A risk neutral monopoly must set output before it knows for sure the market price.There is a 50% chance the firm's demand curve will be P = 20 - Q and a 50% chance it will be P = 40 - Q.The marginal cost of the firm is MC = Q.The expected profit-maximizing quantity is:

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The firm should produce where expected marginal revenue equals marginal cost. For each demand curve, calculate the marginal revenue and set it equal to MC. The expected demand curve is the average of the two possible demand curves: P = (20-Q + 40-Q)/2 = 30-Q. The marginal revenue for this is MR = 30 - 2Q. Setting MR = MC gives 30 - 2Q = Q, solving gives Q = 10.

A Risk Neutral Monopoly Must Set Output Before It Knows