Optimal steady-state in stationary consumption-loan type models

We consider a stationary overlapping generations economy, and prove that an optimal steady state exists. We show that if a government intervention is needed in order to implement the optimal steady state as a competitive equilibrium, it is necessary only in a finite number of periods. If the interest rate associated with the optimal steady state equals the population rate of growth, some outside money may be required in order to make the competitive equilibrium follow the optimal steady state. We show that our existence result enables us to construct Pareto optimal competitive equilibria in some important cases.     

Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.     

Time inconsistency of benevolent government economies

A dynamic Walrasian economy is said to exhibit inconsistency if the competitive equilibrium path resulting from government reoptimization at some time τ>0 is not a continuation of the competitive equilibrium path resulting from the initial government optimization at time 0. The present paper establishes necessary and sufficient conditions for consistency for a general class of dynamic Walrasian economies. It is seen, for example, that reliance on nondistortionary policy instruments is neither necessary nor sufficient for consistency. It is also shown that Pareto optimal paths can be supported as optimal competitive equilibrium paths only if consistency prevails. However, consistent optimal competitive equilibrium paths need not be Pareto optimal.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

On stationary overlapping generations models

Consider a stationary consumption–loan economy with fixed amount of fiat money. We show that although the economy is stationary if the number of goods and the number of ‘types’ of consumers are larger than one, there might be no Pareto optimal stationary competitive equilibrium.     

Money illusion and coordination failure

Economists long considered money illusion to be largely irrelevant. Here we show, however, that money illusion has powerful effects on equilibrium selection. If we represent payoffs in nominal terms, choices converge to the Pareto inferior equilibrium; however, if we lift the veil of money by representing payoffs in real terms, the Pareto efficient equilibrium is selected. We also show that strategic uncertainty about the other players' behavior is key for the equilibrium selection effects of money illusion: even though money illusion vanishes over time if subjects are given learning opportunities in the context of an individual optimization problem, powerful and persistent effects of money illusion are found when strategic uncertainty prevails.     

Balanced equilibrium in a consumption loans model

In a consumption loans model with many generations, Gale's theorem on the existence of balanced equilibrium is generalized, allowing more general preferences. The new theorem shows that there are plausible conditions under which there exists a Pareto optimal (non-optimal) balanced equilibrium whenever there exists (does not exist) a monetary golden rule equilibrium.     

Discrete Walrasian exchange process

In an exchange economy, we define a discrete exchange process, which is Walrasian, since the trades are determined by the equilibrium allocation of the local equilibrium. We prove that this process attains a Pareto optimal allocation after a finite number of steps and the local equilibrium price then supports the Pareto optimal allocation. Furthermore, along the process, the allocation remains feasible and the utility of each consumer is non-decreasing.     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Regular Distributive Efficiency and the Distributive Liberal Social Contract

We consider abstract social systems of private property, made of n individuals endowed with nonpaternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto‐improving lump‐sum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both: (i) a distributive optimum (i.e., is Pareto‐efficient relative to individual interdependent preferences) and (ii) unanimously weakly preferred to the initial market equilibrium. We elicit minimal conditions for meaningful social contract redistribution in this setup, namely, the weighted sums of individual interdependent utility functions, built from arbitrary positive weights, have suitable properties of nonsatiation and inequality aversion; individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima; and the initial market equilibrium is not a distributive optimum. We show that the relative interior of the set of social contract allocations is then a simply connected smooth manifold of dimension n ? 1. We also show that the distributive liberal social contract rules out transfer paradoxes in Arrow–Debreu social systems. We show, finally, that the liberal social contract yields a norm of collective action for the optimal provision of any pure public good.     

