Question

A US electronics firm has a plant in the US and another in China. The production function is the same in both plants q = L1 2 K 1 2 (notice that marginal product of labor is MPL = 1 2L− 1 2 K 1 2 = 1 2 q L and marginal product of capital is MPK = 1 2L1 2 K− 1 2 = 1 2 q K ). The US prices are w = r = 9. In China the firm faces the same cost of capital r∗ = 9 but the wage rate is lower, w∗ = 4.

A.Show the total, average and marginal product of labor with this production function if capital is fixed at K = 100

B.

C.Represent in a diagram the cost minimizing choice of factors to produce q = 100 in each country

D.Write the equilibrium proportions of the factors that the firm is going to use in each country.

E. Write the expressions for cost, obtain the relationships factorsoutput and deduce the cost functions for both countries. Calculate the cost of producing q = 100 units in each country.

There is no question b

Answer 1

A. If capital is fixed at 100, the production function reduces to:

Marginal product of labor is:

Average product of labor is:

B.

C. given q is 100, the production function is:

The MRTS is equal to the factor prices at equilibrium:

In USA:

Substituting the value in the production function:

The cost function for the plant in the US is:

In China:

Using the production function:

Similarly for capital:

The cost function for the plant in China is given by:

The following graph represents these factor choices in both countries:

D. From the previous part, we concluded that:

E. From part C, cost functions for plants in USA and China are:

For q = 100, costs in USA and China are 1800 and 1200 respectively.