Problem Set 2 (6) Assume 10;, = 4 and WK = 1. Please plot both the (short-run) ATC and MC. Where do these curves intersect, if they do? What is special about this point? 2 points (f) In the long run, Charlie can alter his choice of Capital in this case, what would the optimal input bundles be as a function of y, in, and 10K? In other words, what are the input demand functions My, 101,, INK) and K(y, wL, WK)? (Note, for this question, do NOT assume 11.71, = 4 and {UK 2 1.) 7 points (g) For this question, assume wL = 4 and tag = 1. What are the long run total costs as a function of y? 2 points (h) For this question, assume ml, = 4 and 111K = 1. Plot the short run total costs as a function of y. On the same graph, plot the long run total costs as a function of Problem Set 2 y. For what output levels are the short-run total costs larger? Where are they the same? Is there anywhere that the short-run costs are smaller? 3 points (i) For this question, assume in}; = 4 and in}; = 1. What can you infer about the returns to scale from the long run total cost function? How does long run average total cost change as you increase output y? 3 points Problem Set 2 (27 Points) Charlie likes to make candy at his factory, but needs two inputs: (1) Labor in the form of OompaLoompas, which we denote with L, and (2) Capital which we denote with K. The production function is y = (L% + K%)2 (a) In the short run, Capital is xed at K = 64 candy machines. As the manager for Charlie's candy factory, how much labor should you hire if Charlie asks for 3; units of candy? 3 points (b) What are the short run costs to produce 3!, as a function of mg, and 1.0K? (In other words, what is C(y, 10L, wK)?) 3 points (c) Assume wL = 4 and tag = 1. What are the short run xed costs? What are the short run variable costs as a function of y? What is the short run average total cost as a function of y? 2 points (d) Assume 1% = 4 and 10K = 1. What is the short run marginal cost? 2 points