Question

Suppose that the production function is given by Y = K1/2 N1/2. Assume that the size of the population, the participation rate, and the unemployment rate are all constant. Is this production function characterized by constant returns to scale? Explain.

Answer 1

To determine if the production function has constant returns to scale, we need to examine how output changes with respect to proportional changes in inputs.

Let's consider a proportional increase in capital and labor inputs by a factor of z: K' = zK and N' = zN.

Using the original production function, we have:

Y = K1/2 N1/2

Plugging in the new inputs:

Y' = (zK)1/2 (zN)1/2

Simplifying:

Y' = z1/2 K1/2 z1/2 N1/2

Y' = zK1/2 N1/2

Notice that Y' = zY (multiply by z1/2 on both sides).

Since output increases proportionally with input, this production function exhibits constant returns to scale.