Question

Consider the production function
Y = (K)^1/2 (N)^1/2
where Y is output, K is capital, and N is the number of workers (abor)
When K = 46 and N = 82, output is ________ (Round your response to two decimal places.)
If both capital and labor double, given the production function, output will _________.
If output doubles when inputs double, the production function will be characterized by:_________.
A. constant returns to scale
B. decreasing returns to scale.
C. increasing returns to scale.
D. none of the above.

Answer 1

Answer:

Requirement 1: Production Output will be 61.42 Units.

Requirement 2: Production Output will be doubled.

Requirement 3: Constant Returns to Scale

Explanation:

Requirement 1:

The output at K=46 and N=82 is given as under:

Y = (46)^1/2  *  (82)^1/2

Y = 61.42 Units

Requirement 2:

Now if we double "K" and "N" then:

Y' = (2K)^1/2  *  (2N)^1/2

Y' = 2 [(K)^1/2  *  (N)^1/2]

Y' = 2Y

This means that the output will be doubled.

Requirement 3:

Option A. Constant Returns to Scale

Constant returns to scale occurs when the increase in the input causes same proportional increase in the production output. Such same proportional increase in the production output is referred to as Constant Returns to Scale.

In the given scenario, as the production output doubles with the doubling of input which was seen in the requirement above. We can say that the production function is characterized by Constant Returns to Scale.