Non-connectedness of the set of equilibrium money prices: The static economy

A static economy in which nominal taxes and transfers are balanced, under certain conditions, has a set of equilibrium money prices containing a proper interval. Two examples are given in which the entire set must consist of a proper interval. Then, an example is presented in which the set of equilibrium money prices is not connected. While the set contains a proper interval for balanced fiscal policies, the entire set is not in general a single interval.     

Money,nonconvex preferences,and the existence of equilibrium: A note

Nonconvexities play a major role in several theories of money. This note suggests an additional such role. In particular, an economy is presented which fails to have a competitive equilibrium in the absence of fiat money. When fiat money is present, a steady-state competitive, equilibrium does exist and has the feature that money necessarily has value. This is because in any steady state, monetary equilibrium relative prices are bounded in such a way that the discontinuous portions of excess demand functions may become irrelevant.     

A dynamic microeconomic model with durable goods and adaptive expectations

This paper develops a new model of a dynamic economy with durable goods that is simple enough so that interesting examples can be solved, even with limited computational capacity. The model is of temporary equilibrium in continuous time, with money, bonds and durable goods. Individuals form estimates of the marginal values of assets through a learning process of adaptive expectations. Properties of existence and uniqueness are shown for the equilibrium prices. A simple example is considered, to show how the model can simulate many of the dynamic adjustment problems of the business cycle.     

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.     

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.     

A THEORY OF MONEY AND MARKETPLACES*

This article considers an infinitely repeated economy with divisible fiat money. The economy has many marketplaces that agents choose to visit. In each marketplace, agents are randomly matched to trade goods. There exist a variety of stationary equilibria. In some equilibrium, each good is traded at a single price, whereas in another, every good is traded at two different prices. There is a continuum of such equilibria, which differ from each other in price and welfare levels. However, it is shown that only the efficient single‐price equilibrium is evolutionarily stable.     

MONEY,SOCIAL STATUS AND ENDOGENOUS GROWTH IN A GENERALIZED CASH‐IN‐ADVANCE MODEL

This paper analytically examines the equilibrium growth effect of money/inflation in a standard one‐sector AK model of endogenous growth with the most generalized cash‐in‐advance constraint and relative wealth‐induced preferences for social status. We show that on the economy's unique balanced growth equilibrium path, the sign of the correlation between money and output growth depends crucially on: (i) the intertemporal elasticity of substitution in consumption; and (ii) the liquidity‐constrained ratio of consumption to investment expenditure. Moreover, our model economy always exhibits a positive output–growth effect in response to changes of the strength for social status. We also undertake numerical experiments to assess the quantitative importance of our theoretical results under an empirically plausible set of parameters.     

The value of money in a dynamic equilibrium model

Summary. This paper studies the pricing of money in an infinite-horizon economy with heterogeneous agents, incomplete financial markets and arbitrary borrowing restrictions. Purchases of the consumption good are subject to a cash-in-advance constraint. Under general conditions I show that the price of money is equal to its fundamental value, where this value is defined over all state-price processes that are compatible with the existence of no-arbitrage opportunities. This equality implies that the cash-in-advance constraint is binding infinitely often for all agents in the economy. The analysis highlights certain differences in the determination of the price of money with respect to models with money in the utility function that bear on the optimal implementation of economic policies.Received: 23 October 2003, Revised: 26 August 2004 JEL Classification Numbers: D52, E44, G12.M.S. Santos: This paper is an outgrowth of an earlier collaboration with Michael Woodford. I have also benefitted from various discussions with Eduardo Gimenez, Alejandro Hernandez, and Miguel Iraola. Some very useful comments by an anonymous referee are greatly appreciated.     

Pricing of New Assets in an Infinite-Horizon Frictional Economy

This paper studies the pricing of new assets in an infinite-horizon frictional economy. It uses results on state prices to establish conditions under which the valuation structure of the economy (defined as the collection of all state price processes) is unaffected by the introduction of new assets and conditions under which the new assets do not give rise to arbitrage.     

