Problem set 7. Due at the beginning of your tutorial week 9. Problem 1. Production function f ( x 1 , x 2 ) = x 1 x 2 . The prices for the inputs are 2 and 8, respectively. a. If x 2 is fixed at x 2 = 10 derive the short-run cost function of the firm as a function of Y- output level, and the prices for inputs given above. (Hint: with 1 input there is no cost minimization.) b. Now suppose that x 2 is also free to vary. Derive the demands for the inputs and the long-run cost function of the firm. c. What value of Y makes the value of the short-run (in a) and long-run (in b) cost functions equal. Draw the two cost functions on the graph. Do they cross? Which one lies higher? Problem 2. Cost functions. Consider a firm with average cost function AC ( y ) = 1+ y +1/ y . a. What is the firm’s total cost function? b. What is the firm’s variable cost function? What is the firm’s average variable cost ( AVC ) function? c.
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