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answerstohomework2summer2007

answerstohomework2summer2007 - Economics 302 Summer 2007...

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Economics 302 Summer 2007 Answers to Homework #2 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. In your calculations, please round to the two places past the decimal wherever necessary. 1. Suppose that the production function for an economy is given by Y = F(K, L) = AK 1/2 L 1/2 Where Y is output, A is the level of technology, K is capital and L is labor. a. Suppose that A has a value of 10, K has a value of 50, while L varies from 0 to 25 units. Using Excel prepare a spreadsheet showing the possible combinations of labor, capital, technology and output that are possible for this economy. Your table should include a column for labor, a column for capital, and a column for output. I have included a sample of what the table should look like below. Technology Labor Capital Output 10 0 50 0.00 10 1 50 70.71 10 2 50 100.00 10 3 50 122.47 10 4 50 141.42 10 5 50 158.11 10 6 50 173.21 10 7 50 187.08 10 8 50 200.00 10 9 50 212.13 10 10 50 223.61 10 11 50 234.52 10 12 50 244.95 10 13 50 254.95 10 14 50 264.58 10 15 50 273.86 10 16 50 282.84 10 17 50 291.55 10 18 50 300.00 10 19 50 308.22 10 20 50 316.23 10 21 50 324.04 10 22 50 331.66 10 23 50 339.12 10 24 50 346.41 10 25 50 353.55 1
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b. Now, use the data you generated in part (a) to draw the aggregate production function where you will illustrate the relationship between aggregate output on the vertical axis and labor on the horizontal axis. This graph will hold technology and capital constant. Execute this graph using Excel. Aggregate Production Function 0 50 100 150 200 250 300 350 400 1 3 5 7 9 11 13 15 17 19 21 23 25 Labor Output Output c. Now, suppose that this economy experiences a technological advance. A, the measure of technology, now has a value of 12. Redo your calculations from part (a) and with your new data, plot both the initial aggregate production function (where A = 10) and the new aggregate production function (where A’ = 12). Aggregate Production Function 0 100 200 300 400 500 1 3 5 7 9 11 13 15 17 19 21 23 25 Labor Output Output Output d. Now, this economy finds that the value of A is 12, but that its level of capital has increased from 50 units to 60 units. Redo your calculations and generate a new graph illustrating two different production functions: one with A’ = 12 2
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and capital equal to 50 units; and the other with A’ = 12 and capital equal to 60 units. Use Excel to do this work. Aggregate Production Function 0 100 200 300 400 500 600 1 3 5 7 9 11 13 15 17 19 21 23 25 Labor Output Output Output e. Summarize briefly the effect of a change in technology or a change in capital on the aggregate production function. An increase in technology, holding everything else constant, will cause the aggregate production function to shift upwards so that a greater amount of output can be produced from a given amount of labor. An increase in capital, holding everything else constant, will cause the aggregate production function to shift upwards so that a greater amount of output can be produced from a given amount of labor.
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