Question

Question 9 0.5,,0.25 Suppose that a firm had a production function given by: q-2L K . The rental rate for the firm is $10 and the Wage is $5. Solve the optimization condition for K and then fill in the value that appears in front of L. Tries remaining: 1 Flag question K (Round to the nearest 2 decimal places if necessary.)

Answer 1

Production function is as follows -

q = 2L^0.5K^0.25

Calculate MPL -

MPL = dq/dL = d(2L^0.5K^0.25)/dL = K^0.25/L^0.5

Calculate MPK -

MPK = dq/dK = d(2L^0.5K^0.25)/dK = 0.50L^0.5/K^0.75

Optimization condition is as follows -

MPL/MPK = P_L/P_K

(K^0.25/L^0.5)/(0.50L^0.5/K^0.75) = 5/10

K/0.5L = 1/2

K = 0.5L/2

K = 0.25L

Thus,

K = 0.25L