On price uncertainty, nominal assets and uninsurable idiosyncratic risks

The paper discusses a way in which price uncertainty may affect the extent of idiosyncratic, uninsurable risks in an incomplete markets economy with nominal assets and thereby affect output and welfare. Although the returns on these assets are constant and riskfree in nominal terms, price uncertainty causes their real returns to be stochastic. This affects the ability of households to diversify their idiosyncratic risks using these assets and consequently the extent of uninsurable risks in the economy. The paper establishes a relationship between the volume of trade in nominal assets, the stochastic characteristics of the price shocks and the covariance between the price and idiosyncratic shocks.

Asset prices and capital accumulation in a monetary economy with incomplete markets

The paper studies asset prices and capital accumulation in a monetary economy with non-diversifiable idiosyncratic risks (incomplete markets). A government issued unbacked currency is introduced into agent's preferences in a dynamic GEI (General Equilibrium with Incomplete market) model with CARA preferences and normal disturbances. Closed form expressions for equlibrium allocations and prices are derived under finite and infinite horizons. The paper addresses several monetary issues. In particular, money is shown to be neutral but not superneutral at the steady state. The rate of inflation is shown to adversely affect the steady state capital stock under some situations. Finally the Friedman rule is shown to be non-optimal for some economies.

Risk Sharing through Labor Contracts - Risk Aversion, Market Incompleteness and Employment

Labor contracts are a way of sharing idiosyncratic production risks between entrepreneurs and workers, especially when such risks are too complex for contingent contracts to be written on them. So it is important to understand how equilibrium employment and wages are affected by risk re-lated factors, such as risk aversion of entrepreneurs and workers, risk sharing opportunities in the economy etc. The paper develops a general equilibrium model with several sectors of production which are subject to idiosyncratic productivity shocks, two inputs - labor and capital - and stock markets which diversify sectoral risks but not completely. We prove the existence of equilibrium for this general model. The model is then parameterized by CRRAutility functions. We prove that the equilibriumemployment levels vary inversely with the coefficient of relative risk aversion of agents under certain conditions. Numerical simulations show that over a range of the coefficient employment levels are higher when markets are complete than when they are not. A substantive implication of the comparative static results is that a low paying, productively less efficient alter-native to working for private firms may be desirable as an insurance instrument.

Self insurance and public employment programs

The paper studies the labor allocation decision by households faced with non-insurable labor income risks and establishes a case for a government sponsored public employment program as a provider of self-insurance to such households. We study the equilibria of a two period general equilibrium model with incomplete markets and two types of firms - a privately owned one offering a risky wage contract and a public works program offering a relatively riskfree one. We show that the employment level in the public program is higher in our model economy compared to that in a benchmark complete markets economy.

Characterizing Stability Properties in Games with Strategic Substitutes

In games with strategic substitutes (GSS), convergence of the best response dynamic starting from the inf (or sup) of the strategy space is equivalent to global stability (convergence of every adaptive dynamic to the same pure strategy Nash equilibrium). Consequently, in GSS, global stability can be analyzed using a single best response dynamic. Moreover, in GSS, global stability is equivalent to dominance solvability, showing that in this class of games, two different foundations for robustness of predicted outcomes are equivalent, and both can be checked using a single best response dynamic. These equivalences are useful to study stability of equilibria in a variety of applications. Furthermore, in parameterized GSS, under natural conditions, dynamically stable equilibrium selections can be viewed in terms of monotone selections of equilibria. Several examples are provided.Global stability, adaptive dynamics, strategic substitutes, dominance solvable, learning, monotone comparative statics, Correspondence principle

Monotone Comparative Statics for Games with Strategic Substitutes

This paper studies comparative statics of equilibria in models where the optimal responses under consideration are (weakly) decreasing in endogenous variables, and (weakly) increasing in exogenous parameters. Such models include parameterized games of strategic substitutes. The analysis provides a sufficient condition for existence of increasing equilibria at a higher parameter value. This condition is presented first for best-response functions; it can be translated easily to payoff functions with one-dimensional individual strategy spaces, and it has a natural analogue to best-response correspondences. The condition is tight in the sense that with a weakenened condition, the same result may not obtain. The results here apply to asymmetric equilibria, and are applied to two classes of examples -- Cournot duopoly and tournaments. Moreover, sufficient conditions are presented to exhibit strong comparative statics of equilibria (that is, every equilibrium at a higher parameter value is greater than a given equilibrium at a lower parameter value), and to show existence of increasing equilibrium selections.Monotone comparative statics; Weakly decreasing functions; Strategic substitutes; Payoff functions

Monotone Comparative Statics for Games With Strategic Substitutes

Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are available for best-response functions, differentiable payoff functions, and general payoff functions. Results are extended to correspondences, the analysis applies to asymmetric equilibria, and several examples are provided.Monotone comparative statics, Nonincreasing functions, Strategic substitutes, Parameterized games

Comparative Statics with Never Increasing Correspondences

This paper studies models where the correspondences (or functions) under consideration are never increasing (or weakly decreasing) in endogenous variables, and weakly increasing in exogenous parameters. Such models include games of strategic substitutes, and include cases where additionally, some variables may be strategic complements. It is shown that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. For a given parameter value, a pair of distinct equilibria are never comparable. Moreover, generalizing an existing result, it is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games with real-valued action spaces, symmetric equilibria increase with the parameter.) Furthermore, when functions under consideration are weakly decreasing in endogenous variables, a sufficient condition is presented that guarantees existence of increasing equilibria (symmetric or asymmetric) at a new parameter value. This condition is applied to two classes of examples.Monotone comparative statics, Non-increasing functions, Never increasing correspondences, strategic substitutes

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

This paper studies models where the optimal response functions under consideration are non-increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)Monotone comparative statics; Non-increasing functions; Never increasing correspondences; Strategic substitutes; Equilibrium set