Question

2. Consider that a monopolist operates with total costs of TC = cQ and faces the constant

elasticity demand curve P = Q^−α

a. What are the first- and second-order conditions for a profit maximum? When

does the second-order condition hold? (This just means to set up your

maximization problem, find the first order condition and check second order. For

the second order to hold - this is where you may have to restrict α. )

b. Solve for the profit-maximizing level of output and price.

c. Find and sign the comparative statics for a change in marginal cost. (Do this for both price and quantity)

Answer 1

2)

a) First condition for profit maximisation is that the firm's marginal cost should be equal to firm's marginal revenue i.e MC=MR.

Second condition is that at the profit maximizing level, Marginal cost curve should cut the Marginal revenue curve from the bottom, so that after the profit maximizing level marginal cost is greater than marginal revenue.

c) Marginal cost decreases with increase in quantity and increase in price.