Suppose a monopolist has the following cost function C(Q) = Q 2 (with marginal cost MC(Q) = Q). Suppose they face demand is

Suppose a monopolist has the following cost function C(Q) = ¼ Q² (with marginal cost MC(Q) = ½ Q). Suppose they face demand is P = 100 – ⅓ Q.

a) Sketch the market demand, marginal costs, and marginal revenues.

b) What is the monopolist’s optimal level of output and profits?

c) Confirm that demand is elastic at the optimal output.

d) Calculate the firm’s markup.

e) What is the DWL associated with the monopoly output?

f) Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output?

g) Does the DWL fall or rise? Discuss why.