Divisible Money Research Articles

MONEY AND PRODUCT QUALITY UNDER ASYMMETRIC INFORMATION

AbstractThis article examines the effects of money on product quality, as well as the price pattern of heterogeneous quality goods, in a search‐theoretical monetary model with divisible money and divisible commodities. We establish the existence and uniqueness/multiplicity of monetary equilibrium in several different cases. The steady‐state equilibrium of our model displays several properties that are absent or distinct from those of previous studies. In particular, we find that under egalitarian bargaining, the Friedman rule cannot achieve socially efficient allocation due to asymmetric information. We find that the price of informed high‐quality goods is higher than the price of uninformed quality goods. We also find that an increase in inflation can improve product quality. (JEL E40)

Decentralizing constrained-efficient allocations in the Lagos–Wright pure currency economy

This paper offers two ways to decentralize the constrained-efficient allocation of the Lagos–Wright (2005) pure currency economy. The first way has divisible money, take-it-or-leave-it offers by buyers, and a transfer scheme financed by money creation. If agents are sufficiently patient, the first best is achieved for finite money growth rates. If agents are impatient, the equilibrium allocation approaches the constrained-efficient allocation asymptotically as the money growth rate tends to infinity. The second way has indivisible money, take-it-or-leave-it offers by buyers, and no government intervention. We discuss the strict implementation of constrained-efficient allocations and the applicability of our scheme to economies with Lucas trees, endogenous participation, match-specific heterogeneity, and sequential competitive markets.

Money and price posting under private information

We study price posting with undirected search in a search-theoretic monetary model with divisible money and divisible goods. Ex ante homogeneous buyers experience match-specific preference shocks in bilateral trades. The shocks follow a continuous uniform distribution, and the realizations of the shocks are private information. We show that there exists a unique monetary equilibrium for generic values of the inflation rate. In equilibrium, each seller posts a continuous pricing schedule that exhibits quantity discounts. Buyers may spend nothing, a fraction or all of their money holdings, depending on their preference-shock realizations. Inflation reduces the extent of non-linear pricing. The model captures the hot-potato effect of inflation along both the extensive margin, as an increase in the trading probability, and the intensive margin, as higher fractions of money being spent.

Stationary monetary equilibria with strictly increasing value functions and non-discrete money holdings distributions: An indeterminacy result

Abstract In this paper, we present a search model with divisible money in which there exists a continuum of monetary equilibria with strictly increasing continuous value functions and with non-discrete money holdings distributions.

Comment on Cavalcanti and Nosal's 'Counterfeiting as Private Money in Mechanism Design'

In this comment, the author extends Cavalcanti and Nosal's (2010) framework to include the case of perfectly divisible money and unrestricted money holdings. He shows that when trade takes place in Walrasian markets, counterfeits circulate and the Friedman rule is still optimal.

Endogenous buyer–seller choice and divisible money in search equilibrium

In the Lagos-Wright model [R. Lagos, R. Wright, A unified framework for monetary theory and policy analysis, J. Polit. Economy 113 (2005) 463–484], the quasi-linear preferences assumption is not necessary to generate simple distributions of money holdings if individuals choose endogenously to go to the search market as buyers or as sellers. The non-convex buyer–seller choice provides an incentive for gambling in lotteries, and, as a result, the value function has a linear interval. As long as this interval is the relevant one for evaluating their future utilities, individuals behave as if their preferences were quasi-linear. In the stationary equilibrium, individuals remain inside this linear interval if the money supply does not decline.

Bargaining and the value of money

Search models of monetary exchange have typically relied on Nash [1950. The bargaining problem. Econometrica 18, 155–162] bargaining, or strategic games that yield an equivalent outcome, to determine the terms of trade. By considering alternative axiomatic bargaining solutions in a search model with divisible money, we show that the properties of the bargaining solutions do matter both qualitatively and quantitatively for questions of first-degree importance in monetary economics such as: (i) the efficiency of monetary equilibrium; (ii) the optimality of the Friedman rule and (iii) the welfare cost of inflation.

ON THE ROLE OF TAX SUBSIDY SCHEME IN MONEY SEARCH MODELS

This article investigates the roles of policy in search models with divisible money. Recently, real indeterminacy of stationary equilibria has been found in both specific and general search models with divisible money. Thus if we assume the divisibility of money, it would be quite difficult to make accurate predictions of the effects of simple monetary policies. Therefore, in this article, we introduce a certain tax subsidy scheme and show that this is effective in selecting a determinate efficient equilibrium. In other words, for a given efficient equilibrium and for any real number δ > 0, a certain tax subsidy scheme induces a locally determinate equilibrium within the δ-neighborhood of the given equilibrium. Moreover, the size of the tax subsidy can be arbitrarily small.

