Question

The production function ( Q(L, K, M)=25 K⁰.²⁵ L⁰.²⁵ M⁰.²⁵ exhibits :

A. either decreasing or constant returns to scale, but more information is needed to determine which one.
B. increasing returns to scale
C. either decreasing or constant returns to scale, but more information is needed to determine which one
D. constant returns to scale.

Answer 1

The production function Q(L, K, M) = 25 K⁰.²⁵ L⁰.²⁵ M⁰.²⁵ has decreasing returns to scale, as the sum of the exponents of the inputs is less than 1.

Step-by-step explanation:

The question presented here involves determining whether a given production function exhibits increasing, constant, or decreasing returns to scale. The production function provided is Q(L, K, M) = 25 K⁰.²⁵ L⁰.²⁵ M⁰.²⁵, where Q is the quantity of output, L is labor, K is capital, and M is materials. To assess the returns to scale, we sum the exponents of the inputs in the production function. The sum is 0.25 + 0.25 + 0.25 = 0.75, which is less than 1. This indicates that the production function has decreasing returns to scale because increasing all inputs by a certain percentage results in a less-than-proportional increase in output.

Answer 2

The production function exhibits constant returns to scale (D).

Step-by-step explanation:

Constant returns to scale occur when an increase in inputs leads to a proportional increase in output. In this case, the exponents sum to 0.75 (0.25 + 0.25 + 0.25), indicating that a proportionate increase in all inputs (K, L, M) will result in an equivalent increase in output. This proportionality signifies that doubling all inputs would double the output, demonstrating constant returns to scale. There's no diminishing or increasing factor affecting the relationship between inputs and outputs, affirming the constant returns to scale property of the production function.

Therefore, the correct answer is D. constant returns to scale.