(2) Consider a Cobb-Douglas production function, F(K,L) = AL^ß K^1-ß. a. Does th

Question

(2) Consider a Cobb-Douglas production function, F(K,L) = AL^ß K^1-ß.
a. Does the production function exhibit increasing, decreasing or constant returns to scale?
b. Manipulate the production function so that it is expressed in intensive form. Hint: You should end up with a function of the capital-labor ratio, (K/L).
c. Interpret the value A.
d. Find the marginal production functions for labor and capital. Interpret.
e. Find the technical rate of substitution. Interpret.
f. Find the isoquant for output of 50. Interpret.

Explanation / Answer

a) the production function has constant returns to scale if the output elasticities of labor and capital (beta and 1-beta here) sum to 1. Since this is the case (b + 1 -b = 1), the production function has constant returns to scale b) F(K,L) = Y = A*(K/L)^beta c) The variable A is the total factor productivity, and represents technology, efficiency, human capital and other such factors that aren't specifically attributable to labor or capital themselves d) MPL = dY/dL = b * Y/L MPK = dY/dK = (1-b) * Y/K The marginal products are the amount of extra output from an extra unit of the particular input e. the marginal rate of technical substitution is the rate at which one output may be substituted for another while holding output constant. The MRTS of input 1 for input 2 is given by MP2/MP1, so we would have MPK/MPL = (b*Y/L)/[(1-b)*Y/K) would be the mrts of capital for labor f. an isoquant represents all possible combination of inputs that produce the same amount of output 50 = A*(K/L)^b

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