Question

The firm's production function is given as f(LK) = 4L·5K0.5 and input prices are w = 4 and r = 16. In the short-run, the level of capital is fixed at K = 2 What is the firm's short-run marginal cost function? Wählen Sie eine Antwort: O a. 0.25q 32/q O b. 0.125q O c. 4 + 32/q O d. 0.25q

Answer 1

Production function = F(L,K) = Q = 4 (LK)^0.5

K = 2

w = 4

r = 16

q = 4(LK)^0.5

q = 4(2L)^0.5

Squaring on both sides

q^{​​​​​​2}​​​​​ = 32L

L = q^{​​​​2}/32

Total cost function = Variable cost + Fixed cost

Variable cost = WL

Fixed cost = rK

TC = wL + rK

TC = (4*q^{​​​​​​2}/32)+(16*2)

TC = 0.125q²+32

Marginal cost function = MC = d(TC)/dq

MC = d(0.125q²+32)/dq

MC = 0.25q

Answer: d