Question

A farm can use tractors (T), labor (L), and acres of land (A) to produce tons of wheat (Q). The farm's production function is the following: Q = 0.27⁰.³ L⁰.² 4⁰.¹. The production function has

a decreasing returns to scale.
b constant returns to scale.
c increasing returns to scale.
d there is not enough information.

Answer 1

The production function Q = 0.270.3 L0.2 A0.1 exhibits decreasing returns to scale because the sum of the exponents of the inputs is less than 1. This indicates that increasing the amount of inputs will result in less than proportionate increases in output.

Step-by-step explanation:

The student's question pertains to the analysis of a production function; specifically, they need to determine if the farm's production function has decreasing, constant, or increasing returns to scale. The given production function is Q = 0.270.3 L0.2 A0.1. The sum of the exponents of L (labor) and A (land), which are the variable inputs, determines if the production function has decreasing, constant, or increasing returns to scale.

In this function, the sum of the exponents is 0.3 + 0.2 + 0.1 = 0.6. Since the sum is less than 1, this production function exhibits decreasing returns to scale. That means if the farm doubles the inputs, the output will less than double.

Production functions are crucial for understanding how firms can vary input levels to produce different quantities of output. They help determine the production costs and the efficiency of production processes within a firm. Firms in the same industry may have different production functions to reflect their unique methods and resource utilizatuion.