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.     

COMPETITIVE LONG RUN INDUSTRY EQUILIBRIUM AND FACTOR-PRICE UNCERTAINTY*

In this paper we have considered competitive long run industry equilibrium with factor-price uncertainty. We discussed the long run equilibrium output of firms with risk neutrality, output price and their responses to changes in uncertainty, factor price and industry demand. In the first part of this paper we have derived a result that, given risk neutrality, the firms operate at proper capacity, i.e. where expected long run marginal cost is equal to expected long run average cost, as shown in the case of output-price uncertainty. This result is, however, different from that obtained from Sheshinski and Dréze (1976). From the comparative static analysis we first discovered that even under risk neutrality factor-price uncertainty affects the long run industry equilibrium: that is, a mean preserving increase in uncertainty leads firm's to enter the industry, because they can decrease expected long run costs as the variability of factor price increases. Consequently, output price goes down. In contrast, firm size is kept invariable in response to its increase as long as the cost function is separable, i.e. the separability of the cost function holds when production functions are the Cobb-Douglas and CES types used commonly in empirical work, although firm size might, generally, be affected by the increase. It is an interesting fact that firm size and industry size will express different responses to a change in risk. The result that the long run industry equilibrium with cost uncertainty is explicitly affected is a sharp contrast to the result under output-price uncertainty and provides a new aspect for understanding about the behaviour of the industry with uncertainty. Secondly, increased factor-price causes the number of firms in the industry to decline and output price to rise. In addition, firm's size will expand with its increase if that factor is inferior, while the effect on firm size is ambiguous if it is normal. The firm's output, i.e. firm size, is, however, kept constant if the cost function is separable. Thirdly, the long run equilibrium output of the firm remains intact but the number of firms increases as industry demand rises. This result holds, regardless of the firm's attitude towards risk. Finally, we find throughout the paper that the functional form of the cost function plays a significant role in determining the behaviour of the industry with factor-price uncertainty.     

Free Entry under Uncertainty

When focusing on firm’s risk-aversion in industry equilibrium, the number of firms may be either larger or smaller when comparing market equilibrium with and without price uncertainty. In this paper, we introduce risk-averse firms under cost uncertainty in a model of spatial differentiation and show that the impact of uncertainty will increase the number of firms in an industry. With increased uncertainty, the risk premium of the marginal buyer increases by more than the risk premium of the average buyer, so that the price increases by more than the risk premium. When turning to the free entry game, we find that the market generates too many firms.     

Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the inexistence of mutually compatible trades, with non-negative expectation with respect to any risk adjusted prior. These conditions are necessary when agents are not risk neutral at extreme levels of wealths. It is shown that the more uncertainty averse or risk averse the agents, the more likely are efficient allocations and equilibria to exist.     

Social Security and Old Age Unemployment Risk with Efficient Wage Bargaining

I analyze a life‐cycle economy with old age productivity risk where wages, employment, and severance payments are set through efficient bargaining between risk averse unions and risk neutral firms. Allocations with limited union membership are second‐best inefficient as they generate too little labor supply in young age, too much consumption before retirement, too little employment of older workers (early retirement), and too little insurance against old age unemployment. Providing public transfers to early retirees (disability benefits or early pensions) might help to increase the degree of risk sharing at the cost of lower old age employment. Depending on whether absolute risk aversion is increasing or decreasing in consumption, these policies might or might not produce efficiency gains at equilibrium.     

Two-part tariffs set by a risk-averse monopolist

This paper revisits the classical issues of two-part tariffs by considering risk aversion of a monopolistic seller. Under demand uncertainty, equilibrium unit price declines and approaches towards marginal cost as the seller becomes more risk averse. Marginal-cost pricing prevails, irrespective of the seller’s risk attitude, if clients are homogenous. Under cost uncertainty, unit price is higher than marginal cost and monotonically increases in risk aversion. The model is then extended to accommodate buyers’ risk aversion and it is found that demand uncertainty makes unit price decline in the seller’s risk aversion again but increase in buyers’ risk aversion.     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

Uncertainty and sustainability in the management of rangelands

We analyze a dynamic and stochastic ecological-economic model of grazing management in semi-arid rangelands. The ecosystem is driven by stochastic precipitation. A risk averse farmer chooses a grazing management strategy under uncertainty such as to maximize expected utility from farming income. Grazing management strategies are rules about which share of the rangeland is given rest depending on the actual rainfall in that year. In a first step we determine a myopic farmer's optimal grazing management strategy and show that a risk averse farmer chooses a strategy such as to obtain insurance from the ecosystem: the optimal strategy reduces income variability, but yields less mean income than possible. In a second step we analyze the long-run ecological and economic impact of different strategies. We conclude that a myopic farmer, if he is sufficiently risk averse, will choose a sustainable grazing management strategy, even if he does not take into account long-term ecological and economic benefits of conservative strategies.     

Market Size and the Survival of Foreign‐owned Firms*

We develop a general equilibrium model with heterogeneous firms and foreign direct investment cost uncertainty and investigate the survival of foreign‐owned firms. The survival probabilities of foreign‐owned firms depend on firm‐level characteristics, such as productivity, and host country characteristics, such as market size. We show that a foreign‐owned firm will be less likely to be shut down when its parent firm's productivity is higher and its indigenous competitors are less productive. Although a larger market size will always reduce the survival probability of indigenous firms, it can lead to a higher survival probability for foreign‐owned firms if their parent firms are sufficiently productive.     

