Answer to Question #270758 in Macroeconomics for LEMBELANI

Question

Country A and country B both have the production function Y = F(K, L) = K^1/2L^1/2.

a)     Does this production function have constant returns to scale? Explain.         

What is the per-worker production function, y = f(k)? [Hint: use the solow model] 

Answer 1

Solution:

Yes, this production function exhibits constant returns to scale.

Constant returns to scale require that zY = F(zK, zL)

Here, we see that F(zK, zL) = (zK)^1/2 (zL)^1/2  = z(K^1/2L^1/2) = z(K^1/2 L^1/2 )

Therefore, it does exhibit the property of constant returns to scale.

 

The per-worker production function calculation:

Y = F (K, L) = K^1/2L^1/2

The per-worker production function is solved by dividing both sides of the above equation by L:

$\frac{K}{L} = (\frac{K}{L})^{1/2}$

This can be rewritten as y = (k)^1/2

The per-worker production function: y = (k)^1/2