Problem sets for Microeconomics II [110051-0471]

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a. If eight units of the product are to be manufactured, which type of the factory should be chosen How many units need to be produced to justify building type A factory b. Suppose the manufacturing company owns two factories (one of each type). If the total production is big enough it is optimal to maintain production in both factories. Explain why. Let us assume that planned production is 22 units. How the production should be divided between factories to minimize cost of production Exercise 3.9. A multinational firm produces steel at a home facility and at a foreign subsidiary. The demand for the product is different at home and abroad. Furthermore, the production costs are different at both facilities. The home demand is P H = 260 − .1Q H , and foreign is P F = 240. The respective cost curves are: C H = 1, 000 + .4Q 2 H , and C F = 5, 000 + .25Q 2 F . a. Due to taxes or import quotas your products are not shipped overseas. Find firm’s profit-maximizing outputs, sales quantities and prices for both home and foreign market. b. Suppose that the fiscal constraints are lifted. (Shipment cost is negligible). Answer the questions in a. once again. c. Suppose the shipment cost is $16 per ton. Answer the questions in a. once again. Exercise 3.10. A firm produces according to the following production function: Q = K 1/4 L 3/4 , where Q - units of output, K - units of capital, and L - units of labor. Suppose that the price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio Exercise 3.11. Ranger construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K 1/2 L 1/2 , where Q - pot holes filled, K - units of capital, and L - units of labor. Ranger can hire labor at $12 per unit, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accept no more than $96,000 worth of filling this season. a. What is the optimal mix of inputs for Ranger b. How many potholes should Ranger agree to fill 8
Exercise 3.12. Flo is a university administrator. She has found that happy plants only need fertilizer and talk. Where f is the number of bags of fertilizer used and t is the number of hours she talk to her plants, the number of happy plants produced is exactly h = t + 2 f . Suppose fertilizer costs w f per bag and talk costs w t per hour. a. If w t < w f /2, would it be cheaper for Flo to use fertilizer or talk to raise one happy plant b. Flo’s cost function is c ( w f , w t , h ) =............ . c. Flo’s factor demand for talk is t ( w f , w t , h ) = ............ . Exercise 3.13. Henry is a wealthy entrepreneur, who owns a tropical juice factory. Its production function is given by F (K, L) = K 2/3 L 1/4 , where K and L are respectively capital and labor inputs. The price of capital is r, and the cost of labor is w. a. Show the production function on the graph (use isoquants). b. What returns to scale demonstrates the technology used c. Henry is minimizing costs in his factory and he wants to produce Y units of juice. Find Henry’s demand for capital 9
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Problem sets for Microeconomics II [110051-0471]

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