Consider a firm with monopoly power that faces the demand curve

P = 100 - 3Q + 4A^1/2

and has the total cost function

C = 4Q² + 10Q + A

where A is the level of advertising expenditures, and P and Q are price and output.

a. Find the values of A, Q, and P that maximize the firm’s profit.

b. Calculate the Lerner index, L = (P - MC)/P, for this firm at its profit-maximizing levels of A, Q, and P.