Firm A’s production function is the following: Q=Q(L,K)=20LK Calculate the demand functions for labor and capital.

Firm A’s production function is the following:

Q=Q(L,K)=20LK

Calculate the demand functions for labor and capital.

Solutions

Expert Solution

Q = 20LK

Constraint: wL + rK

w = Wage given to the Labor

r = Interest paid on capital

Producer maximises :

Profit = p*Q - wL -rK

Let = p*20LK - wL - rK

d/dL = 20pK - w = 0 (1)

d/dK = 20pL - r = 0

w/K = r/L

K/L = w/r

This is also equal to: Marginal Productivity of Labor/Marginal productivity of Capital = Price of Labor/Price of Capital

K = wL/r

Put this valure of K in (1)

(20p)(wL)/r = w

L^* = r/20p

K^* = w/20p

Rahul Sunny answered 1 year ago

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