Question

According to The Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labor and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.12 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,800. In the study of its production process and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.8 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is ¥1,200,000. Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output.

Instruction: Enter your response for marginal productivity of labor rounded to four decimal places.

Rental rate of capital:

¥ Marginal productivity of labor:

To minimize costs Mitsubishi should hire capital and labor until the marginal rate of technical substitution reaches what proportion?

Instruction: Enter your response rounded to four decimal places.

Answer 1

Part A

Here we need to find the profit function. That is,

..............................(1)

  

  

   ..............................(2)

Substitute the value in the equation 2 and 1, will ger r and MP of labor.

So the rent on capital is, $960,000

Now we substitute the value on w and p in equation 2,

So, the marginal productivity of labor is 0.0015

Part B

The marginal rate of technical substitution is,

Therefore the MRTS is 0.001875