Question

1. What do we mean by a "production function"? Interpret the following production functions. (a) Q = 50L^3/4 K^1/4 (b) Q = 640K L^2-K^2L^3

Answer 1

PRODUCTION FUNCTION: It represents the functional relationship between the quantity of a good produced and factors of production or inputs. It tells us the maximum amount of output that can be produced with the amount of labor and capital.

(a) Q = 50L^3/4 K^1/4

Now,by doubling the inputs K and L ,we get,

= 50 (2L)^3/4 (2K)^1/4

= 50 (2)^{3/4 +1/4} L^3/4 K^1/4

= 2 (50 L^3/4 K^1/4) = 2 Q

This implies that dpubling the inputs K and L , doubles the output . It means increasing inputs K and L will increase the output by same amount . Therefore, this poduction function exhibits constant returns to scale.

(b) Q = 640 K L² - K² L³

Now, by doubling the inputs K and L , we get:

= 640 (2K) (2L)² - (2K)² (2L)³

= 640 (2)³ K L² - (2)⁵ K²L³ > 2Q = 640 (2 K L²) - (K² L³)

This implies that doubling inputs K and L , output will be more than double. This production function exhibits increasing returns to scale.