According to The Wall Street Journal, Mitsubishi Motors recently announced a maj

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
0.15 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive
hourly wage of ¥1,330. In the study of its production process and markets where capital is
procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.5 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
small car is ¥950,000. Determine the rate at which Mitsubishi can rent capital and the marginal
productivity of labor at its new targeted level of output. To minimize costs Mitsubishi should hire
capital and labor until the marginal rate of technical substitution reaches what proportion?

Explanation / Answer

Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,330. In the study of its production process and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.5 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 small car is ¥950,000.

Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output.

Rate of renting capital: (2)(950,000) - 1,300 = 1 898 700

all this means is 950,000 of cars are produced every half-hour, or 2 every hour; we subtract the hourly wage to obtain the per hour receipts:

1 898 700 x 0.15 = ¥284,805 rate of renting capital

MPL (marginal productivity of labor) = (0.85)(0.5 = MP of capital) = 0.425 cars

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

1:1 because minimal costs occur when capital and labor have equal rates of marginal substitution - aka a ratio of 1:1

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