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ps6_questions

# ps6_questions - Problem Set 6 Part I Some practice with...

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Problem Set 6 Part I - Some practice with production functions (30 points) For each of the following production functions : 1) Y AK N ; A , and are strictly positive constants 2) Y A K 1 N 1/ ; A , and are strictly positive constants, and 0 1 3) Y K AN 1 , and A BK ; B , and are strictly positive constants, and 0 1 do the following : (a) (12 points) determine whether the production function exhibits diminishing marginal returns to capital (b) (12 points) determine whether the production function is CRS, DRS or IRS (c) (6 points) if possible, express Y / N as a function of K / N In each of these questions, show the math explicitly and provide extra conditions on the constants , if necessary, to make a determination on the nature of the production function. Part II - A continuous time growth model (70 points) So far, in the lectures and in the textbook, you have dealt with discrete time (ie, the subscript t takes discrete integer values 0,1,2,3 etc.) and the dynamic equation for capital accumulation (equation 11.3 in the textbook) is a difference equation in K / N . This excercise

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