Speculation on Primary Commodities: The Effects of Restricted Entry

We present a model of oligopolistic commodity speculation, in which a limited number of speculators practice non-cooperative storage in an infinite-horizon game. A significant technical difficulty due to the non-negative stock constraint is overcome, and a tractable sub-game perfect equilibrium is presented, in which it is shown that less is stored and prices are more volatile than under perfect competition. It turns out that a tax on consumption of the good would increase storage, stabilize prices, increase welfare and raise speculative profits; the oligopolists would thus lobby for a tariff raised against their own shipments.     

CONTINGENT PRICES AND MONEY*

Price posting with directed search is a widely used trading mechanism. Coles and Eeckhout showed that if sellers are allowed to post prices contingent on realized demand instead of one price, then there is real market indeterminacy. In this article, we fit this contingent price‐posting protocol into a monetary economy. We show that, as long as holding money is costly, there exists a unique equilibrium rather than a continuum. In this equilibrium sellers post a low price for when the buyer is alone, a high price for when several buyers show up, and buyers randomize between sellers and money holdings.     

General Equilibrium Impacts of Monetary and Fiscal Policies on Welfare of Households in South Asia

Impacts of fiscal and monetary policies are assessed in an open economy two sector multi‐household general equilibrium tax model with money for South Asia. Despite impressive growth rates there is evidence for alarming gaps in the distribution of income among households that require very careful design of economic policies. Generally the impacts of fiscal expansions are positive for all categories of households under the flexible price system but the gains are much higher for households in the upper income group than for those in the bottom. In theory the equilibrium relative prices guarantee the optimal allocation of resources in such economy. Simulation results show that demand, output and employment are sensitive to the preferences of consumers, confidence of producers and sector specific production technologies. Monetary policy is super‐neutral under flexible price regime but can complement fiscal policy well when aggregate prices are made sticky. Combination of monetary and fiscal policies in this manner can have extensive impacts in efficiency and redistribution. Higher taxes distort incentives to work and investment from richer households slowing down the economy. This reduces the welfare level of both rich and poor. Flexibility in prices enhances the market mechanism and makes the fiscal policy more effective and efficient.     

Mixed-strategy equilibria in the Nash Demand Game

In the Nash Demand Game, each of the two players announces the share he demands of an amount of money that may be split between them. If the demands can be satisfied, they are; otherwise, neither player receives any money. This game has many pure-strategy equilibria. This paper characterizes mixed-strategy equilibria. The condition critical for an equilibrium is that players’ sets of possible demands be balanced. Two sets of demands are balanced if each demand in one set can be matched with a demand in the other set such that they sum to one. For Nash’s original game, a complete characterization is given of the equilibria in which both players’ expected payoffs are strictly positive. The findings are applied to the private provision of a discrete public good.     

Central bank instruments, fiscal policy regimes, and the requirements for equilibrium determinacy

This paper examines the role of the monetary instrument choice for local equilibrium determinacy under sticky prices and different fiscal policy regimes. Corresponding to Benhabib et al.'s results for interest rate feedback rules [Benhabib, J., Schmitt-Grohé, S., Uribe, M., 2001. Monetary policy and multiple equilibria. American Economic Review 91, 167–185], the money growth rate should not rise by more than one for one with inflation when the primary surplus is raised with public debt. Under an exogenous primary surplus, money supply should be accommodating—such that real balances grow with inflation—to ensure local equilibrium determinacy. When the central bank links the supply of money to government bonds by controlling the bond-to-money ratio, an inflation stabilizing policy can be implemented for both fiscal policy regimes. Local determinacy is then ensured when the bond-to-money ratio is not extremely sensitive to inflation, or when interest payments on public debt are entirely tax financed, i.e., the budget is balanced.     

Robust asset prices with bubbles

We generally establish equilibrium asset prices than can include price bubbles yet (a) be robust to truncations of the economy and (b) exclude trade in non-consumables, like money, stock certificates, or land deeds.     

