation between changes in output prices and changes in variable input prices is significantly lower when fixed costs are likely to be more important.Since our results are similar to the findings in the classic and controversial paper of Hall and Hitch (1939) and subsequent survey evidence, we believe it worth studying the implications of full cost pricing for macroeconomics. We first propose a problem for the firm where full cost pricing can arise as optimizing behavior. We embed this problem, featuring an occasionally binding constraint, into a simple general equilibrium model. We show that when the model is hit by a shock that makes the constraint binding, the response of endogenous variables is amplified significantly more than it would be under the unconstrained regime.     

FIRM DYNAMICS IN AN URBAN ECONOMY *

We develop a new dynamic general equilibrium model to explain firm entry, exit, and relocation decisions in an urban economy with multiple locations and agglomeration externalities. We characterize the stationary distribution of firms that arises in equilibrium. We estimate the parameters of the model using a method of moments estimator. Using unique panel data collected by Dun and Bradstreet, we find that agglomeration externalities increase the productivity of firms by up to 8%. Economic policies that subsidize firm relocations to the central business district increase agglomeration externalities in that area. They also increase economic welfare in the economy.     

Service Quality,Competition, and Regulatory Policies in the Postal Sector

This paper presents a simple model which illustrates the possible policy- and welfare-implications of endogenous product selection in the postal sector. The cost of a unit of mail depends on its "quality" (e.g., speed of delivery) and on the type and location of the addressee (firms, urban households, and rural households). Senders have inelastic demands and differ in their willingness to pay for quality. Addressees are passive but their utility may affect social welfare. Two operators play a two-stage game, first choosing qualities and then prices. We first show that the equilibrium with two private (profit maximizing) operators results in an inefficient provision of quality. Then, we consider the mixed (Nash) equilibrium with one private and one (welfare maximizing) public operator. If the budget constraint of the public firm is not binding, this equilibrium is shown to be first-best efficient even if social welfare accounts for the utility of addressees. If the budget constraint is binding, the mixed equilibrium is not efficient but yields a higher level of welfare than the private equilibrium. Finally, we study the impact of minimum quality standards within our setting.     

Knowledge appropriability, firm size, and growth

Empirical evidence shows that the number of patents per R&D dollar declines with firm size. In this paper, we propose a Schumpeterian growth model that accounts for this evidence. We analyze an economy with firms that engage in cost-reducing innovation resulting from the accumulation of both codified and tacit knowledge: the former occurs through the purchase of patents, while the latter is the result of R&D conducted in-house by firms. We study the relation between knowledge appropriability and market structure, and we show that a shift from patents to in-house research occurs as firm size gets larger. Since innovation statistics concentrate mainly on patents, this process of research reallocation results into an under-estimation of innovative activity and is responsible for the declining ratio of patents to R&D expenditure. Survey data on UK-based firms provide support to our results.     

Production and financial policies under asymmetric information

We propose an extension of the standard general equilibrium model with production and incomplete markets to situations in which (i) private investors have limited information on the returns of specific assets, (ii) managers of firms have limited information on the preferences of individual shareholders. The extension is obtained by the assumption that firms are not traded directly but grouped into ‘sectorial’ funds. In our model the financial policy of the firm is not irrelevant. We establish the existence of equilibria and discuss the nature of the inefficiencies introduced by the presence of asymmetric information. We also illustrate the properties of the model in three simple examples. We would like to thank Alberto Bisin, Armando Dominioni, Piero Gottardi, Tito Pietra, Paolo Siconolfi, and an anonymous referee for useful suggestions and comments.     

ON EMPLOYMENT CONTRACTS WITH ENDOGENOUS ON-THE-JOB SEARCH

We consider an equilibrium search model and employment contracts when workers have endogenous on-the-job search. When a firm tries to retain an employee by matching outside offers, variable search intensity leads to a moral hazard problem. We first consider workers with identical productivities. We derive an equilibrium where firms commit not to respond to outside offers and workers search less. Second, we investigate the case with heterogeneous workers and asymmetric information. Assuming that firms can commit to retain all workers irrespective of their ability, we establish conditions under which it is optimal to do so. This policy again reduces the incentive for active on-the-job search. We discuss an equilibrium where all firms use these so-called ‘pooling’ contracts.     

