Question

The marginal product of a domestic laborer is 5 units per hour. The domestic worker is paid $20 per hour. The management is considering automation. The machine can make 120 units per hour at an hourly cost of $400 per hour.

a. At what level of production can the domestic laborer be competitive with the machine?

b. The union is willing to accept a pay cut to retain jobs. At what salary level does the domestic worker achieve parity with the machine?

c. Non union workers have a marginal product of 3 units per hour. What is their parity wage rate as compared to 1) the machine or 2) the domestic worker?

Answer 1

(a). Marginal product of labour is 5 units/hour.

Wages paid to domestic worker is $20/hour.

The machine produce 120 units/hour.

Machine cost is $400/hour.

So, Machine can produce 120/5 = 24 times more than domestic worker.

Machine cost is higher by $400/$20 = 20 times.

Machine production is higher by 24 times than the domestic workers but Machine cost 20 times higher. So Machine is more useful.

To become competitive with Machine the production level and cost should have increased at same rate.

It means if cost increases by 20 times because then to become competitive production should increase by 20 times.

Therefore, (Machine Production per hour/Domestic worker's production) = 20

Or, (120 units/Domestic worker's production per hour) = 20

Or, Domestic worker's production/hour = 120/20 = 6 units.

So, to become competitive with Machine the level of production by domestic workers should be 6 units/hour. (Ans).

(b). The unions is ready to accept the pay cut. The salary at which domestic worker will be in parity with Machine when the cost is same rate.

The Machine Production is higher by 120/5 = 24 times.

If We use 24 times more Labour then the total cost of domestic workers becomes 24*$20 = $480/hour. But Machine cost is $400/hour.

To maintain parity with Machine the cost 24 labours which is equivalent to Machine should have $400.

The cost of each labour will be = $400/24 = $16.66

Therefore, the pay cut the worker should accept to be parity with Machine is $20 - $16.666 = $3.33

Therefore, the salary level of $16.66/hour domestic worker can be parity with Machine.

(c). Non-union workers have Marginal Product = 3 units/hour

Machine output is higher by 120/3 = 40 times.

So Parity wage rate of Non-union workers with Machine is -

$400/$40 = $10/hour.

Parity wage rate with Machine is $10/hour. (Ans)

Output produced higher by unionised domestic worker is 5/3 = 1.666 times.

To become parity with unionised domestic worker the wage rate of Non-union workers should be $20/1.666 = $12/hour.

Therefore, Parity wage rate of Non-union workers with domestic worker is $12/hour. (Ans)