Econ 302 HW 4

Econ 302 HW 4 - Rebecca Chapman Econ 302 Spring 2008 Homework#4 Discussion 303 Homework will be graded for both content and neatness This homework

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Rebecca Chapman Econ 302 Spring 2008 Homework #4 Discussion 303 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 _ 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. Y=K^(1/3) L^(2/3) Y/L=y =(K^(1/3) L^(2/3)) /L =K^(1/3) L^(-1/3) =(K^(1/3))/(L^(1/3)) =k^(1/3)=f(k) Output per worker y, depends on the amount of capital per worker (k) b) With the production function in a), fill out the first row of the table above. year s δ k y c I deprec change k 1 0.2 0.05 20 2.72 2.18 0.54 1 -0.46 c) Again using the production function from a), find the steady state level of capital in this economy. k*/f(k*)=s/ δ k*/k^(1/3)=0.2/0.05 (k*/(k^1/3))^(3)=(4)^3 (k*^(3)/(k*))=64 sq. root of (k*)^(2)=sq. root of 64 k*=8
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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). year
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This note was uploaded on 10/03/2008 for the course ECON 302 taught by Professor Gold during the Spring '07 term at Wisconsin.

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Econ 302 HW 4 - Rebecca Chapman Econ 302 Spring 2008 Homework#4 Discussion 303 Homework will be graded for both content and neatness This homework

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