Question

The Greasy Wrench shop specialising in auto repairs rents a building at the corner of 77th and Moonawalker . In the short run ,it can vary its output (the number of cars fixed) only by varying the number of mechanics it employs. Each greasy wrench employee is paid a fixed wages

Over the years , Wu Wei , the owner of Greasy Wrench ,has tried hiring different number of workers . The data about the average productivity of each worker ( also known as average product of labour) for each number of workers are given in the table below

No. of Workers      Average productivity        Total product           marginal product

1                                                 5                                                  -                                  -

2                                                 7                                                 -                                  -

3                                               10                                                 -                                   -

4                                                11                                                -                                 -

5                                               10                                                -                                  -

6                                                9                                                  -                                  -

a) compute the table by calculating the total product of labour and marginal product of labour corresponding to each number of workers

b) At which worker does the law of diminishing marginal returns start wprking ? How do you know ?

c) using the Greasy wrench example , explain why every firm , as it hires more people in an attempt to increase its output , will sooner or later hit the range of diminishing marginal returns

d) When Mr Wei's son looked at the table , he said to his dad , hiring 5th and 6th person makes no sense , Do you agree ? Explain

e) Currently , greasy Wrench employs three (3) workers each of whom is paid $ 300 a day .Determine the average labor cost of repairing a car .

Answer 1

(a) The table would be as below.

L	APL	Q=TPL	MPL
1	5	5	-
2	7	14	9
3	10	30	16
4	11	44	14
5	10	50	6
6	9	54	4

The total product of labor would be , ie average labor product times labor. The marginal product of labor would be the change in total product of labor for a unit increase in labor, ie
MPL = = Γ. ΔΤΡΙ ΑΙ
, and since labor increases by unit, we have $MPL = \Delta TPL$ .

(b) The diminishing marginal product of labor starts working at where L=4. Until L=3, the MPL increases, but at and after L=4, the MPL starts to decrease. Hence, the diminishing MPL starts at where L=4.

(c) As Greasy Wrench, other firms would also face the diminishing MPL as the output increases. In the short run, the firms can change only one factor of production (viz labor). Keeping capital fixed, increasing labor would increase the total product at an increasing rate (positive MPL), but since the capital is fixed, an over-increase in labor would create problems in productions, and decrease the rate of increase in output or TPL (the MPL starts to decrease).

(d) One mayust agree to the claims of Mr. Wei, depending on the price of the product in the market or wage of labor. As the MPL starts to decrease, the APL also decreases, meaning that the average cost of production increases, which happens after L is increased from L=4. But, the firm produces where MRPL (marginal revenue product of labor) is equal to the price, which may happen after L=4. If the price is lower enough, then employing 5th and 6th labor would make sense. If price is not low enough, then employing those 5th and 6th labor would lead to a loss.

(e) We have wage as $300. The average costs would be as below.

L	Q=TPL	(SR)TC (in $)	AC (in $)
1	5	300	60
2	14	600	42.86
3	30	900	30
4	44	1200	27.27
5	50	1500	30
6	54	1800	33.33

The total cost would be the labor employed times the wages. The average cost would be total cost divided by the total product, ie .

4C =

For L=3, we have the total cost as or
TC = 3* $300
or
TC = $900
, and the average cost would be
LAC = TC = $900 – $30
.