# Ps6_answers - 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

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PartI-Somepract ice 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. (1) (a) F K AK 1 N F KK 1 AK 2 N ,sofor 1, the production function has diminishing returns (b) F K , N AK N F K , N for any 0 so for 1, the production function is CRS 1, the production function is IRS 1, the production function is DRS (c) It is possible to represent y ( Y / N as a function of k ( K / N in the CRS case : y Ak (2) (a) F K A 1 K N 1 F KK A 1 K N 1 1 . 1 . 1 . K 1 N 0, so this production function always has diminishing returns (b) Clearly F K , N F K , N for any 0, so the production function is CRS (c) When the production function is CRS, it can always be representated in the form y f k In this case y A k 1 1/ (3) First substitute for A into the production function, so Y K 1 B 1 N 1 (a) F K 1  K 1 1 B 1 N 1 F KK 1  1 1 K 1 2 B 1 N 1 For

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## This note was uploaded on 11/29/2009 for the course 14 14.02 taught by Professor Geurrieri during the Fall '09 term at MIT.

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Ps6_answers - 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

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