Stochastic and structural fiscal policy in a monetary stationary economy

In the framework of a monetary asset pricing model which is simple enough to generate closed form formulae for equilibrium price functions the interactions between output, fiscal policy, and asset markets is investigated. With money yielding liquidity services in the exchange process real stock prices are negatively correlated with anticipated (stochastic) fiscal policy changes, while the impact of unanticipated (structural) fiscal policy on the stock market depends qualitatively on the ‘business cycle’ of the economy. It is shown that the monetary character of the economy, more precisely the role of money in the exchange process, is critical for the relationship between fiscal policy and real share prices. Moreover, while contingent fiscal policy measures may be successful in stabilizing the real interest rate on money they are incapable of achieving a stable term structure of the real rate on stocks. In contrast, uncontingently higher public expenditures generally promote the volatility of the real rates on financial assets.     

Equilibrium in economies with incomplete financial markets

This paper analyses an exchange economy in the absence of Arrow-Debreu complete markets. It is assumed that trading takes place in the sequence of spot markets and futures markets for securities payable in units of account. Unlimited short-selling in securities is allowed. A general equilibrium in such an economy is a set of current and future prices (contingent on uncertain events) and a set of individual plans such that all markets are cleared. The existence of such an equilibrium is proved under usual assumptions. This is in contrast to the case of futures markets for contingent futures commodities where an equilibrium may not exist. The optimality of equilibrium allocations is also discussed.     

Regulating collateral-requirements when markets are incomplete

In this paper we examine the effects of default and collateral on risk sharing. We assume that there is a large set of assets which all promise a risk less payoff but which distinguish themselves by their collateral requirements. In equilibrium agents default, the assets have different payoffs, and there are as many linearly independent assets available for trade as there are states of the world. We derive necessary and sufficient conditions for equilibria to be Pareto-efficient in the presence of uncertainty. We explore some examples for which the collateral equilibrium allocation is identical to the Arrow–Debreu allocation, either when agents have a high preference for the durable good, or when the endowment distribution of the durable good is relatively homogeneous. We examine a series of examples to understand which collateral-levels prevail in equilibrium and under which conditions there is scope for regulating margin-requirements, that is, restricting the sets of tradable assets through government intervention. In these examples equilibrium is always sub-optimal but regulation never leads to a Pareto-improvement. While the competitive equilibria are constrained efficient, there do exist regulations which make large groups of agents in the economy better off. These regulations typically restrict all trades to take place in the low-collateral loans and benefit the poor and the rich agents in the economy through their effects on the equilibrium interest rate and the equilibrium prices of the durable goods.     

The workings of a commodity money system in an incomplete information macro model

This paper compares the properties of a token money system with that of a commodity money system in an uncertain environment. In an incomplete information world, relative prices are not known with certainty. However, a commodity money system provides some information because the nominal price of the monetary commodity is known. The benefits of this information-enhancing function may be offset, though by distortions in relative prices relative to their full information Walrasian equilibrium values. Because the two systems have vastly different structural parameters, we cannot unambiguously state which system is welfare superior.     

Mises and the moderns on the inessentiality of money in equilibrium

The challenge of rendering monetary exchange intelligible within a Walrasian general equilibrium framework is well known. Perhaps less well known is the difficulty of integrating monetary and exchange economies in decentralized conceptions of equilibrium, of which the evenly rotating economy of Ludwig von Mises (1949) is an early example. After reviewing the prospect for money in the evenly rotating economy, I survey the modern literature on frictions that make money useful for exchange. While exploring techniques commonly used to generate a useful role for money in this environment, I make a distinction between exchange frictions and epistemic frictions. Although theoretical efforts have largely focused on exchange frictions, recent experimental evidence suggests that epistemic frictions warrant further attention. I conclude that Mises should be seen as a pioneer in this literature, though recent advances demonstrate that the set of frictions capable of rendering money useful is much larger than he envisioned.