Question

Assume that the cost function for a multiproduct firm is given by �(�1, �2), where �1 is the number of units produced of product 1 and �2 is the number of units produced of product 2. The multiproduct cost function thus defines the cost of producing �1 units of product 1 and �2 units of product 2 assuming all inputs are used efficiently. Suppose that the multiproduct cost function of firm A, which produces the two goods, is given by: �(�1,�2) = 200 + 5�1�2 + 2 (�1)! + 4(�2)! 1. Define in few words economies of scope. Give an example different from the one in the textbook. 2. Under what conditions do economies of scope exist for this firm? 3. Suppose that firm A is currently producing 5 units of product 1 and 10 units of product 2. 3.1 Does the cost function for the multiproduct firm A exhibits economies of scope in this case? 3.2 What is the fixed cost of producing 5 units of product 1 and 10 units of product 2? 3.3 What is the variable cost of producing 5 units of product 1 and 10 units of product 2? 3.4 What is the total cost of producing 5 units of product 1 and 10 units of product 2? 4. Explain in few words when cost complementarities exist. Give an example. 5. Do cost complementarities exist for this firm? Explain your answer. 6. Firm A is considering selling the subsidiary that produces product 2 to firm B, in which case it will produce only product 1. What will happen to firm A’s costs if it continues to produce 5 units of product

ONLY 4 & 5

HWS Assume that the cost function for a multiproduct firm is given by C(Q1, Q2), where Q1 is the number of units produced of product 1 and Q2 is the number of units produced of product 2. The multiproduct cost function thus defines the cost of producing Q1 units of product 1 and Q2 units of product 2 assuming all inputs are used efficiently. Suppose that the multiproduct cost function of firm A, which produces the two goods, is given by: C(Q1, Q2) = 200 +5Q1Q2 + 2 (Q1)+ 4(02)2 1. Define in few words economies of scope. Give an example different from the one in the textbook 2. Under what conditions do economies of scope exist for this firm? 3. Suppose that firm A is currently producing 5 units of product 1 and 10 units of product 2. 3.1 Does the cost function for the multiproduct firm A exhibits economies of scope in this case? 3.2 What is the fixed cost of producing 5 units of product 1 and 10 units of product 2? 3.3 What is the variable cost of producing 5 units of product 1 and 10 units of product 2? 3.4 What is the total cost of producing 5 units of product 1 and 10 units of product 2? 4. Explain in few words when cost complementarities exist. Give an example, 5. Do cost complementarities exist for this firm? Explain your answer. 6. Firm A is considering selling the subsidiary that produces product 2 to firm B, in which case it will produce only product 1. What will happen to firm A's costs if it continues to produce 5 units of product 17

Answer 1

A from broduces multiproduct : Product f and broduct a c(Q,, Q2) = 200 +5Q, Q2 + 207 + 402 Economies of Scobe This situation arises when booducing two or more goods together results in a lower costº than producing them separately Dairy Joomers separate mille into whey and curds, with the cards going on to become cheese. In the process, they also end up with a lot of whey, which they can use as a high protein feed for livelistuck to reduce their fixed cost or they can sell as a nutritional broduch. 2. A from can get benefits from the economies of scope when cost of producing similas broducts together is less than producing them separately. 3. Let Q1 = 5 ; Q2 = 10 ^ cl@,, 02) - 200+ 5(5)(10) + 2 (5)*+461012 = 200+250 + 50+400 = 900 NOW, Clai) = 200+ 2012

c(s) - 200 + 2(25) - 250 CCQ2) = 200+40022 - 200 + 4(10)2 = 600 c(01)+c(02) - 250 +600 = 850 < 900 = c(0.,Q.) fiom do not exhibit economies of scope. i. fixed Cost CCQ, Qz) = (200 =) vaxable Cost variable CIQ,, Q2) = 58.Q2 + 2(01)2 + 4922 = 5(50) + 2(25) + 4(100) - 700 Total cost = 200 + 700 - 900 d) to cost complement arity of any output must product or any other decline, when output is Marginal cost the output of that increased 5. a²c(Q.,O2) aQ, aQz = 5 70 but this should be negative. .. Cost complement asities do not exist for this fiom.