Question

3. A US. textbook publisher is introducing a new economics textbook, Managerial Economics-It is no Graphing matter, to the domestic market. Each book is produced at a constant marginal cost of S98 per book. Management predicts that annual domestic demand for the book is Po- 278-03QD, where Po-price of a book in dollars, and Qp denotes the number of books (as measured in thousands). a. Assuming no costs beyond the MC of $98 per book, state the profit equation for the domestic market: l point b. State the marginal profit equation for the domestic market: 1 point c. Determine the optimal quantity and price of the book in the domestic market: 2 points Using your answers to parts a and b, compute the total profit in the domestic market, assuming no fixed costs: d. 1 point

Answer 1

Mc = $98 P_B = 278 - 0.3 Q_B profit = Total revenue - total costs = p times Q - 98 Q profit = (278 - 0.3 Q)Q - 98 Q pi = 278 Q - 0.3 Q^2 - 98 Q pi = 180 Q - 0.3 Q^2 implies profit Equation for the domestic market b) marginal profit equation is pi = 180 Q - 0.3 Q^2 dpi/dQ = differentiation w.r.t Q of the profit function d/dQ(180Q - 0.3Q^2) = dpi/dQ dpi/dQ = 180 - 0.6Q implies marginal profit equation \r\n dpi/dQ = 180 - 0.6Q dpi/dQ = 0 180 - 0.6Q = 0 Q = 1800/6 implies Q = 300 optimal quantity be Q^* = 300 price be P = 278 - 0.3Q P = 278 - 0.3 times 300 P = $188 proof dpi/d phi = 180 - 0.6 Q implies d^2pi/dQ^2 = -0.6 = -ve mean max care profit = 180 Q - 0.3Q^2[from a bove] = 180 times 300 - 0.3 times 90000 = 54000 - 27000 pi = $27000