Andrew Caplin

AGGREGATION AND IMPERFECT COMPETITION: ON THE EXISTENCE OF EQUILIBRIUM

We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.

Menu Costs and the Neutrality of Money

A model of endogenous price adjustment under money growth is presented. Firms follow (s, S) pricing policies and price revisions are imperfectly synchronized. In the aggregate, price stickiness disappears and money is neutral. The connection between firm price adjustment and relative price variability in the presence of monetary growth is also investigated. The results contrast with those obtained in models with exogenous fixed timing of price adjustment.

Psychological Expected Utility Theory and Anticipatory Feelings

We extend expected utility theory to situations in which agents experience feelings of anticipation prior to the resolution of uncertainty. We show how these anticipatory feelings may result in time inconsistency. We provide an example from portfolio theory to illustrate the potential impact of anticipation on asset prices.

State-Dependent Pricing and the Dynamics of Money and Output

Standard macroeconomic models of price stickiness assume that each firm leaves its price unchanged for a fixed amount of time. We present an alternative model in which the pricing decision depends on the state of the economy. We find a method of aggregating individual price changes that allows a simple characterization of macroeconomic variables. The model produces a positive money-output correlation and an empirical Phillips curve. In addition, the impact of monetary shocks depends crucially on the current level of output, which points to a natural connection between state-dependent microeconomics and state-dependent macroeconomics.

Aggregation and Social Choice: A Mean Voter Theorem

A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voters most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates differ in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voters most preferred outcome is unbeatable according to a 64%-majority rule. The weaker conditions supporting this result represent a significant generalization of Caplin and Nalebuff (1988). The proof of our mean voter result uses a mathematical aggregation theorem due to Prekopa (1971, 1973) and Borell (1975). This theorem has broad applications in economics. An application to the distribution of income is described at the end of this paper; results on imperfect competition are presented in the companion paper [CFDP 937].

On 64%-Majority Rule

Many electoral rules require a super-majority vote to change the status quo. Without some restriction on preferences, super-majority rules have paradoxical properties. For example, electoral cycles are possible with anything other than 100 percent majority rule. The auth ors show that these problems do not arise if there is sufficient simi larity of attitudes among the voting population. Their definition of social consensus involves two restrictions on domain: one on individu al preferences, the other on the distribution of preferences. When th is consensus exists, 64 percent majority rule has many desirable prop erties, including the elimination of all electoral cycles. Copyright 1988 by The Econometric Society.

Testing the reward prediction error hypothesis with an axiomatic model

Neuroimaging studies typically identify neural activity correlated with the predictions of highly parameterized models, like the many reward prediction error (RPE) models used to study reinforcement learning. Identified brain areas might encode RPEs or, alternatively, only have activity correlated with RPE model predictions. Here, we use an alternate axiomatic approach rooted in economic theory to formally test the entire class of RPE models on neural data. We show that measurements of human neural activity from the striatum, medial prefrontal cortex, amygdala, and posterior cingulate cortex satisfy necessary and sufficient conditions for the entire class of RPE models. However, activity measured from the anterior insula falsifies the axiomatic model, and therefore no RPE model can account for measured activity. Further analysis suggests the anterior insula might instead encode something related to the salience of an outcome. As cognitive neuroscience matures and models proliferate, formal approaches of this kind that assess entire model classes rather than specific model exemplars may take on increased significance.

AGGREGATION AND OPTIMIZATION WITH STATE-DEPENDENT PRICING

The literature on the aggregation of (S,s) policies has generally ignored the impact of aggregates on individual decisions. In the case of pricing, the feedback effects are clear. Not only do pricing strategies determine the evolution of the price level, the evolution of the price level influences pricing strategies. The authors provide a consistent treatment of aggregation and optimization and study three issues in the pricing literature: the relationship between strategic complementarity and the real effects of money; the relationship between the variance of money and the correlation between money and output; and the relationship between the cost and size of price adjustment.

Miracle on Sixth Avenue: Information Externalities and Search

After a long dormant period, lower Sixth Avenue in New York has undergone a rapid revitalization. The authors show that a simple search theoretic model with information spillovers can explain both the period of underuse and the rapid turnaround. The model reduces to a simple equation, which allows them to do comparative statics on the duration of vacancies. The authors show how the solution reacts to changes in market structure and changes in search technology. The model is suggestive of difficulties that may occur in many markets in which there are changes over time in the optimal use of resources.

The Supply of Information by a Concerned Expert

How much information should a policy maker pass on to an ill-informed citizen? In this paper, we address this classic question of Crawford and Sobel (1982) in a setting in which beliefs impact utility, as in Kreps and Porteus (1978). We show that this question cannot be answered using a utility function with standard revealed preference foundations. To solve the model, we go beyond the classical model in two respects, relying on the psychological expected utility model of Caplin and Leahy (2001) to capture preferences, and the psychological game model of Geanakoplos et al. (1989) to capture strategic interactions.