Question

Based on your understanding of cost minimization, match each of the three situations below with one of the three possible responses (use each response once).

Option 1: Rent more capital and reduce the number of workers employed.

Option 2: leave the mix of labbour and capital unchanged.

Option 3: hire more labour and reduce the amount of capital rented.

(A) You've recently been hired as the manager of a small factory. The factory employs both labour (hired at an hourly wage of $16) and capital (rented at an hourly wage of $20). On your first day, you observe that the marginal product of labour is 47 units of output per hour and the marginal product of capital is 60 units of output per hour. In order to minimize costs.

(B) You've recently been hired as the manager of a small factory. The factory employs both labour (hired at an hourly wage of $15) and capital (rented at an hourly wage of $20). On your first day, you observe that the marginal product of labour is 50 units of output per hour and the marginal product of capital is 60 units of output per hour. In order to minimize costs.

(C) You've recently been hired as the manager of a small factory. The factory employs both labour (hired at an hourly wage of $15) and capital (rented at an hourly wage of $25). On your first day, you observe that the marginal product of labour is 42 units of output per hour and the marginal product of capital is 70 units of output per hour. In order to minimize costs.

Answer 1

.To get info about employment and deployment of input we need to check their per unit output produced by the extra unit input employed. Whichever input is giving higher output return than the other  , that input would be employed.

Let the marginal product in each case be MPL and marginal product of capital be MPC. Let the price per unit output of labour and capital be PL and PC respectively in each case

(A) MPL=47 , PL=16 AND MPC=60, PC=20

Per unit output of extra labour employed= MPL/PL= 47/16 = 2.93

Per unit output of extra capital employed=MPC/PC=60/20= 3

Here per unit of extra capital employed is giving more output thus more of capital would rented and number of labours reduced. Hence Option 1 will be suitable.

B) MPL=50 , PL=15 AND MPC=60, PC=20

Per unit output of extra labour employed= MPL/PL=50/15=3.33

Per unit output of extra capital employed=MPC/PC=60/20= 3

Here per unit of extra labour employed is giving more output than extra unit of capital, thus more of labour would be hired and capital rented would be reduced. Hence Option 3 will be suitable.

C) MPL=42 , PL=15 AND MPC=70, PC=25

Per unit output of extra labour employed= MPL/PL=42/15= 2.8

Per unit output of extra capital employed=MPC/PC=70/25= 2.8

Here extra unit of both the capital and labour is giving the same output return, thus this is optimum point and no change should be brought. Hence Option 2 will be suitable.