Question

Suppose the supply curve for life guards is Ls = 40. (Perfectly inelastic labor supply.) Suppose the demand curve for lifeguards is LD = 100 – 20W, where L is the number of lifeguards and W is the hourly wage. Graph the supply and demand curves together. Find the equilibrium wage and employment level. Suppose the government imposes a $1 tax per hour per lifeguard on beaches employing lifeguards. Find the new wage the beach pays, the wage the lifeguard receives, the post-tax employment level and the amount of tax revenue the government collects. What is the incidence of tax in this problem (i.e. how much of the tax do firms pay? How much do workers pay?)

Answer 1

Supply curve for life guards is Ls = 40 and demand curve for lifeguards is LD = 100 – 20W, The graph is shown

below. Equilibrium wage rate is found to be

Ls = Ld

40 = 100 - 20W

W = (100 - 40)/20 = $3 per hour and equilibrium number of lifeguards = 40

There is a $1 tax per hour per lifeguard imposed on the demand side. New equilibrium level of wage rate is

40 = 100 - 20(W + 1)

40 = 100 - 20W - 20

W = (80 - 40)/20 = $2 per hour (received by lifeguards)

W = $3 per hour (after tax wage paid by beaches)

L = 40 lifeguards

Revenue = 40 x 1 = $40.

New wage the beach pays is $3 per hour, the wage the lifeguard receives is $2 per hour, the post-tax

employment level is 40 lifeguards and the amount of tax revenue the government collects is $40.

Firms pay no tax because they are able to shift the entire tax burden on workers (lifeguards). Lifeguards had

perfectly inelastic supply so they bear the entire tax burden of $1 per hour.