
Accession Number : AD0645957
Title : COMPETITIVE PRODUCTION FOR CONSTANT RISK UTILITY FUNCTIONS,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : McCall,J. J.
Report Date : JAN 1967
Pagination or Media Count : 8
Abstract : The purpose of the paper is to obtain the optimal competitive outputs for three different firms having constant risk utility functions. Each firm is assumed to maximize the utility of profits where profits, pi(y), are related to output, y, in the following way: pi(y) = py  C(y); p is the price per unit and C(y) is the total cost of producing y units of product. The derivative C'(y) is positive and monotone increasing, i.e., C''(y) > 0 and pi(y) is concave. In the sequel it is assumed that firms must produce before the price is known. The environment is competitive and the firm having no control over price merely sells all of its output at the going price. For simplicity, no storage is permitted from one selling period to the next. The price is a random variable with a known probability distribution. Given this distribution the firm chooses output to maximize its expected utility. The optimal output decisions are obtained for the three utility functions described above. The main result is that for an arbitrary probability distribution the optimal output for constant risk averse firms is no more than that for risk indifferent firms which in turn is no more than the output of constant risk preference firms.
Descriptors : (*INDUSTRIAL PRODUCTION, *OPTIMIZATION), UNCERTAINTY, STATISTICAL FUNCTIONS, GAME THEORY, ECONOMICS, OPERATIONS RESEARCH
Subject Categories : Administration and Management
Economics and Cost Analysis
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE