COMPETITIVE PRODUCTION FOR CONSTANT RISK UTILITY FUNCTIONS,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD0645957
Entities
People
- J. J. Mccall
Organizations
- RAND Corporation