homework4Spring2008answers

homework4Spring2008answers - Economics 302 Spring 2008...

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Economics 302 Spring 2008 Answers to Homework #4 Homework will be graded for both content and neatness. This homework requires the use of Microsoft Excel. Please put your section number or discussion section meeting time on the front page when turning in your homework. 1) Consider the Solow Growth model without population growth or technological change. The parameters of the model are as described in the table below: Year s δ k y c i depreciation change in k 1 0.2 0.05 20 where s is the saving rate, δ is the depreciation rate, k is the capital stock per worker, y is output per worker, c is consumption per worker, and i is investment per worker. a) Assume that our production function is given by 3 / 2 3 / 1 L K Y = . Rewrite this production function in terms of output per worker as a function of capital per worker. We divide both sides by L to get output per worker on the left hand side, so we have: 3 / 1 3 / 1 3 / 1 3 / 2 3 / 1 k L K L L K L Y y = = = = b) With the production function in a), fill out the first row of the table above. We fill in the table as follows: 3 / 1 k y = , i = sy, c = y – i, depreciation = δ* k, change in k = i –depreciation. This yields the values below. Year s δ k y c i depreciation change in k 1 0.2 0.05 20 2.714418 2.171534 0.542884 1 -0.457116477 c) Again using the production function from a), find the steady state level of capital in this economy. We know that at steady state, the change in the capital stock must be 0. Thus, looking at the formulas above, we set i = depreciation, so k k k sy i 05 . 0 20 . 0 3 / 1 = = = δ . Solving this equation for k gives us 3 / 1 05 . 0 20 . 0 k k = , so 3 / 2 4 k = , so k = 8 in steady state. d) Use Excel to fill out the above table for years 1-10. Then extend the table until the level of capital per worker is within 1 of the steady state value. In which year does k reach this point? (Note: you need only turn in the first 10 years of the table). Using Excel, we get a table as below:
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Year s δ k y c i depreciation change in k 1 0.2 0.05 20 2.714418 2.171534 0.542884 1 -0.457116477 2 0.2 0.05 19.54288 2.693578 2.154862 0.538716 0.97714418 -0.438428587 3 0.2 0.05 19.10445
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homework4Spring2008answers - Economics 302 Spring 2008...

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