Question

As an economic consultant, you visit a production plant (a factory). During your visit, you explain the concept of returns to scale to the manager of the factory. The manager responds as follows: “If we would double all our input then our production would also be doubled. But our revenues would not be doubled. That is because, doubling output would require decreasing our price to sell all these extra products. So our technology has decreasing returns to scale.”

1. Why is the manager wrong?
2. What is the actual returns to scale in this production facility?

3. ) Suppose that the production technology is Cobb-Douglas

   Compute  .

Answer 1

a) The manager is wrong because decreasing returns to scale is not related to the revenues the firm earns. It means that if the inputs of production are doubled, the output will be less than doubled, irrespective of its effect on revenues. But here, the doubling of inputs exactly doubles the output.

b) In this case, there is constant returns to scale in this production facility.

c) The Cobb Douglas production function may be given by:

Y = L^a K^1-a

Where Y is the output, K is the capital stock, and L is the amount of labour.

Suppose, we double both L and K, the new output will be:

Y' = (2K)^a(2L)^1-a

Y' = 2 KL = 2Y

This shows that the new output is exactly the double of the initial output, showing that the production function exhibits constant returns to scale.