Question

Michael's Dairy farm production function is given by , where K is the number of machine milkers and L is the amount of labour hours he uses.

a) Does this production function exhibit increasing, constant or decreasing returns to scale?

b) Holding the number of machine milkers constant at 16, is the marginal product of labour increasing, constant, or decreasing as more labour is used?

Answer 1

Michael's Dairy farm production function is given by Y = 2*K^0.5*L^(1/3), where K is the number of­ machine milkers and L is the amount of labour hours he uses.

a) This production function exhibits decreasing returns to scale, because its increase is slower than there is an increase in use of inputs.

b) If K = 16, the marginal product of labour is MPL = Y(L)' = 2*16^0.5*(1/3)*L^(-2/3) = 8/3*L^(-2/3), so it is decreasing as more labour is used.