Suppose a Firm's Production Function Is Given by Q =

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Examlex · Accepted Answer

The Answer is a)The tangency condition requires that the MRTS_LK equal the ratio of input prices.For a Cobb-Douglas production function,MRTS_LK = (a/b)(K/L),so the tangency condition is (a/b)(K/L)= W/R,where W is the wage rate and R is the rental rate of capital.Substituting gives K/L = $100/$50 = 2,so K = 2L.Substituting this into the production function yields Q = 5L(4L)= 20L,which implies that L = Q/20.To produce 1000 units of output,the firm would require 50 workers.Since K = 2L,the firm would employ 100 units of capital.
b)From the answer to part a,we know that L = Q/20.We also know that the firm uses K = 2L = 2Q/20 units of capital.The cost function is therefore
C(Q)= 50 (Q/20)+ 100 (2Q/20)= 12.5Q
c)The short-run production function is written as Q = 5L(10)= 50L,so
Q/50 = L.The short-run cost function is C_SR(Q)= 50(10)+ 100(Q/50)= 500 + 2Q.

Suppose a Firm's Production Function Is Given by Q =

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