Problem Set #4 Solutions - Baylor University

More documents

Recommendations

Info

SOLUTION: The firm would need to estimate profits for these additional years and include them in the present value calculations. 10. The Hassman Company produces two joint products, X and Y. The isocost curve corresponding to a total cost of $500,000 is Q = 1, 000 −10Q − 5 Q Y X 2 X where QY is the quantity of product Y produced by the firm and Q X is the quantity of product X produced. The price of product X is 50 times that of product Y. a. If the optimum output combination lies on this isocost curve, what is the optimal output of product X? SOLUTION: Hassman maximizes its profits, given it is spending $500,000 on inputs, by choosing quantities of X and Y so that the slope of the isorevenue function equals the slope of the isocost function. The slope of the isorevenue function is –PX/PY = –50 and the slope of the isocost function is dY/dX = –10 – 10QX. Solving –50 = –10 – 10QX ⇒ QX = 4. b. What is the optimal output of product Y? SOLUTION: QY = 1,000 – 10(4) – 5(4) 2 = 880. c. Can you be sure that the optimum output combination lies on this isocost curve? Why or why not? SOLUTION: We have determined the profit maximizing combination of outputs given the $500,000 expenditure on inputs. There is no certainty that this is the profit maximizing level of input expenditures. Solutions for assigned problems from Chapter 12 (problems 2, 4, 12 on pp. 55-556 and 559-560. 2. The can industry is composed of two firms. Suppose that the demand curve for cans is P = 100 - Q where P is the price (in cents) of a can and Q is the quantity demanded (in millions per month) of cans. Suppose that the total cost function of each firm is TC = 2 + 15q 4
where TC is total cost (in tens of thousands of dollars) per month and q is the quantity produced (in millions) per month by the Firm. a. What are the price and output if the firms set price equal to marginal cost? SOLUTION: Since each firm has a constant marginal cost of $.15, the price must also equal $.15 for price to equal marginal cost. Since marginal cost equals price equals average variable cost in this case, each firm loses an amount equal to their fixed costs, $20,000. b. What are the profit-maximizing price and output if the firms collude and act like a monopolist? SOLUTION: If they collude, they will produce where marginal revenue equals marginal cost. Marginal revenue is given by MR = 100 – 2Q. Setting marginal revenue equal to marginal cost, we get the joint profit maximizing combined output is Q = 42.5. Since the firms have constant marginal costs, only one firm should operate; thereby they avoid the fixed costs of the other firm. Their combined profits would be π = 57.5(42.5) – [2 + 15(42.5)] = 1,804.25, or $18,042,500. If they cannot avoid the fixed costs of one of the firms by shutting it down, their combined profits would be $18,022,500. c. Do the firms make a higher combined profit if they collude than if they set price equal to marginal cost? If so, how much higher is their combined profit? SOLUTION: Since they lose $40,000 if they compete and earn $18,022,500 if they collude, they earn $18,062,500 more if they collude than if they compete. 4. James Pizzo is president of a firm that is the price leader in the industry; that is, it sets the price and the other firms sell all they want at that price. In other words, the other firms act as perfect competitors. The demand curve for the industry’s product is P = 300 - Q, where P is the price of the product and Q is the total quantity demanded. The total amount supplied by the other firms is equal to Q r , where Q r = 49P. (P is measured in dollars per barrel; Q, Qr , and Qb are measured in millions of barrels per week.) a. If Pizzo’s firm’s marginal cost curve is 2.96 Q b where Q b is the output of his firm, at what output level should he operate to maximize profit? SOLUTION: The residual demand faced by Pizzo is Q - Qr = 300 – P – 49P = 300 – 50P, which can be written as P = 6 – 0.02Qb. Setting his marginal revenue equal to his marginal cost, 6 – 0.04Qb = 2.96Qb ⇒ Qb = 2, Pizzo determines that the profit maximizing quantity is 2. 5
Page 1 and 2: ECO 5315 Problem Set #4 Solutions J
Page 3: 6. If the Rhine Company ignores the
Page 7 and 8: TC = 10 + 50 Q + 20 Q R R 2 R where

Problem Set #4 Solutions - Baylor University

Create successful ePaper yourself

Delete template?

Save as template?