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Consider a monopolist facing an uncertain inverse demand curve p = a - bq + θ. When setting its price or quantity the monopolist does not know θ but knows that E[θ] = 0 (expected value) and E[θ 2 ] = σ 2 (variance). The cost function of the monopolist is given by C(q) = c1q + c2q 2 2 with a > c1 > 0 and c2 > 2b. Show that the monopolist prefers to set a quantity if the marginal cost curve is increasing and a price if the marginal cost curve is decreasing. Provide a short intuition for the result.
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