A Search-Theoretic Monetary Business Cycle Model with Capital Formation

Search-theory has become the main paradigm for the micro-foundation of money. But no comprehensive business cycle analysis has been undertaken yet with a search-based monetary model. This paper extends the model with divisible goods and divisible money of Shi (JET, 1998) to allow for capital formation, analyses the monetary propagation mechanism and contrasts the model's implications with US business cycle stylized facts. The propagation mechanism based on a feedback between increased search intensity and depleted inventories only survives in the presence of non-negligible capital adjustment costs. With intermediate adjustment costs the model is able to replicate fairly well the volatility and cross-correlation with output of key US time series, including sales and inventory investment.

Real indeterminacy of stationary equilibria in matching models with divisible money

In this paper, it is shown that real indeterminacy of stationary equilibria generically arises in most matching models with perfectly divisible fiat money. In other words, the real indeterminacy follows from the condition for stationarity of money holdings, and surprisingly it has nothing to do with the other specifications, e.g., the bargaining procedures, of the models.

Existence of Equilibria in Matching Models of Money: A New Technique

This paper develops a new technique for proving the existence and indeterminacy of monetary equilibria in money search models with divisible money. Our technique is substantially simpler than standard constructive proofs in the literature.

On the existence of single-price equilibria in a matching model with divisible money and production cost

The present paper investigates Zhou's (1999) money search model, where money is divisible, agents can hold any amount of money and production of goods is costly, and presents a sufficient condition, expressed in terms of exogenously given parameters, for the existence of single-price equilibria.

Bargaining and the Value of Money

Search models of monetary exchange have typically relied on Nash (1950) bargaining or strategic games that yield an equivalent outcome to determine the terms of trade. By considering alternative axiomatic bargaining solutions in a simple search model with divisible money, we show how this choice matters for important results such as the ability of the optimal monetary policy to generate an efficient allocation. We show that the quantities traded in bilateral matches are always inefficiently low under the Nash (1950) and Kalai-Smorodinsky (1975) solutions, whereas under strongly monotonic solutions such as the egalitarian solution (Luce and Raiffa, 1957; Kalai, 1977), the Friedman Rule achieves the first best allocation. We evaluate quantitatively the welfare cost of inflation under the different bargaining solutions, and we extend the model to allow for endogenous market composition.

Existence of a monetary steady state in a matching model: divisible money

Existence of a monetary steady state is established in a random matching model with divisible goods, divisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the distribution over money holdings has full support. The approach is to show that the “limit” of the nice steady states for indivisible money, existence of which was established in an earlier paper, as the unit of money goes to zero is a monetary steady state for divisible money. For indivisible money, the marginal utility of consumption at zero was assumed to be large; for divisible money it is assumed to be large and finite.

The distribution of money and prices in an equilibrium with lotteries

We construct a tractable ‘fundamental’ model of money with equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible “tokens” and can offer lotteries on monetary transfers. By studying a simple trading pattern, we can analytically characterize the monetary distribution. Interestingly, such distributions match those observed in numerically simulated economies with fully divisible money and price heterogeneity.

Equilibrium Price Dispersion in a Matching Model with Divisible Money*

The main purpose of this article is to show that, for any given parameter value, an equilibrium with dispersed prices (two‐price equilibrium) exists in Green and Zhou's matching model with divisible money. The welfare effect of price dispersion is also analyzed.

The Distribution of Money and Prices in an Equilibrium with Lotteries

We construct a tractable model of divisible money and equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible 'tokens'. By studying a simple trading pattern, we can generate monetary distributions that match those observed in numerically simulated economies with fully divisible money and price heterogeneity.

On the Friedman Rule in Search Models with Divisible Money

This paper studies the validity of the Friedman rule in a search model with divisible money and divisible goods where the terms of trades are determined endogenously. We show that ex post bargaining generates a holdup problem similar to the one emphasized in the labour-market literature. Buyers cannot obtain the full return that an additional unit of money provides to the match, which makes the purchasing power of money inefficiently low in equilibrium. Consequently, even though the Friedman rule maximizes the purchasing power of money, it fails to generate the first-best allocation of resources unless buyers have all the bargaining power.

Money and the gains from trade*

This article studies the role of money in environments where in each meeting there is a double coincidence of real wants. Traders who meet at random finance their purchases through current production, the sale of divisible money or both. It is shown that in the absence of valued money if traders have asymmetric tastes for each other's good, they produce and exchange socially inefficient quantities. With valued money, however, traders exchange efficient quantities if the asymmetry of tastes is not too large. It is shown that the gains from trade in the monetary economy are strictly greater than those in the corresponding barter economy, that the Friedman rule holds, and that the allocation of resources in the monetary economy converges to the allocation in the barter economy as the growth rate of the money supply is increased.

On the Friedman Rule in Search Models with Divisible Money

This paper studies the validity of the Friedman rule in a search model with divisible money and divisible goods in which the terms of trades are determined endogenously. We show that ex post bargaining generates a holdup problem similar to the one emphasized in the labor-market literature. Buyers cannot obtain the full return that an additional unit of money provides to the match, which makes the purchasing power of money inefficiently low in equilibrium. Consequently, even though the Friedman rule maximizes the purchasing power of money, it fails to generate the first-best allocation of resources unless buyers have all the bargaining power.