Explain how to derive the demand for an inputSolutionSuppose

Explain how to derive the demand for an input.

Solution

Suppose Q = 100 K^0.5 L^0.5

Equilibrium condition = MPL/MPK = w/r

Now differentiating Q with respect to K and L

MPK = (50) L^0.5 /K^0.5

MPL = (50) K^0.5/L^0.5

Now MPK/MPL = L/K

L/K =r/w

K = (w/r)L

Hence demand for capital K = (w/r)L