Question

3. What is the scale elasticity of F(K,L) K22L, where K denotes capital and L denotes labor? What relationship between capital and labor must hold for scale elasticity to equal one?

Answer 1

Q = F(K, L) = K² + 2L^0.5

(1)

Scale elasticity (E) = ($\dpi{80} \partial$Q/$\dpi{80} \partial$K) x (K/Q) + ($\dpi{80} \partial$Q/$\dpi{80} \partial$L) x (L/Q)

= 2K x (K/Q) + [(2 x 0.5) / L^0.5] x (L/Q)

= (2K²/Q) + (L^0.5/Q)

= (1/Q) x (2K² + L^0.5)

= (2K² + L^0.5) / (K² + 2L^0.5)

(2)

When E = 1,

(2K² + L^0.5) = (K² + 2L^0.5)

K² = L^0.5

Squaring,

K⁴ = L (Required condition)