micro-ex-8

# micro-ex-8 - Ani Guerdjikova Department of Economics...

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Ani Guerdjikova Fall 2006 Department of Economics Intermediate Microeconomics Cornell University ECON 313 Problem Set 8 Problem 31 (Cost minimization, profit maximization) A firm produces good y using inputs v 1 and v 2 and the technology y f ( v 1 ; v 2 ) = 2 v 1 / 2 1 v 1 / 2 2 . Let the prices of the inputs be w 1 = 4 and w 2 = 1 . The price of the output is p = 6 . Assume first that the input of v 2 is fixed at ¯ v 2 = 4 in the sort-run. a) Derive the short-run production function and draw it in a diagram. Determine the equation of the isoprofit lines and draw the isoprofit line for a level of profit ¯ π = 20 . b) Derive the short-run profit maximization problem of the firm and determine the optimal pro- duction plan. Assume now that the firm can choose the quantities of both inputs. c) State the cost minimization problem of the firm and derive the firm’s demand for inputs v 1 ( w 1 ; w 2 ; y ) and v 2 ( w 1 ; w 2 ; y ) . d) Determine the profit function of the firm as a function of the produced quantity y and prices w 1 , w 2 and p .

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