The trade-offs from pattern bargaining with uncertain production costs

Pattern bargaining is a negotiating strategy that is often employed by industry-wide unions in oligopolistic industries to set wages. The conventional wisdom is that pattern bargaining “takes labor out of competition” and therefore softens bargaining between the union and firms, resulting in higher industry wide wages. However, this does not explain why firms agree to pattern bargaining. We introduce a model in which the agents face uncertainty about the relative product-market positions of the firms and compare the trade-offs involved in adopting different bargaining mechanisms. We show that with sufficient heterogeneity in non-labor costs, there are situations in which both the union and the firms prefer pattern bargaining. We also show that in such situations, the adoption of pattern bargaining harms consumers. This provides an explanation as to how pattern bargaining can arise in equilibrium and why there is often strong political opposition to it.     

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.     

Coalitional bargaining games with random proposers: Theory and application

We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Wage bargaining and turnover costs with heterogenous labor and perfect history screening

We study effects of mobility costs in a model of (Nash) wage bargaining between workers and firms, with instantaneous matching, heterogeneous workers, identical firms and free firm entry, and where firms can screen workers perfectly according to their previous work history but not their actual productivity. We derive the employment level and the minimum worker quality standard, in the market solution, and in the efficient solution established by a social planner. When workers have positive bargaining power, there is always some inefficient unemployment among desired workers in the market solution. The lowest hiring standard chosen by firms is higher than the planner's standard when firing costs are high relative to hiring costs, but may be lower in the opposite case. We show that any higher established hiring standard corresponds to a market equilibrium. The model explains a tendency for a high initial unemployment rate to remain high, particularly for low-skilled workers.     

The trade paradox persists under excise taxes

Brander and Krugman (1983) and Sertel (1988) followed by Krugman (1989), showed two sides of a ‘trade paradox’: The paradox in competition, viz. that opening trade (or increasing competition) may cause welfare to decline, and the paradox in efficiency, viz. that an increase in unit transport cost may increase welfare. In this paper, we consider the situation in an environment where interventionist trade policies are not permitted but each country is sovereign to impose an excise tax (or subsidy). The paradoxes persist under equilibrium excise taxes, reckoned both at the non-cooperative (Nash or dominant strategy) equilibrium and at the cooperative solution among tax-imposing authorities maximizing welfare. We also see that the paradoxes persist in a taxless environment where market equilibrium is Stackelberg rather than Cournot.     

Labor market distortions and China's WTO accession package:: an applied general equilibrium assessment

The economic implications of China's accession to the World Trade Organization have been analyzed using applied general equilibrium techniques. We explore the consequences of trade reform in the presence of labor market distortions. A formal model of imperfect labor mobility is incorporated into a large-scale, stochastic applied general equilibrium framework with which the consequences of China's trade reform for net welfare are considered. The simulations suggest that distortions in China's labor market, including imperfect labor mobility, rural-urban migration, dual urban markets and surplus rural labor, have significant effects on trade liberalization outcomes and in some cases produce unexpected second-best results. Journal of Comparative Economics 31 (4) (2003) 774–794.     

Noncooperative Equilibrium and Chamberlinian Monopolistic Competition

This paper addresses the existence of equilibrium for a nonatomic Bertrand game in a Chamberlinian environment. We reformulate O. Hart′s model (Rev. Econ. Stud. 52, 1985, 529–546) as a nonatomic game and show that under dispersion of tastes and continuity of the tastes density, there exists a pure-strategies ε-equilibrium where prices exceed marginal cost. Unlike Hart′s model there is no need to impose uniformity (or even independence) on the distribution of the m-tuple of differential commodities that consumers care about. Moreover, demand curves are allowed to vary across firms and in equilibrium firms may earn profits. Journal of Economic Literature Classification Numbers: B21, D43, L13.     

The Location of Firms in Unionized Countries*

This paper develops a two‐country economic geography model with Cournot competition, where the labor markets are unionized so that trade unions bargain efficiently with each firm over wages and employment. Agglomeration forces are present due to wage premia obtained by the trade unions. It is shown that if the bargaining power of unions differs across countries then, as trade costs are reduced, the country with relatively weak unions gradually acquires all firms. However, for a range of trade costs, it is also a locally stable equilibrium for all firms to locate in the country with strong unions.     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

Warranty markets and public policy

Search equilibrium models in the Economics of Information concern themselves exclusively with consumer ignorance of the prices that different firms charge. Legal regulation dealing with information, on the other hand, concerns itself primarily with contact terms. In particular, firms are often required to warrant against product related defects on the supposed ground that firms respond to consumer ignorance only by degrading contract quality. This paper is the beginning of an attempt to make the Economics of Information useful to policymakers. It models a market for warranties under imperfect information and shows that firms are more likely to respond to consumer ignorance by raising prices for the warranties that consumers prefer rather than deleting warranties from consumer contracts. Hence, policymakers should be concerned more with reducing supracompetitive prices than with “improving” contract quality.     

