Suppose a company could produce a high and low quality good. Each consumer can buy a high quality good (with quality exogenously given as s2), a low-quality good (with quality s1), or no good. In other words, each consumer makes, at most, one purchase.

Each consumer’s preferences can be described as: U = θs − p if he buys a good with quality s at price p, 0 otherwise, with θ distributed U[0, 1] (uniform from 0 to 1; the mass of consumers is equal to 1). θ represents the degree to which the consumer prefers the high quality good. Assume that the low-quality (high-quality) good has marginal cost c1 (c2), where c1 < c2.

a. Derive the demand for each good.

b. Assume both goods are produced. Compute the prices that the monopolist charges. What profits will it earn? Do the sufficient second order conditions hold?

c. Will the monopolist ever produce only the low-quality good? How about only the high quality good? Both goods? If so, what are the conditions independent of the prices for each case (include only si and ci for i ∈ {1, 2} in the conditions).