Answer:
(a) MPL = 1/2
(b) MPK = 1/2
(c) APL = 1/2+ K/2L
(d) APK = = L/2K+ 1/2
(e) TRSL,K = 1
Explanation:
Q = (L+K)1/2 = L/2 + K/2 ……………………………………………………. (1)
Where Q is the total output, L is Labour and K is capital
(a) What is the Marginal Product of Labor (MPL)?
To get MPL, differentiate equation (1) with respect to L as follows:
MPL = dQ/dL = 1/2
(b) What is the Marginal Product of Capital (MPK)?
To get MPK, differentiate equation with respect to K as follows:
MPK = dQ/dL = 1/2
Both MPL and MPK are diminishing since each of them is 1/2 which less than one.
(c) What is the Average Product of Labor (APL)?
To calculate APL, divide equation (1) by L as follows:
APL = Q/L = (L/2)/L + (K/2)/L
= 1/2+ K/2L
(d) What is the Average Product of Capital (MPK)?
To calculate APK, divide equation (1) by K as follows:
APL = Q/K = (L/2)/K + (K/2)/K
= L/2K+ 1/2
(e) What is the TRSL,K ?
TRSL,K implies Technical Rate of Subsitution of L for K = MPK/MPL
TRSL,K = MPK/MPL
Since both MPK and MPL are each equal to 1/2 as calculated under (a) and (b) above, we substitute for them in the TRSL,K as follows:
TRSL,K = MPK/MPL = (1/2)/(1/2) = 1
(e.1.) Is the absolute value of TRSL,K diminishing in L or K?
No, it neither diminishing in L nor K since the answer is equal to 1.
(e.2.) Are there constant, decreasing, or increasing returns to scale?
Since the TRSL,K is equal to 1, it implies there is a constant return to scale.
I wish you the best.
