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4. Suppose a firm’s inverse demand curve is given by P = 120 – 0.5Q and its cost equation is C = 420 + 60Q + Q2
a. Find the firm’s optimal quantity (Q), price, and profit (1) by using the profit and marginal profit equations and (2) by setting MR = MC.
b. Suppose instead that the firm can sell any and all of its output at the fixed market price of P = 120. Find the firms optimal output.