s07ak1 - Econ 365 Answer Key Problem Set 1 M. Muniagurria...

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Econ 365 M. Muniagurria Answer Key Problem Set 1 (I) In the Solow model without population growth or technological change: (1) ) k = i- * k , where k is capital per worker, i investment per worker and * the rate of depreciation of the capital stock. Since investment per worker equals savings per worker, we have that (2) ) k = s f(k) - * k , where s is the savings rate and f(k) output per worker (equal to income per worker). Let k* be the level of capital per worker along a BGP. Since at the BGP : ) k=0, using (2) we have that: (3) s f(k*) = * k* Notice that at the BGP the function s f(k) crosses the function * k. Both functions are increasing (see Figure 4-4, page 82 in RP1). As the savings rate increases, the function s f(k) increases for positive values of k so the intersection occurs at a higher level of k. Since output or income per worker (f(k) ) is increasing in k, the level of income per worker at the BGP increases (see Figure 4-5 , page 86 in RP1). At the BGP, the growth rate of capital per worker is zero and therefore the growth rate of income per worker is zero. Since this is independent of the level of k, the savings rate has no influence on the growth rate of output/income per worker along a BGP
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This note was uploaded on 08/08/2008 for the course ECON 365 taught by Professor Muniagurria during the Spring '07 term at Wisconsin.

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s07ak1 - Econ 365 Answer Key Problem Set 1 M. Muniagurria...

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