PS2 solutions

PS2 solutions - #2 0 0 1,000 1,000 2,000 1,260 3,000 1,442...

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Suggested Solutions for Problem Set #2 0 0 1,000 1,000 2,000 1,260 3,000 1,442 4,000 1,587 5,000 1,710 6,000 1,817 7,000 1,913 8,000 2,000 9,000 2,080 10,000 2,154 1. (2.5 points total; ½ point each) A. Graph the production function for values of K/L from 0 to 10,000 (increasing 1,000 at a time), assuming E =  1,000.  Label it 
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B . Graph the same production function, on the same axes, for the same range of K/L, assuming E = 2,000.  Label it  K/L 1A. Y/L when E  = 1,000 1B. Y/L when E  = 2,000 0 0 0 1,000 1,000 1,587 2,000 1,260 2,000 3,000 1,442 2,289 4,000 1,587 2,520 5,000 1,710 2,714 6,000 1,817 2,884 7,000 1,913 3,037 8,000 2,000 3,175 9,000 2,080 3,302 10,000 2,154 3,420
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K/L 1A. Y/L when  α   = 1/3 1C. Y/L when  α   = 0.6 0 0 0 1,000 1,000 1,000 2,000 1,260 1,516 3,000 1,442 1,933 4,000 1,587 2,297 5,000 1,710 2,627 6,000 1,817 2,930 7,000 1,913 3,214 8,000 2,000 3,483 9,000 2,080 3,737 10,000 2,154 3,981 C. On a new set of axes, re-graph the production function from part (A),   for  values of K/L from 0 to 10,000  (increasing 1,000 at a time), assuming E = 1,000.    Label it    On the same axes, graph the production function  for values of K/L from 0 to 10,000 (increasing 1,000 at a time), assuming E = 1,000.  Label it  D. In which case, when   = 1/3 or when   = 0.6, are the returns to investment greater?   The returns to investment are greater when   = 0.6.  Returns to investment refer to how much more  output per worker we get from adding more capital per worker to the existing stock of capital per worker.  When we add more capital per worker to the existing stock of capital per worker, we get a greater increase  in output per worker the higher the value of  . For example, consider what happens to Y/L when K/L increases from 1,000 to 2,000.  When    = 1/3, Y/ L increases by 260 (from 1,000 to 1,260), whereas when   =0.6, Y/L increases by 516 (from 1,000 to  1,516).  Since 516 > 260, the increase in Y/L is greater when   = 0.6. E. Explain, in words that would make sense to someone who doesn’t yet understand, what it means for the returns  to investment to be greater.  (When someone doesn’t understand, an example is often the best way to start.) Suppose you have two different economies:  one that is very developed and one that is still developing.  Now suppose each economy experiences the net investment in capital that increases each economy’s  capital stock per worker (machines and buildings per worker) by the same dollar amount.  Will both enjoy  the same increase in output?   Probably not.  Probably the developed economy, which already has lots of capital (machines) for each of 
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PS2 solutions - #2 0 0 1,000 1,000 2,000 1,260 3,000 1,442...

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