1. Given the production function: Q = A L½ K½ What returns to scale, does this function exhibit? Why?

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.

Step-by-step 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.

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step-by-step explanation:

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