Question

Consider the production function Y = 2F(L, K, II, N). Suppose F(12, 10, 9, 7) = 100 and F(24, 20, 18, 14) = 180. Does the production function have the property of constant returns to scale? Why or why not?

Answer 1

The production function does not exhibit constant returns to scale because when all inputs are doubled, the output increases from 100 to 180, not to the expected 200. This indicates decreasing returns to scale.

Step-by-step explanation:

To determine if this production function has constant returns to scale, we need to analyze the effect of scaling all inputs by the same proportion on the output (Y). Initially, the function, with inputs (12, 10, 9, 7), yields an output of 100. Doubling each input (24, 20, 18, 14) results in an output of 180. If the production function has constant returns to scale, doubling the inputs would double the output from 100 to 200. However, since the output increases only to 180 and not 200, the production function does not exhibit constant returns to scale.

In a constant cost industry, we would expect the doubling of all inputs to result in a doubling of the output, which is not observed here. This suggests that as the firm increases its inputs, the proportional increase in output is less than the proportional increase in inputs, indicative of decreasing returns to scale.