Question

Prove whether the following production functions exhibit increasing, decreasing or constant returns to scale: (a) Y = AKαL 1−α, (b) Y = 500 ∗ (x − F), where x in an input and F is a fixed cost.

Answer 1

A) Y(k,L)=A*k^a*L^{1-a}

Doubling the scale,

Y(2k,2L)=A*(2k)^a*(2L)^(1-a)

Y(2k,2L)=2*A*K^a*L^{1-a}

Y(2k,2L)=2*Y(k,L)

So doubling the scale ,lead to doubling the output,so function exhibits constant return to scale .

B)Y(x,F)=500*(x-F)=500x-500F

Let x=10 and F=1

Y=500*10-500*1=4500

Doubling the scale,( only x will double, F is not

Y(2x,F)=500*(2x-F)=500*(2*10-1)=500*19=9500

So doubling the scale lead to increase in output more than double.

So function exhibits increasing return to scale.