A Dual Characterization of Incentive Efficiency

We show that incentive e cient allocations in economies with adverse se- lection and moral hazard can be determined as optimal solutions to a linear programming problem and we use duality theory to obtain a complete charac- terization of the optima. Our dual analysis identi es welfare e ects associated with the incentives of the agents to truthfully reveal their private information. Because these welfare e ects may generate non-convexities, incentive e cient allocations may involve randomization. Other properties of incentive e cient allocations are also derived

General Equilibrium with Asymmetric Information: A Dual Approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive trans- actions, the environment is described as a continuum economy with indivis- ible commodities. We characterize incentive constrained eÆcient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external e ects in these markets. Because under certain conditions such e ects may generate non-convexities, random- ization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external e ects may have critical implications for market eÆciency. With ad- verse selection, in fact, cross-subsidization across agents with di erent private information may be necessary for optimality, and so, the market need not even achieve an incentive constrained eÆcient allocation. In contrast, for the case of a single commodity, we nd that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external e ects are fully internalized at a market equilibrium

Incentive compatibility and pricing under moral hazard

We study a simple insurance economy with moral hazard, in which random contracts overcome the non-convexities generated by the incentive-compatibility constraints. The novelty is that we use linear programming and duality theory to study the relation between incentive compatibility and pricing. Using linear programming has the advantage that we can impose the incentive-compatibility constraints on the agents that are uninformed (the insurance firms). In contrast, most of the general equilibrium literature imposes them on the informed agents (the consumers). We derive the two welfare theorems, establish the existence of a competitive equilibrium, and characterize the equilibrium prices and allocations. Our competitive equilibrium has two key properties: (i) the equilibrium prices reflect all the relevant information, including the welfare costs arising from the incentive-compatibility constraints; (ii) the equilibrium allocations are the same as when the incentive-compatibility constraints are imposed on the consumers

A Note on Walrasian Equilibria with Moral Hazard and Aggregate Uncertainty

In a fundamental contribution, Prescott and Townsend (1984) [PT] have shown that the existence and efficiency properties of Walrasian equilibria extend to economies with moral hazard, when agents' trades are observable (exclusive contracts can be implemented). More recently, Bennardo and Chiappori (2003) [BC] have argued that Walrasian equilibria may (robustly) fail to exist when the class of moral hazard economies considered by Prescott and Townsend is generalized to allow for the presence of aggregate, in addition to idiosyncratic, uncertainty and for preferences which are nonseparable in consumption and effort. We re-examine here the existence and efficiency properties of Walrasian equilibria in the moral hazard economy considered by Bennardo and Chiappori. We show that Walrasian equilibria always exist in such economy and are incentive efficient, so the results of Prescott and Townsend continue to hold in the more general set-up considered by Bennardo and Chiappori

Precautionary balances and the velocity of circulation of money

Inflation, as a tax on money, gives buyers an incentive to reduce their money balances. Sellers are aware of this incentive and try to attract buyers by announcing price offers that induce buyers to spend a larger fraction of their money. We examine the effect of inflation on equilibrium price offers and associated trades in a competitive search environment where buyers experience preference shocks after they are matched with a seller. With full information,equilibrium price offers consist of a flat fee applied equally to all buyers independently of the quantities they purchase. If buyers'preferences are private information, sellers must charge more to buyers who purchase larger quantities due to incentive compatibility restrictions. In this case, equilibrium price offers consist of a non-linear price schedule. However, as inflation rises, price schedules become relatively flat. This implies that buyers with a low desire to consume purchase higher quantities and spend their cash more rapidly. Buyers with a high desire to consume purchase lower quantities because, as their money balances fall, they become liquidity constrained. This is in contrast with the full information benchmark where inflation reduces the quantities purchased by all buyers. The equilibrium is efficient at the Friedman rule and inflation reduces welfare both with full and private information

Inflation, Prices, and Information in Competitive Search

We study the effects of inflation in a competitive search model where each buyer’s utility is private information, and money is essential. The equilibrium is efficient at the Friedman rule, but inflation creates an inefficiency in the terms of trade. Buyers experience a preference shock after they are matched with a seller, and thus they have a precautionary motive for holding money. Sellers, who compete to attract buyers, post non-linear price schedules. As inflation rises, sellers post relatively flat price schedules, which reduce the need for precautionary balances. These price schedules induce buyers with a low desire to consume to purchase inefficiently high quantities because of the low marginal cost of purchasing goods. In contrast, buyers with a high desire to consume purchase inefficiently low quantities as they face binding liquidity constraints. The model fits historical US data on velocity and interest rates.Publicad

