Question

A firm produces 400 units of output per week and this firms faced with both input and output competitive markets. This produces a revenue of $20,000 per week. The firm could use capital technology (K1) to produce output together with labor in which case each worker would need 2hours to produce 1 unit of output per unit of K1. The firm could use capital technology (K2) in which case the worker would be able to produce 1 unit of output in 30minutes. Each hour of labor time costs $5 and due to the government regulation labor can only work 8 hours per day, 5 days per week.

a. How many workers and units of capital will the firm hire if they use K1 type of capital?

b. How many workers and units of capital will the firm hire if they use K2 type of capital?

c. Suppose the weekly rental cost of capital K1 for each unit of capital is $250 and for each K2 unit is $1,800. What capital will the firm rent? How many workers will the firm employ? How much profit will the firm earn?

d. Suppose the government imposes a 20 percent payroll tax (paid by employers) on all labor and offers a 20 percent subsidy on the rental cost of capital. What equipment will the firm rent? How many workers will the firm employ? How much profit will the firm earn?

Answer 1

Due to government regulation labor can only work 40 hours(8×5) per week.

Answer a)

With capital technology (K1) each worker need 2 hours to produce 1 unit of output.

So 1 worker can produce 20 units(40 hours/2) of output in 1 week and to produce 400 units 20 workers would be required and also 20 units of capital K1.

Answer b)

With capital technology (K2) each worker need 30 minutes or ½ hour to produce 1 unit of output.

So 1 worker can produce 80 units (40 hour/1/2) of output in 1 week and to produce 400 units 5 workers would be required and also 5 units of capital K2.

Answer c)

Given the rental cost of K1=$250 & K2=$1800

If firm works with K1, the unit of capital and worker required will be 20 each and their cost will be (250×20+5×40×20)=$9000.

If firm works with K2, the unit of capital and worker required will be 5 each and their cost will be (1800×5+5×40×5)=$10000.

With technology K1 cost is less so firm will rent K1 and will employ 20 workers.

Given the revenue as $ 20000 the firms profit will be $ 10000.

Answer d)

If govt. imposes 20 % tax on labor then the cost of the labor would increase to $ 6 per hour($5+20% of $5)

If govt. offers 20 % subsidy on rental cost of capital then the cost of the capital K1 will decrease to $ 200 per week($250-20% of $250) and the cost of the capital K2 will decrease to $ 1440 per week($1800-20% of $1800)

At new costs for K1=$200, K2=$1440 & Labor=$6 per hour

If firm works with K1, the unit of capital and worker required will be 20 each and their cost will be (200×20+6×40×20)=$8800.

If firm works with K2, the unit of capital and worker required will be 5 each and their cost will be (1440×5+6×40×5)=$8400.

With technology K2 cost is less so firm will rent K2 and will employ 5 workers.

Given the revenue as $ 20000 the firms profit will be $ 11600.