Question

4. output Q according to the production function

Q = 6K^1/3L^1/2, where K = capital and L =labor.

A. Calculate the marginal product of capital.

2. Calculate the marginal product of labor.

3. Calculate the marginal rate of technical substitution

A technological advance occurs which changes the production function to Q = 2KL.

D. Calculate the new marginal product of capital.

E. Calculate the new marginal product of labor.

F. Calculate the new marginal rate of technical substitution for Lazy J Enterprises.

G. Is the technological change labor-saving, capital-saving, or neutral? Justify your answer.

Answer 1

The production function is : Q = 6K^(1/3)L^(1/2)

Where, K = capital and L = Labor

A.

The marginal product of capital = MPK = dQ/dK = 6*(1/3)*K^((1/3)-1)*L^(1/2)

=2K^(-2/3)L^(1/2)

The marginal product of labor = MPL = dQ/dL = 6*(1/2)*K^(1/3)*L^((1/2)-1)

=3K^(1/3)L(-1/2)

The marginal rate of technical substitution = MRTS L, K = MPL/MPK

=(3K^(1/3)L(-1/2))/(2K^(-2/3)L^(1/2))

=1.5K^((1/3)+(2/3))/(L^(1/2)+(1/2))

=1.5K/L

The new production function is Q = 2KL

D.

The new marginal product of capital = MPK = dQ/dK = 2L

E.

The new marginal product of labor = MPL = dQ/dL = 2K

F.

The marginal rate of technical substitution = MRTS L, K = MPL/MPK

=2K/2L

=K/L

G.

Thus, with the technological change the MRTS L, K has changed from 1.5K/L to K/L

This means that for one additional unit of labor, the amount of capital that is given up falls. Thus, technological change is capital saving.