In the text, we discussed deadweight losses that arise from wage taxes even when labor supply is perfectly inelastic. We now consider wage subsidies.
A: Suppose that the current market wage is w∗ and that labor supply for all workers is perfectly inelastic. Then the government agrees to pay employers a per-hour wage subsidy of $s for every worker hour they employ.
(a) Will employers get any benefit from this subsidy? Will employees?
(b) In a consumer diagram with leisure ℓ on the horizontal and consumption c on the vertical axes, illustrate the impact of the subsidy on worker budget constraints.
(c) Choose a bundle A that is optimal before the subsidy goes into effect. Locate the bundle that is optimal after the subsidy.
(d) Illustrate the size of the subsidy payment S as a vertical distance in the graph.
(e) Illustrate how much P we could have paid the worker in a lump sum way (without distorting wages) to make him just as well off as he is under the wage subsidy. Then locate the deadweight loss of the wage subsidy as a vertical distance in your graph.
(f ) On a separate graph, illustrate the inelastic labor supply curve as well as the before and after subsidy points on that curve. Then illustrate the appropriate compensated labor supply curve on which to measure the deadweight loss. Explain where this deadweight loss lies in your graph.
(g) True or False: As long as leisure and consumption are at least somewhat substitutable, compensated labor supply curves always slope up and wage subsidies that increase worker wages create deadweight losses.
B: Suppose that, as in our treatment of wage taxes, tastes over consumption c and leisure ℓ can be represented by the utility function u(c,ℓ) = cαℓ(1−α) and that all workers have leisure endowment of L (and no other source of income). Suppose further that, again as in the text, the equilibrium wage in the absence of distortions is w∗ = 25.
(a) If the government offers a $11 per hour wage subsidy for employers, how does this affect the wage costs for employers and the wages received by employees?
(b) Assume henceforth that α = 0.5. What is the utility level us attained by workers under the subsidy (as a function of leisure endowment L)?
(c) What’s the least (in terms of leisure endowment L) we would need to give each worker in a lump sum way to get them to agree to give up the wage subsidy program?
(d)What is the per worker deadweight loss (in terms of leisure endowment L) of the subsidy?
(e) Use the compensated labor supply curve to verify your answer.