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hw7-06-2 - w 1 on the f rm’s use of each input and on its...

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ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 7 1. Suppose that the output q of a fi rm depends on the quantities of z 1 and z 2 that it employs as inputs. Its output level is determined by the production function q = 26 z 1 + 24 z 2 7 z 2 1 12 z 1 z 2 6 z 2 2 (a) Write down the fi rm’s pro fi t function when the price of q is $1 and the factor prices are w 1 and w 2 ( per unit) respectively. (b) Find the levels of z 1 and z 2 which maximize the fi rm’s pro fi ts. Note that these are the fi rm’s demand curves for the two inputs. (c) Verify that your solution to [2] satis fi es the second order conditions for a maxi- mum. (d) What will be the e ff ect of an increase in
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Unformatted text preview: w 1 on the f rm’s use of each input and on its output q ? [hint: You do not have to explicitly determine the f rm’s supply curve of output to determine ∂ q/ ∂ w 1 . Instead write out the total derivative of q and make use of the very simple expressions for ∂ q/ ∂ z 1 and ∂ q/ ∂ z 2 at the optimum that can be obtained from the f rst order conditions.] (e) Is the f rm’s production function strictly concave? Explain 2. Do question #2 from Exercise 11.6 (page 341) 3. Do question #1 from Exercise 11.7 (page 345) 1...
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