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Intermediate Microeconomics Spring 2013 Homework 2 – Part A Exercise 1: The following production plans are feasible: (10;??10;??70) ; (10;??20;??40) ; (10;??35;??35) ; (10;??40;??20) ; (10;??80;??10) ; (20;??40;??80) ; (20;??50;??60) ; (20;??80;??40) The negative numbers stand for inputs and the positive one for output. a. In a graph with the two inputs in each axis, plot all 8 production plans. b. Technology is convex1 and has constant returns to scale. Which produc- tion plans can you eliminate for being non-e¢ cient? Graph the isoquants for output equal to 20 and 10. c. New technology is discovered. Now the production plan (20;??80;??30) is feasible. Eliminate non-e¢ cient production plans and graph the new isoquant for y = 20: d. Show that (10,-40,-20) is not e¢ cient either. Exercise 2: For the following production function: y = KLa. Show whether the function exhibits constant, increasing or decreasing returns to scale for di¤erent parameter values (of ). b. Select three values for parameter , one representing decreasing, one constant and one increasing returns to scale. Draw two isoquants in a graph, one for y = 1 and one for y = 2: Use the graph to show the returns to scale of the production function. c. Dene the long-run cost minimization problem for the rm. d. Obtain the long-run input demands, total cost and average cost all as a function of output y, input prices w1;w2 and technology parameter . Also, obtain the short-run average costs for K = 1: e. Graph the (long-run) average cost functions for all three cases in part (b). They should have a very essential di¤erence. Why? (your answer should point towards returns to scale). f. For the case of decreasing returns to scale in part (b) assume that the market operates under perfect competition. Obtain Quantity produced and 1To be more specic, assume that combining e¢ cient production plans produces new pro- duction plans that are not only feasible, but also e¢ cient. 1
prots for the rm (as a function of…