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.     

Trade,Growth, and Increasing Returns to Infrastructure: The Role of the Sophisticated Monopolist*

Equilibrium in international trade with increasing returns in infrastructure depends on whether the infrastructure provider is “naïve” or sophisticated. A monopolist produces infrastructure under decreasing cost using fixed equipment. Unlike similar work, we derive a unique closed‐economy equilibrium. In a small open economy, with “naïve” infrastructure provider(s), multiple equilibria obtain. The industrial export potential of the economy depends on unexhausted economies of scale, and equilibria are possible where manufactures are exported despite an autarky price higher than the world price. With a sophisticated infrastructure provider, even an open economy has a unique equilibrium, which, at least as long as economies of scale are unexhausted, also involves more industrialization than the “naïve” equilibria. Access to the unlimited world market is necessary for significant industrialization but is not sufficient: one may also require “Schumpeterian” entrepreneurs, monopolists with a panoramic vision of the economy and of their catalytic role in it.     

Trade Policy in the Presence of Economies of Scale and Product Variety*

It is well known that laissez faire may not be the ‘first-best’ policy in a closed economy where economies of scale are present. Corden has shown that this conclusion can carry over into an open economy, though under his assumption that imported goods are perfect substitutes for home-produced goods, interference with international trade could not raise real income. We have shown that where there are economies of scale, and imported goods are not identical to the home produced goods, interference with trade could raise real national income, though such a form of intervention would not normally be optimal. Further, it could even be desirable to support home production of more than one ‘variety’. Measurements of ‘costs of protection’ that aggregate several varieties into one may mislead not only regarding the size of the cost but even regarding its sign.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

Unit Versus Ad Valorem Taxes: The Private Ownership of Monopoly in General Equilibrium

Employing a general equilibrium framework, Blackorby and Murty prove that, with a monopoly and under 100% profit taxation and uniform lump‐sum transfers, the utility possibility sets of economies with unit and ad valorem taxes are identical. This welfare equivalence is in contrast to most previous studies, which demonstrate the superiority of the ad valorem tax in a partial equilibrium framework. In this paper, we relax the assumption of 100% profit taxation and allow the consumers to receive profit incomes from ownership of shares in the monopoly firm. We find that, under certain regularity conditions, for any fixed vector of profit shares, the utility possibility sets of economies with unit and ad valorem taxes are not generally identical. But it does not imply that one completely dominates the other. Rather, the two utility possibility frontiers cross each other. Additionally, employing a standard partial equilibrium welfare analysis, we show that the Marshallian social surpluses resulting from the two tax structures are identical when the government can implement unrestricted transfers.     

Public infrastructure,production organization,and economic development

We develop a political economy model of growth to examine economic development led by the interactions between an economic decision concerning a firm’s production technology (CRS vs. IRS technology) and a political decision concerning public infrastructure. We show that multiple equilibrium growth paths occur due to differences in expectations regarding the quality of public infrastructure. These multiple paths illustrate why economies with poor initial conditions can catch up to and, furthermore, overtake economies with better initial conditions. Our result could explain the experiences of some East Asian countries where the co-evolution of public infrastructure and industrial transformation spurred economic development.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

Multiple equilibria, coordination, and transitional growth

We study a small open economy with two sectors and two factors of production. In one of the sectors, external economies of scale are generated through the industry-level capital input. This leads to a divergence between private and social production possibility frontiers as well as to multiple equilibria. The equilibrium selection problem that arises is solved by agents who follow a simple trial-and-error learning rule. The growth path of the economy as agents learn lies below the production possibility frontier and may display cyclical transitional dynamics. We also show that coordination problems which may prevent the economy from attaining the “good” equilibrium may be alleviated by the temporary use of policy instruments that shape the allocation of resources.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

Unhedgeable shocks and statistical economic equilibrium

We develop a statistical concept of economic equilibrium as the stationary distribution of a random walk on the exchange equilibrium set (the contract set) of a pure exchange economy induced by unhedgeable shocks that perturb the economy from the exchange equilibrium set and subsequent disequilibrium trading that returns the economy to a new equilibrium. The Fokker–Planck equation for the resulting drift-diffusion process implies that the stationary distribution is independent of the size of the shock so that a small-disturbance limiting distribution is well defined. We present explicit solutions for the statistical equilibrium for the cases of quasilinear and Gorman-aggregatable Cobb–Douglas economies, and illustrate the results in the context of a generic dividend-discount model to emphasize the distinction between insurable risk and unhedgeable uncertainty in this context. The statistical equilibrium of income or wealth for quasilinear economies is described by an exponential Gibbs distribution. The statistical equilibrium income and wealth distributions for Gorman-aggregatable Cobb–Douglas economies can take a wider variety of forms, including power-law and gamma distributions. The statistical equilibria calculated for these examples suggest a close relation to widely observed statistical distributional regularities in real-world economies.     

