EC202 PS3solution

EC202 PS3solution - Fall 2015 EC202 Sections D Problem Set...

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Fall 2015 - EC202 Sections D - Problem Set 3 Solutions Textbook Questions Chapter 10 Question 3 Consider the production function: Y = Y K a. Compute output when K = 49 and N = 81. Solution: Y = 49 81 = 7(9) = 63 b. If both capital and labor double, what happens to output? Solution: K = 2(49), N = 2(81) Y = p 2(49) p 2(81) = 2 27(9) = 2(63) = 126 c. Is this production function characterized by constant returns to scale? Explain! Solution: Yes: F ( xK, xN ) = xK xN = x K x N = x K N = xY d. Write this production function as a relation between output per worker and capital per worker. Solution: 1
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Plug in x = 1 N above: Y N = r K N r N N = r K N e. Let K N = 4. What is Y N ? Now double K N to 8. Does Y N double as a result? Solution: K/N=4 implies Y/N=2. K/N=8 implies Y/N=2.83. Output less than doubles. f. Does the relation between output per worker and capital per worker exhibit constant returns to scale? Solution: No. g. Is your answer to (f) the same as your answer to (c)? Why or why not?
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