Question

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A firm has a production function f(LK) = L1/3K1/3 The cost of labor is w = 20 and the cost of capital is r = 5. The equation for long-run total cost is: Wählen Sie eine Antwort: O a. TC(Q) = 5Q34 b. TC(Q) 202 3/2 OC. TC(Q)300 d. TC(R)-2034

Answer 1

Answer b. TC(Q)= 20Q^3/2

First we find MRTS which is K/L

Then equate this to ratio of factor price i.e w/r= 20/5=4

Put this value in production function

Find K and L in terms of Q.

Finally put all values in TC and solve

TC= w.L+r.K

Complete solution is given in the picture.

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