Informative advertising by heterogeneous firms

This paper introduces a model to analyze the role of the cost of information dissemination in large markets where firms have varying degrees of intrinsic efficiency reflected in their marginal costs. Firms enter a market and discover how efficient they are. Those firms with high enough efficiency stay, others exit. Remaining firms then compete to attract consumers by disseminating information about their existence and their prices using a common advertising technology. The properties of the model’s equilibrium are analyzed. The model is then used to study the effect of the cost of information dissemination on the competitiveness of the market and key industry aggregates, such as price distribution and the distribution of firm value.     

INCENTIVE EFFICIENT PRICE SYSTEMS IN LARGE INSURANCE ECONOMIES WITH ADVERSE SELECTION

We decentralize incentive efficient allocations in large adverse selection economies by introducing a competitive market for mechanisms, that is, for menus of contracts. Facing a budget constraint, informed individuals purchase (lottery) tickets to enter mechanisms, whereas firms sell tickets and supply slots at mechanisms at given prices. Beyond optimization, market clearing, and rational expectations, an equilibrium requires that firms cannot favorably change, or cut, prices. An equilibrium exists and is incentive efficient. An equilibrium can be computed as the solution to a programming problem that selects the incentive efficient outcome preferred by the highest type within an appropriately defined set. For two‐types economies, this is the only equilibrium outcome.     

Macroeconomic fluctuations and bargaining

I study the limit rule for bilateral bargaining when agents recognize that the aggregate economy (and thus the match surplus) follows a finite-state Poisson process. The rule derived in this paper is of special importance for decentralized exchange economies with bargaining. Two simple applications are presented to illustrate this fact. The first example is a model of wage bargaining and trade externalities. I show that in such situations sophisticated bargaining tends to increase the volatility of the wage bill. The second example is based on the Kiyotaki-Wright model of money. I explain how equilibrium prices depend in a fundamental way on the dynamic bargaining solution.     

Achieving efficiency with manipulative bargainers

Two agents bargain over the allocation of a bundle of divisible commodities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a family that includes the Nash and the Raiffa–Kalai–Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent's features to virtually implement the Nash bargaining solution.     

Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights

The problem of longevity risk has recently received considerable attention. In this paper, we apply economic modeling methods to longevity risk securitization, which is now regarded by pension and insurance industries as a solution to the problem. Specifically, we model the trade of a longevity security as a two-player bargaining game, and use Nash's bargaining solution to determine the outcome of it. Our work not only offers an alternative method for pricing longevity securities, but also reveals several properties about the market for longevity securities. First, a trade would occur if the longevity security is an effective hedging instrument, and the trade would benefit all agents involved. Second, a trade of longevity risk can reduce pension plans' bankruptcy risk, safeguarding the financial security of pension plan members. Finally, compared to the competitive equilibrium, Nash's bargaining solution yields higher trading prices. Therefore, as the market becomes more competitive, pension plans may hedge longevity risk at a lower cost.     

Switching error-correction models of house prices in the United Kingdom

This paper develops error-correction models of real house prices in the UK in which the adjustment coefficient switches stochastically between a stable regime where disequilibrium correction takes place and an unstable regime where such a correction does not occur. The generating mechanism of the shifts is modelled as a Markov process with transition probabilities which are either time-invariant or depend on the extent to which the system is out of disequilibrium. Estimation of error-correction models for the UK reveals that the observed booms in real house prices are associated with an unstable regime. We also find that the probability that the system remains in an unstable regime decreases as deviations from equilibrium increase.     

Upstream mergers,downstream mergers,and secret vertical contracts

In an industry characterized by secret vertical contracts, we consider a benchmark case where two vertical chains exist, with two upstream manufacturers selling to two downstream retailers, and show that the equilibrium prices are independent of whether upstream or downstream firms have all the bargaining power. We then analyse two alternative mergers, and show that a downstream merger (which gives the downstream monopolist all the bargaining power) is more welfare detrimental than an upstream merger (which gives the bargaining power to the upstream monopolist). We also show that downstream and upstream mergers have the same effects when contracts are observable.     

Duopoly pricing and waiting lines

The paper deals with a model of duopoly pricing in the context of firms providing services to consumers. Each of the firms has a waiting line of customers arriving randomly. The service provided by both firms is identical and the service time of both firms is assumed to obey the same distribution. Different consumers have different time costs and have to decide whether or not to join one of the lines. It is shown that the Cournot-Nash equilibrium is such that the two firms charge in general different prices. One of the firms specializes in servicing individuals with high cost of time (and the other the rest). Moreover, some examples of non-existence of Cournot-Nash equilibrium and permanent oscillations of prices are shown.