House prices, sales, and time on the market : a search-theoretic framework

We build a search model of the housing market which captures the illiquidity of housing assets. In this model, households experience idiosyncratic shocks over time which affect how much they value their residence (e.g. the location of their job could change). When hit by a shock, households become mismatched and seek to buy a new home. Yet they take time to locate an appropriate housing unit and to sell their current home. Competitive forces are present in the housing market since, by posting lower prices, sellers increase the average number of buyer visits they get and sell their property faster. We characterize a stationary equilibrium for a fixed housing stock. We then calibrate a stochastic version of the model to reproduce selected aggregate statistics of the U.S. economy. The model is consistent with the high volatility of prices, sales and average time on the market, the positive correlation of prices and sales, and the negative correlation of prices and average time on the market observed in the data. This is not the case when we consider the perfectly competitive version of the modelHouse prices, Sales, Time on the market, Search frictions, Competitive search

A Note on Walrasian Equilibria with Moral Hazard and Aggregate Uncertainty

In a fundamental contribution, Prescott and Townsend (1984) [PT] have shown that the existence and efficiency properties of Walrasian equilibria extend to economies with moral hazard, when agents' trades are observable (exclusive contracts can be implemented). More recently, Bennardo and Chiappori (2003) [BC] have argued that Walrasian equilibria may (robustly) fail to exist when the class of moral hazard economies considered by Prescott and Townsend is generalized to allow for the presence of aggregate, in addition to idiosyncratic, uncertainty and for preferences which are nonseparable in consumption and effort. We re-examine here the existence and efficiency properties of Walrasian equilibria in the moral hazard economy considered by Bennardo and Chiappori. We show that Walrasian equilibria always exist in such economy and are incentive efficient, so the results of Prescott and Townsend continue to hold in the more general set-up considered by Bennardo and Chiappori.Moral Hazard, Aggregate Risk, Incentive Efficiency, Walrasian Markets

PRECAUTIONARY BALANCES AND THE VELOCITY OF CIRCULATION OF MONEY

Inflation, as a tax on money, gives buyers an incentive to reduce their money balances. Sellers are aware of this incentive and try to attract buyers by announcing price offers that induce buyers to spend a larger fraction of their money. We examine the effect of inflation on equilibrium price offers and associated trades in a competitive search environment where buyers experience preference shocks after they are matched with a seller. With full information,equilibrium price offers consist of a flat fee applied equally to all buyers independently of the quantities they purchase. If buyers'preferences are private information, sellers must charge more to buyers who purchase larger quantities due to incentive compatibility restrictions. In this case, equilibrium price offers consist of a non-linear price schedule. However, as inflation rises, price schedules become relatively flat. This implies that buyers with a low desire to consume purchase higher quantities and spend their cash more rapidly. Buyers with a high desire to consume purchase lower quantities because, as their money balances fall, they become liquidity constrained. This is in contrast with the full information benchmark where inflation reduces the quantities purchased by all buyers. The equilibrium is efficient at the Friedman rule and inflation reduces welfare both with full and private information.

Inflation, Prices, and Information in Competitive Search

We study the effects of inflation in a competitive search model where each buyer's utility is private information, and where money is essential in facilitating trade. The equilibrium is efficient at the Friedman rule, but inflation creates an inefficiency in the terms of trade. Buyers experience a preference shock after they are matched with a seller, and thus they have a precautionary motive for holding money. Sellers, who compete to attract buyers, post non-linear price schedules to screen out different types of buyers. As inflation rises, sellers post relatively flat price schedules which reduce the need for buyers to hold precautionary balances. These price schedules induce buyers with a low desire to consume to purchase inefficiently high quantities because of the low marginal cost of purchasing goods. In contrast, buyers with a high desire to consume purchase inefficiently low quantities as they face binding liquidity constraints. The reduction of precautionary balances as inflation rises allows the model to fit historical US data on velocity and interest rates.inflation; precautionary money demand; competitive search; private information.