Suppose a firm’s inverse demand curve is given by P = 120 - .5Q and its cost equation is C = 420 + 60Q + Q2.
a. Find the firm’s optimal quantity, price, and profit
(1) By using the profit and marginal profit equations and
(2) By setting MR equal to MC. Also provide a graph of MR and MC.
b. Suppose instead that the firm can sell any and all of its output at the fixed market price P = 120. Find the firm’s optimal output.