Externality Policy Reform: A General Equilibrium Analysis

We characterize Pareto‐improving and equilibrium‐preserving policy reforms in a second‐best (Diamond/Mirrlees) world with a consumption externality. A counterintuitive finding is that, starting from an initial equilibrium with no direct quantity control on the externality, it is possible that all Pareto‐improving and equilibrium‐preserving directions of change require an increase in a negative externality. We provide intuition for these results by establishing a nexus between Guesnerie's approach to designing (tax) policy reforms and the standard Kuhn–Tucker technique for identifying the manifold of feasible Pareto‐optimal states, given the instruments available to the policy maker.     

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

In this paper, we show that within the set of stochastic three-period-lived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk-sharing and find that it requires state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are short-run Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model.     

A Search Model of Money and Circulating Private Debt With Applications To Monetary Policy

A search-theoretic model is used to examine the coexistence of money and circulating private debt. Money is still valued even though there coexists credit which circulates among agents and dominates in the rate of return. When there coexist multiple equilibria, the equilibrium with credit Pareto dominates the one without credit if money supply is not extremely plentiful. This article also provides some predictions about the effects of monetary policies. A policy of open market operations whereby government discounts less for second-hand debt decreases the value of money, credit, and interest rate prevailing in the market. This policy can also improve welfare by making credit trade feasible when the only equilibrium entails no credit without intervention.     

Implementing the Friedman rule

In cash-in-advance models, necessary and sufficient conditions for the existence of an equilibrium with zero nominal interest rates and Pareto optimal allocations place restrictions mainly on the very long-run, or asymptotic, behavior of the money supply. When these asymptotic conditions are satisfied, they leave the central bank with a great deal of flexibility to manage the money supply over any finite horizon. But what happens when these asymptotic conditions fail to hold? This paper shows that the central bank can still implement the Friedman rule if its actions are appropriately constrained in the short run.     

Budget Balancedness and Optimal Income Taxation

We make two contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents' preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.     

Educational choice, endogenous inequality and economic development

This paper investigates the mechanics through which wealth may, in the long run, trickle down from the rich to the poor. In the presence of indivisibilities in investment of human capital and impossibility of borrowing money, investment in education is financed through an intergenerational transfer. In an OLG model where aggregate production requires capital and both skilled and unskilled labor, it is shown that the long run equilibrium outcome depends on the values of few key parameters. A complete characterization of the steady state is provided. Under some configurations of the parameter values a unique invariant equilibrium exists where inequality vanishes asymptotically. Under others, multiple equilibria exist and the equilibrium outcome crucially depends on the initial conditions of the system. These equilibria are characterized by a negative relationship between inequality and economic development.     

Digital technologies,knowledge spillovers,innovation policies,and economic growth in a creative region

We theoretically study the impact of two innovation policies on economic growth in a region that is creative in the sense of Richard Florida and that uses digital technologies to produce a final consumption good. The use of these digital technologies in our creative region gives rise to incomplete knowledge spillovers. Our analysis generates three salient findings. First, we characterize the balanced growth path (BGP) equilibrium. Second, we solve the social planner's problem, describe the Pareto optimal allocation of resources, and then compare the Pareto optimal allocation with the BGP equilibrium allocation. Finally, we study the impacts that a research subsidy and a particular patent policy have on economic growth in our creative region and then we relate our findings to the incompleteness of the above-mentioned knowledge spillovers.     

Serial dictatorship and Pareto optimality

In a deterministic allocation problem in which each agent is entitled to receive exactly one object, an allocation is Pareto optimal if and only if it is the outcome of a serial dictatorship. We extend the definition of serial dictatorship to settings in which some agents may be entitled to receive more than one object, and study the efficiency and uniqueness properties of the equilibrium allocations. We prove that subgame perfect equilibrium allocations of serial dictatorship games are not necessarily Pareto optimal; and generally not all Pareto optima can be implemented as subgame perfect equilibrium allocations of serial dictatorship games, except in the 2-agent separable preference case. Moreover, serial dictatorship games do not necessarily have unique subgame perfect equilibrium allocations, except in the 2-agent case, hence their outcomes are indeterminate and manipulable.     

On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

Fiat money and the value of binding portfolio constraints

We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.