Influence of market-level and inter-firm differences in costs on product positioning and pricing

The objective of this article is to study the impact of differentiation and firm positioning on firm’s pricing decisions in a horizontally differentiated competitive market. We build a parsimonious game-theoretic model and analyse simultaneous entry of firms. The effect of differentiation is modelled as an additional cost incurred by both firms based on the degree of differentiation between the firms. The cost of positioning is modelled as a market level cost affecting both firms whereby firms incur a cost if they want to position themselves away from the centre of distribution of consumers. Our analysis provides some surprising results, explains some conflicting empirical observations documented in previous research and may also be useful for further empirical research in this area by providing sharper predictions about the impact of various types of costs on market outcomes. For example, we find that if the cost of positioning is sufficiently high, then a firm with lower cost of differentiation charges a higher price in equilibrium, even when no differences in exogenous costs exist. We also find that under some circumstances the cost disadvantaged firm can enjoy higher price-cost margins compared to the cost leader thereby suggesting that higher costs could be a blessing in disguise.     

The Role of Expectation on Job Search and the Firm Size Effect on Wages

We formulate dynamic games which give a rationale to the firm size–wage effect that the sheer firm size increases wages. We postulate that past wages of large firms are known to new employees, while those of small firms are not. Large firms can credibly induce workers to expect high future wages and reduce turnover, while small firms have no choice but to be myopic and pay low wages. The equilibrium wage differential obtains under the same worker characteristics and production function. We provide empirical evidence that workers' expectations depend on firm size and affect wages as predicted by our model.     

FIRMS’ CHARACTERISTIC AND EQUILIBRIUM WITH TRADEABLE PERMITS MARKET*

We study, in a simple model, the partial equilibrium of an industry with n firms endowed by different Cobb‐Douglas technologies which have different pollution effects. The price of input (labour) and the demand curve to the industry are given. Pollution is restricted by a tradeable market of permits in the industry. Each firm is characterised by a parameter combining production efficiency and pollution effect, its e‐characteristic. The equilibrium depends mainly on these e‐characteristics which are linked to the performance of the technologies. In the long run performances are defined per unit of capital. Last, we analyse the consequences of permits’ allocations on the profitability of the firms.     

Downstream mode of competition with upstream market power

In a two-tier oligopoly, where the downstream firms are locked in pair-wise exclusive relationships with their upstream input suppliers, the equilibrium mode of competition in the downstream market is endogenously determined as a renegotiation-proof contract signed between each downstream firm and its exclusive upstream input supplier. We find that the upstream–downstream exclusive relationships credibly sustain the Cournot (Bertrand) mode of competition in the downstream market, when the goods are substitutes (complements). In contrast to previous studies, this result holds irrespectively of the degree of product differentiation and the distribution of bargaining power between the upstream and the downstream firm, over the pair-specific input price.     

The impact of trade on employment,welfare, and income distribution in unionized general oligopolistic equilibrium

This paper sets up a multi-sector general oligopolistic equilibrium trade model in which all firms face wage claims of firm-level unions. By accounting for productivity differences across industries, the model features income inequality along multiple lines, including inequality between firm owners and workers as well as within these two groups of agents, and involuntary unemployment. We use this setting to study the impact of trade liberalization on key macroeconomic performance measures. In particular, we show that a movement from autarky to free trade with a fully symmetric partner country lowers union wage claims and therefore stimulates employment and raises welfare. Whether firms can extract a larger share of rents in the open economy depends on the competitive environment in the product market. Furthermore, the distribution of profit income across firm owners remains unaffected, while the distribution of wage income becomes more equal when a country opens up to trade with a fully symmetric trading partner. We also analyze how country size differences and technological dissimilarity of trading partners affect the results from our analysis.     

