COMPETITIVE PRODUCTION FOR CONSTANT RISK UTILITY FUNCTIONS,
RAND CORP SANTA MONICA CALIF
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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, piy, are related to output, y, in the following way piy py - Cy p is the price per unit and Cy is the total cost of producing y units of product. The derivative Cy is positive and monotone increasing, i.e., Cy 0 and piy 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.
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- Operations Research