Purchase decisions made prior to the revelation of price: simple analytics of the consumer's problem.

• Author: Beard, T. Randolph
• Position: Communications

1. Introduction

   Recent years have witnessed substantial progress in the economic analysis of the welfare consequences of price uncertainty, price stabilization, and related matters. This literature |5; 2; 6; 3~ has established expected indirect utility as a primary tool of theoretical economics, and the expected indirect utility approach has found wide application in the analyses of risk sharing, public utility pricing under uncertainty, and numerous other topics.

   Despite the widespread success of expected indirect utility formulation, there is a class of consumer choice under uncertainty problems for which the usual expected indirect utility approach is not appropriate. In particular, the expected indirect utility model typically assumes that, while future prices may be unknown, prices are always revealed to consumers prior to the consumer making a binding purchase decision. For any instantiation of price, the consumer solves a utility maximization program whose value is, in fact, the consumers (indirect) utility over which expectations are taken in the first instance. Therefore, price uncertainty enters only ex ante and, ex post, optimal decisions are always made. In many cases, however, it is completely unrealistic to imagine that consumers know prices perfectly before they buy. In the public utility sphere, complex nonlinear tariffs, fuel price adjustment clauses, and variable metered service make the assumption of perfect price information prior to purchase unrealistic. Additionally, the hiring of virtually any kind of repair services on a "per hour" basis must usually be arranged prior to knowing the final cost. More generally, whenever perfect price information is sufficiently costly to obtain ex ante, consumers might quite rationally proceed with a consumption decision in at least partial ignorance of the prices of what they are buying.

   The purpose of this note is to initiate the analysis of consumption decisions made under time of sale price uncertainty. Although this problem is related to issues arising in the analysis of dynamic consumption/investment models, the focus of our work has largely escaped notice.(1) Our thrust is two fold. First, we utilize an informal and strongly intuitive approach to derive an approximate condition characterizing the consumer's optimal consumption plan which illustrates the intertwined roles of risk aversion (in the Arrow-Pratt sense), preferences for goods, and price risk in determining consumer behavior. Second, we note the potential import of our conclusions for demand estimation in circumstances likely to be characterized by uncertain or suitable complex price systems.

2. Analysis

   In order to make our analysis as simple as possible, we focus on the choice problem of a consumer who purchases two products, one subject to time of sale price uncertainty, the other a composite of all...