A profit-maximizing competitive firm uses inputs 1, . . . to produce one output

Question

A profit-maximizing competitive firm uses inputs 1, . . . to produce one output . Let () be the maximum profit attainable at prices = (, 1, . . . , ), where is the price of the output and the price of the -good.

Question: Suppose that the firm faces randomly fluctuating prices due to an exogenous factor. We imagine that the price vector is with probability and with probability 1 so that average prices are = + (1 ) . Is the price fluctuation better for the firm than a price stabilization at ? Why?

Explanation / Answer

In this case the price fluctuation is better for the firm than price stabilization as by convexity, the average profits with fluctuating price are large as with the stabilized prices.

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