Question

Hi Can you please help me to do this. I have tried doing MPL/PL=PMK/PK but I could not get the same answers . I don't know whether it is my math or if I have the wrong formula to LCCI (Least Cost Combination) Thank you

. 1. A firm produces according to the following production function: Q = K^0.25L^0.5 . Suppose that the price of K is $4 per unit, and the price of L is $6 per unit. When L=5 and K=10, is the firm minimizing costs?

No, the least cost combination of inputs (LCCI) produces LCCI labor = 0.066 LCCI capital = 0.025 Use more labor or less capital

2. A firm produces according to the following production function: Q = K^0.33L^0.5. Suppose that the price of K is $6 per unit, and the price of L is $12.5 per unit. When L=15 and K=13, is the firm minimizing costs?

No, the least cost combination of inputs (LCCI) produces LCCI labor = 0.024 LCCI capital = 0.038 Use more capital or less labor

Answer 1

(1)

Q = K^0.25L^0.5

MPL = Q/L = 0.5 x K^0.25 / L^0.5 = 0.5 x (10)^0.25 / (5)^0.5 = 0.5 x 1.78 / 2.24 = 0.4

MPK = Q/K = 0.25 x L^0.5 / K^0.75 = 0.25 x (5)^0.5 / (10)^0.75 = 0.25 x 2.24 / 5.62 = 3.15

MPL/PL = 0.4/6 = 0.067

MPK/PK = 3.15/4 = 0.7875

Since (MPL/PL) < (MPK/PK), currently firm is using too less labor and too much capital. So cost will be minimized if firm uses more labor and less capital.

(2)

Q = K^0.33L^0.5

MPL = Q/L = 0.5 x K^0.33 / L^0.5 = 0.5 x (13)^0.33 / (15)^0.5 = 0.5 x 2.33 / 3.87 = 0.3

MPK = Q/K = 0.33 x L^0.5 / K^0.67 = 0.33 x (15)^0.5 / (13)^0.67 = 0.33 x 3.87 / 5.58 = 0.23

MPL/PL = 0.3/12.5 = 0.024

MPK/PK = 0.23/6 = 0.038

Since (MPL/PL) < (MPK/PK), currently firm is using too less labor and too much capital. So cost will be minimized if firm uses more labor and less capital.