Human–capital investment and the wage gap

Summary. According to empirical studies, the wage differential by skills evolved non–monotonically in the past decades although the relative supply of skilled labor steadily increased. The present paper provides a theoretical explanation for this finding. In our setting, technological change intertemporally alters the human–capital investment incentives of heterogeneous individuals. As a consequence of changing incentives, the time path of the relative wage is U–shaped while there is a rise in the share of skilled workers. Received: November 28, 2000; revised version: January 30, 2001     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

The Zilcha criterion for dynamic inefficiency

Summary. This paper reexamines the condition (1 + n), which Zilcha (1991) presents as a necessary and sufficient condition for dynamic inefficiency of stationary allocations in overlapping generation models with stochastic production. We show that this condition is necessary but not sufficient for a stationary allocation to be dynamically inefficient by Zilchas definition. We also show that there is a narrow but widely studied class of specifications in which the Zilcha test is both necessary and sufficient for dynamic inefficiency of stationary competitive equilibrium allocations. Outside this class, however, counterexamples can be constructed relatively easily.Received: 30 September 2002, Revised: 13 August 2004, JEL Classification Numbers: D51, D90, E13, E22. Correspondence to: Steven RussellWe thank Jon Burke, Subir Chakrabarti, Itzhak Zilcha and an anonymous referee for helpful conversations and/or comments.     

Endogenous fluctuations in unionized economies with productive externalities

Summary. We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factors substitutability).Received: 16 January 2002, Revised: 18 March 2004, JEL Classification Numbers: E32, J51, D60, D62. Correspondence to: Leonor ModestoThis paper is a much revised version of our former working paper Unions, Increasing Returns and Endogenous Fluctuations. Financial support from Fundação para a Ciência e Tecnologia under the POCTI, is gratefuly acknowledged.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

Is capital a collusion device?

Summary. We examine how irreversible capital reduces the possibility of a duopoly to sustain implicit collusion by grim strategies, when the product is homogenous and firms compete in quantities. Compared with the case of reversible capital, there are two countervailing effects: Deviation from an existing collusion is less attractive, because capital once installed causes costs forever. But the punishment will also be less severe due to the high capacity the deviating firm can build before punishment starts. The last effect dominates, meaning that the commitment value of capital is negative for all firms. If capital is irreversible, collusion breaks down for realistic magnitudes of interest rates. Received: April 30, 1999; revised version: November 30, 2001     

The equilibrium set of two-player games with complementarities is a sublattice

Summary. I prove that the equilibrium set in a two-player game with complementarities, and totally ordered strategy spaces, is a sublattice of the joint strategy space. Received: May 31, 2001; revised version: October 4, 2002     

Double Moral Hazard,Monitoring, and the Nature of Contracts

generalized double-sided moral-hazard model, with risk-averse parties who mutually monitor each other (to get a reasonable idea of outcome/effort). The model considers trade-off between monitoring costs and moral hazard costs, which are endogenously determined by the extent of monitoring. Using this model, we formally prove a generalized version of Coase's conjecture – that the optimal contract minimizes the agency and risk costs. We then show how varying assumptions about the feasibility or cost of monitoring of the outcome or the worker's effort lead to different contracts being optimal. The analysis is then used to explain the nature of contracts observed in practice under many different situations. We will give an explanation as to why industrial workers typically work under wage contracts, while share contracts are common in agriculture and will explain why profit sharing is more common for senior managers than for the production workers. Received September 19, 2000; revised version received October 30, 1997     

A strategic market game with seigniorage costs of Fiat money

Summary. A model that includes the cost of producing money is presented and the nature of the inefficient equilibria in the model are examined. It is suggested that if one acknowledges that transactions are a form of production, which requires the consumption of resources, then the concept of Pareto optimality is inappropriate for assessing efficiency. Instead it becomes necessary to provide an appropriate comparative analysis of alternative transactions mechanisms in the appropriate context. Received: September 5, 2000; revised version: May 3, 2001     

Winner-take-all price competition

Summary. We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes. Received: April 7, 2000; revised version: September 14, 2000