PS 7 Sol - UNIVERSITY OF WISCONSIN Economics 101 Spring...

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UNIVERSITY OF WISCONSIN Economics 101 – Spring 2007 Problem Set 7 Solutions Problem 1 (Question 11 at page 255) (a) The isoquant curve is convex. The isocost line has a slope of 1/4, given Labor is on the horizontal axis. The total cost is TC=$80*5+$20*20=$800. This is point A on the above graph. (b) The new level of labor is 39.2. To find this, use the production function 2 / 1 2 / 1 10 L K q = , and substitute 140 in for output and 5 in for capital. Then, the equation is 2 / 1 2 / 1 5 * 10 140 L = , and derive the value of L. This is the point B on the above graph. (c) This is point C on the above graph. Write the parallel isocost curve which is a tangent to the isoquant curve with q=140. (d) Set the marginal rate of technical substitution equal to the ratio of the inputs cost so that 4 1 80 20 = = L K , so 4 L K = . Now substitute this into the production function for K, set q equal to 140, and solve for L: 2 / 1 2 / 1 ) 4 ( 10 140 L L = . Then, L=28 and K=7. Problem 2 (a) (Question 1 at page 296) At first, the table is as follows. Next, at a price of $60, the firm should produce 10 units of output to maximize profits because this is the point closest to where price equals marginal cost without having marginal cost exceed price.
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