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answerstohomework2summer2006

answerstohomework2summer2006 - Economics 302 4 Week Summer...

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Economics 302 4 Week Summer Session 2006 Answers to Homework #2 Due Monday, June 5, 2006 5/31/06 Homework will be graded for content as well as neatness. Sloppy or illegible work will not receive full credit. This homework requires the use of Excel which is a spreadsheet program. 1. Suppose that the production function for an economy is given by Y = F(K, N, A) = AK 1/2 N 1/2 where Y is output, K is capital, N is labor, and A is the level of technology. a. Suppose that the value of A is equal to 1. Fill in the table below based on this information and the given production function. Labor (N) Capital Output MPN MPN Using a Using the Derivative change in output/change in labor 0 25 0 --- ---- 4 25 10 1.25 2.5 9 25 15 0.833333 1 16 25 20 0.625 0.714285714 25 25 25 0.5 0.555555556 36 25 30 0.416667 0.454545455 b. Suppose that the value of A increases to 10. Fill in the table below based on this information and the given production function. Labor (N) Capital Output MPN MPN Using a Using the Derivative change in output/change in labor 0 25 0 --- --- 4 25 100 12.5 25 9 25 150 8.333333 10 16 25 200 6.25 7.142857143 25 25 250 5 5.555555556 36 25 300 4.166667 4.545454545 c. Draw a picture of the two production function relationships you computed in parts (a) and (b) placing output on the vertical axis and labor on the horizontal axis. Verbally explain the effects of a change in technology on the aggregate production function.
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An increase in the level of technology enables the economy to produce a higher level of real GDP for every positive level of labor usage. This is illustrated when you graph these two aggregate production functions since for a given level of labor the level of real GDP is greater with the enhanced technology. d. In the tables you computed the MPN using a derivative and the MPN using a formula for discrete data (the change in output/the change in labor). Provide an explanation for why these two measures would not be equivalent and use a graphical explanation to explore what would make these two measures numerically closer to one another. The gist here is that the derivative uses continuous data while the formula uses discrete data. The formula provides an approximation while the calculus is precise. The two methods will approach one another the smaller the changes in the level of labor used in the formula: for example, if labor was initially 4 units and then we used the formula to calculate the MPN for labor equal to 5 units we would get a closer approximation than if we used 4 units of labor versus 9 units of labor. (You might actually check this out.) 2. Suppose that the production function for an economy is given by Y = F(K, N, A) = K 1/2 N 1/2 A where Y is output, K is capital, N is labor, and A is the level of technology.
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a.
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