Question

From the following production functions determine the type of returns to scale increasing, decreasing or constant. Develop using λ

Y=4K+7L

Y=10KL/K+L

Y=K²L

Answer 1

When both inputs in a production function are doubled, the production function exhibits

(i) Increasing returns to scale (IRS) if output more than doubles,

(ii) Decreasing returns to scale (DRS) if output less than doubles,

(iii) Constant returns to scale (CRS) if output exactly doubles.

(1) Y = 4K + 7L

Let us double both the inputs such that new production function becomes

Y* = 4 x (2K) + (7 x 2L) = 8K + 14L = 2 x (4K + 7L) = 2 x Y

Y* / Y = 2

There is CRS.

(2) Y = 10KL / (K + L)

Let us double both the inputs such that new production function becomes

Y* = (10 x 2K x 2L) / (2K + 2L) = (40KL) / (2K + 2L) = (40KL) / [2 x (K + L)] = (20KL) / (K + L) = 2 x [10KL / (K + L)]

= 2Y

Y* / Y = 2

There is CRS.

(c) Y = K²L

Let us double both the inputs such that new production function becomes

Y* = (2K)² x 2L = 4 x K² x 2L = 8 x K²L = 8 x Y

Y* / Y = 8 > 2.

There is IRS.