Answer:
a. This function therefore exhibits a constant return to scale.
b. The reason is that the sum of the exponents of the multiplicative factor a is equal to 1.
Explanation:
The given production function is first correctly stated as follows:
Q = A L^½ K^½ .......................... (1)
In order to know the returns to scale this function exhibits, the input K and L are scaled by the multiplicative factor a which is included in equation (1) as follows:
Q = A (aL)^½ (aK)^½
Q = A a^½L^½ a^½K^½
Q = A a^½ a^½ L^½ K^½
Q = A a^(½+½) L^½ K^½
Q = A a^1 L^½ K^½ ......................... (2)
Based on the equation (2), we now answer the following questions:
a. What returns to scale, does this function exhibit?
This function therefore exhibits a constant return to scale.
b. Why?
The reason is that the sum of the exponents of the multiplicative factor a in equation (2) is equal to 1.