Efficiency in an Economy with Fixed Costs

It is by now well known that in an economy with increasing returns, first-best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two-part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump-sum taxes if the initial endowment is efficient in the economy without the production technology.     

Kantian Equilibrium

Consider a game whose strategies are "contributions". A strategy profile is a Kantian equilibrium if  no  player would like  all  players to alter their contributions by the  same multiplicative factor.  Kantian equilibria are Pareto efficient. We characterize the allocation rules on several domains of environments that can be implemented as Kantian equilibria. The concept unifies the  proportional solution  on production economies and the  linear cost-share equilibrium  on public-good economies. We study Kantian equilibrium in the prisoner's dilemma, in a voting problem, and in a political economy where redistribution is the issue. The Kantian dictum engenders considerable but not unqualified cooperation.     

Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes

We model an economy with clubs (or jurisdictions) where individuals may belong to multiple clubs and where clubs sizes are arbitrary—clubs may be restricted to consist of only one or two persons, or as large as the entire economy, or anything in-between. Notions of price-taking equilibrium and the core, both with communication costs, are introduced. These notions take into account that there is a small communication cost of deviating from a given outcome. We demonstrate that, given communication costs, for all sufficiently large economies the core is nonempty and the set of price-taking equilibrium outcomes is equivalent to the core.     

Short-memory equilibrium in stochastic overlapping generations economies

In stochastic OLG exchange economies, we show that short-memory equilibria—the natural extension from deterministic economies of steady states, low-order cycles, or finite state-space stationary sunspots equilibria—fail to exist generically in utilities. As a result, even with independent and identically distributed exogenous shocks there is serial correlation in endogenous economic variables in equilibrium. This arises even if utilities are time-separable, some goods inferior, and there are no technological lags. Hence, the origins of economic fluctuations can be traced only to the demographic structure of a heterogeneous agent, multiple-good economy.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Linear economies are “gross substitute” systems

The uniqueness of the equilibrium price in linear exchange economies is proved by exploiting their “gross substitute” properties. A necessary and sufficient condition for the uniqueness is that no equilibrium price decomposes the economy. By a familiar mathematical tool — restriction and projection, the demand correspondence becomes a smooth function. We can then apply properties of the Jacobian matrix, which always has a dominant or quasi-dominant diagonal. The combination of convex and differential analysis can be used in piecewise linear economies. The uniqueness of the equilibrium price is a special case of the equilibrium index formula for regular piecewise linear economies.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Land rents,optimal taxation and local fiscal independence in an economy with local public goods

A general equilibrium model of an economy with cities, farms and free migration of population is constructed. The cities produce internationally traded goods via production functions subject to economies of scale. They also produce housing and a local public good. Two areas are defined to be disjoint if households performing an economic activity in one area are not operating in the other. An area is exclusive if it is disjoint to its complement. The economic surplus of an area is then defined to be the value of the area's net export of goods and resources. Local efficiency of an area is defined to be a state in which its economic surplus attains its maximum value. This state is proved to be a necessary condition for Pareto optimality of the economy. It is then proved that beside Piguvian corrective taxes the only taxes necessary and sufficient to finance local government activities efficiently, are taxes on land rents. Furthermore, if jurisdiction of a local government is over an exclusive area no intervention of central government is necessary, and local authorities can be fully autonomous. If the economy can be divided into pairwise disjointed exclusive areas, those areas are optimal jurisdictions in the sense that efficiency in the economy can be achieved with local authorities only.     

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

Arbitrary small indivisibilities

Summary. Arbitrary small indivisibilities may play an important role when the strong survival assumption does not hold. A hierarchic price is a finite ordered family of price vectors . It extends the notion of exchange values proposed by Gay [15]. These price notions were introduced in order to establish the existence of a generalized competitive equilibrium without the strong survival assumption. We show that a hierarchic price models phenomena related to small indivisibilities which the standard approach may not capture. More precisely, we prove in the framework of linear exchange economies that a hierarchic price may be seen as a standard price of an economy with arbitrary small indivisibilities. Received: September 25, 2001; revised version: November 25, 2002 RID="*" ID="*" This paper was partly written at Departamento de Matemáticas of Universidad de Vigo.