Question

Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring it'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 US$ 15. In the study of production process and markets where capital is procured, suppose that Mitsubishi determine 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 smallest car is US$ 9500. Determine the rate at which Mitsubishi can rent capital and marginal productivity of labour at its new targeted level of output. To minimize costs Mitsubishi should hire capital and labour until the marginal rate of technical substitution reaches what proportion?

Answer 1

a.$(i)$ Rate at which Mitsubishi can rent capital at its new targeted output:

Rental rate of capital$=$ MPK $\times$ P

Rental rate of capital$=$ 0.5$\times$ 9500$=$ US $ 4750

$(ii)$ Rate at which Mitsubishi can rent marginal productivity of labour at new targeted level output:

MPL$=$$\frac {MPK}{P(K)}$ $\times$ P(L)

MPL$=$ $\frac {0.5}{4750}$ $\times$ 15

MPL$=$ 0.0016

b. Costs are minimized when $\frac {w}{r}$

$=$ $\frac{1580}{4750}$

$=$ 0.3326