Question

Let a production function for a country, Eastasia, be defined as: Y=5*L^1/3*K^2/3.

Suppose L=27 and K=64. Find the level of GDP.Now, suppose L=13.5 and K=32. Find the level of output in the economy.

Does this function have constant returns to scale? Explain.

Now, let Y=5*L^1/3*K^2/3+L. Does this function have constant, increasing, or decreasing returns to scale? Explain.

Answer 1

1) Level of GDP when L = 27 and K = 64

GDP = 5 x 27^1/3 x 64^2/3 = 240

when L = 13.5 and K = 32

Output = 5 x 13.5^1/3 x 32^2/3 = 120

The function has constant returns to scale because when the inputs are halved, the output is also halved. (can be seen in the example above)

Y = 5 x L^1/3 x K^2/3 + L

When L and K are both doubled:

Y' = 5 x (2L)^1/3 x (2K)^2/3 + 2L

Y' = 10 x L^1/3 x K^2/3 + 2L = 2Y

The function has constant returns to scale because when the inputs are doubled, the output is also doubled.