Answer Key - Problem Set 5

Answer Key - Problem Set 5 - Econ 102 Prof Akbulut Answer...

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Econ 102 Prof. Akbulut Answer Key - Problem Set 5 (10 points) 1. (3 pts.) Nicholson Ch. 8, Problem 8.4 (a) q = min(5 k , 10 l ) v = 1 w = 3 C = v k + w l = k + 3 l The cost function is a function of v, w, and q. Since we have values for v and w, it will be a function of q only. In the long run, keep 5 k =10 l , hence k =2 l. C = 2 l + 3 l = 5 l = 0.5 q AC = MC = 0.5 (b) k =10 q = min(50, 10 l ) If l < 5, q = 10 l C = 10 + 3 l = 10 + 0.3 q AC = (10/q) + 0.3 If l > 5, q = 50 C = 10 + 3 l AC = ( 10 + 3 l ) / 50 MC is infinite for q>50 MC 10 = MC 50 = 0.3 MC 100 = infinite 2. (1 pt.) These are general questions. “Throughout” here means for any level of output. (a) If Marginal Cost falls throughout, does Average Cost necessarily fall? Yes. At the vertical axis, AC is greater than or equal to MC (If there are fixed costs, AC is infinite at the axis and hence greater than MC.) As MC falls from its initial level along the vertical axis, AC falls as well. Each additional output with lower marginal cost brings the average cost down. (b) If Average Cost falls throughout, does Marginal Cost necessarily fall?
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