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# HW3solution - Micro 3101 Homework 3 solution Production...

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Unformatted text preview: Micro 3101 Homework 3 - solution Production function 1. (25 pt.) (a) AP L = f ( L;K ) L = AL : 7 K : 3 L = AK : 3 L : 3 (The last simpli&cation is not required). Similarly, AP K = f ( L;K ) K = AL : 7 K : 3 K = AL : 7 K : 7 (b) MP L = f L ( L;K ) = 0 : 7 AL & : 3 K : 3 = : 7 AK : 3 L : 3 MP K = f K ( L;K ) = 0 : 3 AL : 7 K & : 7 = : 3 AL : 7 K : 7 (c) TRS = & f L ( L;K ) f K ( L;K ) = & MP L MP K = & : 7 AL & : 3 K : 3 : 3 AL : 7 K & : 7 = & : 7 K : 3 L (d) f ( &L;&K ) = A ( &L ) : 7 ( &K ) : 3 = &AL : 7 K : 3 = &f ( L;K ) This production function exhibits Constant Returns to Scale (CRS). In general, Cobb-Douglas production function with exponents that sum up to 1, is constant returns to scale. (e) The isoquant can be de&ned implicitly as L : 7 K : 3 = 100 or, explicitly K = & 100 L : 7 ¡ 1 : 3 1 Isoquant 50000 100000 150000 200000 250000 300000 350000 100 200 300 400 500 L K K 2 2. (25 pt.) (a) AP L = f ( L;K ) L = aL + bK L AP K = f ( L;K ) K = aL + bK K (b) MP L = f L ( L;K ) = a MP K = f K ( L;K ) = b (c) TRS = & f L ( L;K ) f K ( L;K ) = & a b (d) f ( &L;&K ) = a ( &L ) + b ( &K ) = & ( aL + K ) = &f ( L;K ) This production function exhibits Constant Returns to Scale (CRS)....
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HW3solution - Micro 3101 Homework 3 solution Production...

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