Oligopolistic Competition and New Technology Adoption under Uncertainty

The paper examines the adoption of a new technology in oligopoly, where there is ex ante uncertainty about variable costs of the new technology. Each firm can either adopt the new process by bearing some up-front investment or may continue to use the old one, after which firms play a Cournot market game. If in equilibrium both technologies are employed, more uncertainty about the new technology increases (decreases) the number of innovating firms and decreases (increases) the product price if the up-front investment is large (small). Our model applies readily to vertical integration if integrated firms neither buy nor sell the intermediate good on the market. However, if buying and selling is allowed, the number of integrated firms is independent of input price uncertainty.     

Imperfect competition in two-sided matching markets

This paper considers a simple equilibrium model of an imperfectly competitive two-sided matching market. Firms and workers may have heterogeneous preferences over matches on the other side, and the model allows for both uniform and personalized wages or contracts. To make the model tractable, I use the Azevedo and Leshno (2013) framework, in which a finite number of firms is matched to a continuum of workers.In equilibrium, even if wages are exogenous and fixed, firms have incentives to strategically reduce their capacity, to increase the quality of their worker pool. The intensity of incentives to reduce capacity is given by a simple formula, analogous to the classic Cournot model, but depends on different moments of the distribution of preferences. I compare markets with uniform and personalized wages. For fixed quantities, markets with personalized wages always yield higher efficiency than markets with uniform wages, but may be less efficient if firms reduce capacity to avoid bidding too much for star workers.     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

A Bayesian Approach to Uncertainty Aversion

The Ellsberg paradox demonstrates that people's beliefs over uncertain events might not be representable by subjective probability. We show that if a risk averse decision maker, who has a well defined Bayesian prior, perceives an Ellsberg type decision problem as possibly composed of a bundle of several positively correlated problems, she will be uncertainty averse. We generalize this argument and derive sufficient conditions for uncertainty aversion.     

Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives

In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.     

Extraction of an Exhaustible Resource: The Effects on Investment of Several Parameters Being Subject to Uncertainty*

This article shows that the effect on investment of the introduction of uncertainty about the size of one parameter depends on what other parameters are simultaneously uncertain. Further, two parameters may be linked with positive or negative covariances. The covariances are here shown to have important effects on the investor, whether risk neutral or risk averse. Governments are advked to consider policies that affect the covariances of those parameters that are key influences on in vestment.     

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.     

INEQUALITY AVERSION CAUSES EQUAL OR UNEQUAL DIVISION IN ALTERNATING‐OFFER BARGAINING

A solution to Rubinstein (1982)'s open‐ended, alternating‐offer bargaining problem for two equally patient bargainers who exhibit similar degrees of inequality aversion is presented. Inequality‐averse bargainers may experience envy if they are worse off, and guilt if they are better off, but they still reach agreement in the first period under complete information. If the guilt felt is strong, then the inequality‐averse bargainers split a pie of size one equally regardless of their degree of envy. If the guilt experienced is weak, then the agreed split is tilted away from the Rubinstein division towards a more unequal split whenever the degree of envy is smaller than the discounted degree of guilt. Envy and weak guilt have opposite effects on the equilibrium division of the pie, and envy has a greater marginal impact than weak guilt. Equally inequality‐averse bargainers agree on the Rubinstein division if the degree of envy equals the discounted degree of guilt. As both bargainers' sensation of inequality aversion diminishes, the bargaining outcome converges to the Rubinstein division.     

Brotherhood of competition: Foreign Direct Investment and domestic mergers

We examine the effects of mergers on Foreign Direct Investment (FDI), and on shaping national policies regarding FDI. In this work we develop a partial equilibrium model of an oligopolistic industry in which a number of domestic and foreign firms compete in the market for a homogeneous good in a host country. It is assumed that the number of foreign firms is endogenous and can be affected by the government policy in the host country. The government sets the policy (subsidies) to maximise social welfare. We allow domestic mergers. Our main results suggest that when the host country government imposes discriminatory lump-sum subsidy in favor of foreign firms, a merger of domestic firms will increase the number of FDI if the subsidy level is exogenous. With an endogenous level of subsidy, a merger of domestic firms will decrease (increase) the welfare if the domestic firms are more (less) efficient.     

DISTRIBUTIONAL CONFLICT, FINANCIAL ADAPTATION AND DELAYED STABILIZATIONS

In this paper we model delayed stabilizations as the rational outcome of a distributional conflict between two risk averse groups in the presence of post-stabilization payoff uncertainty and costly policy reversion. We show that in the initial stages of an extreme inflation episode there is a bias towards maintaining the current inefficient (but certain) revenue collection system which prevents the adoption of the required fiscal adjustment program. The access by those with higher income to a financial adaptation technology increases the average rate of inflation through time for any given government deficit, raising the welfare costs of not reaching an agreement and increasingly redistributing the burden of inflation to those with lower income. This process, if strong enough, will eventually trigger the necessary political support for the required fiscal adjustment. Delayed stabilizations will, nevertheless, induce the poor into accepting conditions that they did not find optimal before.     

THE OPTIMAL RISK CHOICE OF COOPERATIVE AND NONCOOPERATIVE R&D IN DUOPOLY WITH SPILLOVERS

This study examines the R&D risk choice in a duopoly market with technology spill overs. The firms conduct R&D programmes with different degrees of risk but an identical expected outcome and they compete or cooperate in R&D. Findings indicate that, in equilibrium, the R&D risk level decreases in the spill over rate under noncooperative R&D, while it may increase under cooperative R&D. Firms are more likely to engage in higher R&D risks under cooperative R&D than they are under non‐cooperative R&D. Moreover, the equilibrium R&D risk level both under competition and cooperation R&D is always too low from the perspective of social welfare, and the extent of this inefficiency increases with the spill over rate if the size of the spill over is large, but the opposite may occur if the size of the spill over is small.