Problem 1. The original revenue function for the microchip producer is R=170Q-20Q2. Derive the expression for marginal revenue, and use it to find the output level at which revenue is maximized. Confirm that this is greater than the firm's profit-maximizing output, and explain why.
Problem 2. 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.
Problem 3. Suppose a firm assesses its profit function as
profit =-10-48Q+15Q2-Q3
(A) Compute the firm's profit for the following levels of output:
Q=2, 8, and 14.
(B) Derive an expression for marginal profit. Compute marginal profit at Q=2, 8, and 14. Confirm that profit is maximized at Q=8. (Why is profit not maximized at Q=2?)