Answer:
1. The function exhibits a constant returns to scale. The reason is that the power of t is equal to 1.
2. Since MRST = MPL / MPK = - ΔK / ΔL, it is therefore proved that:
MRST = MPL / MPK
Step-by-step explanation:
1. What returns to scale, does this function exhibit? Why?
Note: The production function is properly written before answering the question as follows:
Q = A L^(½) K^(½) ……………….. (1)
To determine the type of return to scale, the input usages K and L are scaled by the multiplicative factor t, and substituting it into equation (1) and then solve as follows:
Q = A ((Lt)^(½) (Kt)^½)
Q = AL^(1/2)t^(1/2)K^(1/2)t^(1/2)
Q = AL^(1/2)^(1/2)t^(1/2)t^(1/2)
Q = AL^(1/2)^(1/2)t^(1/2 + 1/2)
Q = AL^(1/2)^(1/2)t^1
The function exhibits a constant returns to scale.
The reason is that the power of t is equal to 1.
2. Prove that MRTS = MPL / MPK
Given the production function:
Q = LK .............................. (1)
We can obtain the change in Q as follows:
ΔQ = MPL * ΔL + MPK * ΔK .................. (2)
Equating equation (2) to zero and solve for MPL/MPK, we have:
0 = MPL * ΔL + MPK * ΔK
MPL * ΔL = - MPK * ΔK
MPL / MPK = - ΔK / ΔL .................. (3)
The equation (3) above is the marginal product of technical substitution (MRST) as follows:
MRST = MPL / MPK = - ΔK / ΔL
It is therefore proved that:
MRST = MPL / MPK