Price search and spatial competition

In this paper we study a model where two spatially scattered sellers face a population of consumers dispersed over a given geographical area; they have to incur a transaction cost to place their purchase order. Moreover these consumers have imperfect knowledge of prices, but obtain full information about prices at the first shop they solicit. We study price competition between these firms. The main outcomes of our analysis are as follows. First we show that whenever a price equilibrium exists for given locations of firms, it will necessarily display price dispersion. Second we study location configurations which ensure the existence of a price equilibrium. Furthermore we show that when it exists, a price equilibrium is unique. Finally we analyze firms revenues when merchants anticipate the consequences of their locational choice on subsequent price competition. Then we find that there is an incentive for a firm to get as close as possible to its competitor.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

International Trade,Offshoring and Heterogeneous Firms

Recent trade models determine the equilibrium distribution of firm‐level efficiency endogenously and show that freer trade shifts the distribution towards higher average productivity because of entry and exit of firms. These models ignore the possibility that freer trade also alters the firm‐size distribution via international firm migration (offshoring); firms must, by assumption, produce in their “birth nation.” We show that when firms are allowed to switch locations, new productivity effects arise. Freer trade induces the most efficient small‐nation firms to move to the large nation. The large country gets an “extra helping” of the most efficient firms while the small nation's firm‐size distribution is truncated on both ends. This reinforces the large‐nation productivity gain while reducing or even reversing the small‐nation productivity gain. The small nation is nevertheless better off allowing firm migration.     

Price and quantity regulation in general equilibrium

We consider a general equilibrium model with a production externality (e.g. pollution), where the regulator does not observe firm productivity shocks. We examine quantity (permit) regulation and price (tax) regulation. The quantity of permits issued by the regulator are independent of the productivity shock, since shocks are unobserved. Price regulation implies use of the regulated input is an increasing function of the productivity shock because firms take advantage of a good productivity shock by increasing input use. Thus price regulation generates higher average, but more variable, production. Therefore, we show that in general equilibrium the relative advantage of quantity versus price regulation depends not only on the slopes of marginal benefits and costs, but on general equilibrium effects such as risk aversion. The general equilibrium effects are often more important than the slopes of the marginal benefits and cost curves. In the simplest model, a reasonable risk aversion coefficient implies quantity regulation generates higher welfare regardless of the benefit function.     

PRODUCTIVITY GROWTH AND WORKER REALLOCATION*

Productivity dispersion across firms is large and persistent, and worker reallocation among firms is an important source of productivity growth. An equilibrium model of growth and firm evolution designed to clarify the role of worker reallocation in the growth process is studied. We show that it explains the correlations between size measures and labor productivity found in Danish firm data. Conditions under which the reallocation of workers from less to more productive firms contributes to aggregate productivity growth in the economy modeled are derived. Finally, a proof of existence of an equilibrium solution to the model is also provided.     

How to allocate forward contracts: The case of electricity markets

Several regulatory authorities worldwide have imposed forward contract commitments on electricity producers as a way to mitigate their market power. In this paper we analyze the impact of such commitments on equilibrium outcomes in a model that reflects important institutional and structural features of electricity markets. We show that, when firms are asymmetric, the distribution of contracts among firms matters. In the case of a single dominant firm, the regulator can be confident that allocating contracts to that firm will be pro-competitive. However, when asymmetries are less extreme, certain contract allocations might yield anti-competitive outcomes by eliminating more competitive equilibria. Our analysis thus suggests that forward contracts should be allocated so as to (virtually) reduce asymmetries across firms.     

Price dispersion in a model of identical agents with perfect information

Abstract. The objective of this paper is to demonstrate that price dispersion is possible even in a world of perfect information and identical consumers and firms. The driving force in the model is service capacity and congestion cost. Each firm chooses a service capacity. Customers of a firm bear a congestion cost which, for a fixed service capacity, is an increasing function of the number of customers served by this firm. We demonstrate that under certain conditions the combined profit of two firms and the total surplus are higher in a price-dispersion equilibrium than in a single-price equilibrium.     

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.