ans prob 2 (1) - Problem Set 2 FE312 Fall 2007 Rahman...

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Unformatted text preview: Problem Set 2 FE312 Fall 2007 Rahman Partial Answer Key 1) Assume that production is a function of capital and labor, and that the rate of savings, depreciation, population growth, and are all constant, as described in Chapter 7s version of the Solow Model. Further, assume that the production per effective worker can be described by the function: = 2 1 2 1 L K Y where K is capital and L is labor. a . What is the per-worker production function y=f(k) ? Show your work. 2 / 1 2 / 1 2 / 1 k y L L L K L Y = = b . If the saving rate ( s ) is 0.4, what are capital per worker, production per worker, and consumption per worker in the steady state? (Note: you need to set k = 0, to get an equation in s , , n , and k , and then solve for k ). 2 2 * 4 . + = + = n n s k + = + = n n s y 4 . * ( 29 ( 29 ( 29 + = +- = +- =- = n n n s s y s c ss 24 . 4 . 4 . 1 1 1 * c . Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8. 2 * 8 . + = n k Page 1 of 7 Problem Set 2 FE312 Fall 2007 Rahman + = n y 8 . * ( 29 + = +- = n n c 16 . 8 . 8 . 1 * d. Is it possible to save too much? Why? Yes, it is possible to save too much, in the sense that long-run consumption could actually be higher if you saved less. Indeed, s = 0.8 appears to be too high a savings rate, since steady state consumption per person is definite smaller with s = 0.8 than with s = 0.4. Notice that we can conclude this even without knowing what the population growth rate or the depreciate rate for the economy are. By the way, could we figure out what the actual best savings rate is, based on just the information given? Yes, with a bit of deductive reasoning. The golden rule level of capital is where MPK = n + 2 2 / 1 5 ....
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ans prob 2 (1) - Problem Set 2 FE312 Fall 2007 Rahman...

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