Question

Water's Edge is a small company in Minnesota that makes high-quality,
hand-made sweaters. To produce each sweater, the company must use exactly 1 unit
of capital, 20 hours of labor, and 50 yards of wool. If labor costs $5/hour, wool is
$1/yard, and Pk=$50.
A. Does this production technology exhibit constant, increasing, or decreasing returns to
scale?
B. Here is another production function q = L1/3K2/3 . Does this production technology
exhibit constant, increasing, or decreasing returns to scale? (Show how you get an
answer in detail for full credit)

Answer 1

A.

There are three inputs of production – Capital (K), Labor (L), and Wool (W). Since there is the word “and”, all these are added to get the production function (Q).

Q = K^1 + 20L^1 + 50W^1

The power of each input is 1; these powers should be multiplied to get returns to scale.

Answer: Since (1 × 1 × 1 =) 1, this is constant returns to scale.

B.

Given, Q = L ^(1/3) K ^(2/3)

Here the powers should be added, since the inputs have multiplication in between.

Addition of powers = (1/3) + (2/3)

                                    = (1 + 2) / 3

                                    = 3/3

                                    = 1

Answer: Since the addition is equal to 1, the production function has constant returns to scale.