Question

The production function for a firm is given by q = L0.75 K0.3 where q denotes output; L and K labor and capital inputs

. (a) Determine marginal product of labor. Show whether or not the above production function exhibits diminishing marginal productivity of labor.

(b) Calculate the output (or production) elasticity with respect to labor.

c) Determine the nature of the Return to Scale as exhibited by the above production function. Show and explain all calculations

Answer 1

q=L^0.75K^0.3

Marginal Product of Labor=dq/dL=0.75K^0.3*L^(-0.25)

Marginal Product of Capital=dq/dK=0.3L^0.75*K^(-0.7)

Both these marginal products keep on decreasig as we increase additional unit of L or K hence both the inputs exhibit diminishing marginal productivity of labor/capital

ANs b)

Output elasticity=dq/q(L/dL)

dq/dL(L/q)=0.75K^0.3*L^(-0.25)(L/L^0.75*K^0.3 )
=0.75K^0.3*L^(-0.25)(L^0.25/K^0.3 )=0.75

Ans c)
If we increase the inputs by some positive proportion and then if output increases by scale more than that of inputs we say the production function exhibits increasing return to scale else decreasing return to scale or constat return to scale

q(K,L)=L^0.75*K^0.3

q(@K,@L)=(@L)^0.75*(@K)^0.3=@^(1.05)*q(K,L)

Hence this production function exhibits increasing return to scale