Question

According to The Wall Street Journal, Mitsublshi Motors recently announced a major restructuring plan In an attempt to reverse declining global sales. Suppose that as part of the restructuring plan MItsublshi conducts an analysis of how labor and capltal are used In Its production process. Prior to restructuring Mitsublshi's marginal rate of technical substitutlon Is 0.14 (In absolute value). To hire workers, suppose that MItsubishi must pay the competitive hourly wage of 1,580. In the study of Its productlon process and markets where capltal is procured, suppose that Mitsublshi determines that Its marginal productivity of capltal 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 1,100,000. 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 capltal: Marginal productivity of labor To minimize costs Mitsublshi should hire capltal and labor until the marginal rate of technical substitution reaches what proportlon? Instruction: Enter your response rounded to four declmal places.

Answer 1

The cost minimisation problem states that the cost function should be tangent to the isoquant in order to minimise costs. This means that at this point, the slope of the isoquant is equal to the slope of the cost function. Slope of the isoquant is given by the Marginal Rate of Technical Substitution (MRTS) and the slope of the cost function is given by w/r where w is the wages of workers and r is the rent of capital. So, we have:

MRTS=

1580 0.14

1580 = 11285.7143 0.14 . . r

It is also known to us that MRTS is the ratio of the marginal productivity of labour and capital as:

MPL MPK MRTS

MPL 0.5

$\therefore MP_{L} = 0.14*0.5 = 0.07$

As stated earlier, we know that in order to minimise costs, a company should hire labour and capital to a level until the MRTS equals the ratio of w/r, that is, till the point where we attain this equality.

$MRTS = \frac{MP_{L}}{MP_{K}}=\frac{w}{r}$