Question

ATVs are producedin a competitive labor.Labor demand in this market is given by Ed=100−w and labor supply is given by Es=25+4W.Given the high number of on-the-job injuriesduring product testing, the government hasdecided that workers irrationallyunderestimate the need for worker’s compensation insurance coverage. The government is trying to choose whether to provide worker’s compensation through a payroll tax, or to mandate that all firms in this market must provide their own private worker’s compensation insurancecoverage to all employees. a.Find the initial equilibrium wage and employment before worker’s compensation is provided.

b.If the government implemented apayroll tax to provide worker’s compensation, it would need to tax firms at a rate of $5per hour worked. Find the equilibrium wage and employmentlevel, the firm’s total costof hiring a worker, and the value of the workers’compensation.

c.Now suppose that the government mandates thatfirms provide their own worker’s compensation coverage. The cost to the firms is $5 perhour worked, and on average the workers value the benefit at $2.50 per hour worked. Find the equilibrium wage and employment level,the firm’s total costof hiring a worker, and the value of the workers’ compensation.

d.If the government’s goal is to maximize employment in in this market, should it implement the payroll tax or mandate that firms provide worker’s compensation?

Answer 1

A. In a competitive market, equilibrium wage happens when labor demand=labor supply. In our case, it will happen when

E_d=E_s OR 100-W=25+4W OR 5W=75 OR W=15.

B. In this case, the firm is not paying W, but rather W+5. As is intuitive, this would reduce the demnd they have for labor. Now,

E_d= 100-(W+5) OR 95-W.

Please note tha the worker does not get the extra 5 dollars. So the supply remains the same. Hence, the new equilibrium

95-W=25+4W OR 95-25=5W OR 70=5W OR W=14.

Employment level is 95-14=81.

Firm's cost of hiring a worker is 14+5=19.

Value of worker's compensation is 14, since the worker doesnt value the benefit of coverage.

C. In this case, the cost to firm is W+5, while the value to the worker is w+2.5. So, at equilibrium

100-(W+5)=25+4*(W+2.5) OR 95-W=25+4W+10 OR 95-35=5W OR 60=5W OR W=12.

Employment level= 100-12=88.

Firm's cost of hiring a worker= 12+5=17.

value of worker's compensation=12+2.5=14.5

D. As seen above, payroll tax gives an emplyment level of 81, while firm providing the compensation gives an employment level of 88. So the government should let the firm provide the compensation.