Question

2. Suppose a labor market where demand and supply for labor are given by: Ld = 1;000 25w Ls = 100+20w where w is the wage rate. Suppose that the government decides that everyone who works ought to exercise. They are considering two ways to do this, either through a payroll tax on workers of $3 per hour per worker which would then be used to provide workers with free health club memberships or through mandating provision of access to health clubs at work (which would also cost $3 an hour per worker). Assume initially that the workers derive no value from the health club membership.

(a) What is the equilibrium before the policies are implemented?

(b) Suppose the policy is implemented through a payroll tax. What is the new equi- librium wage, total compensation for a worker, cost of employing a worker, and labor supplied? What is the tax revenue and DWL? Who bears more of the burden of the tax?

(c) Suppose the government instead imposes a mandate. What is the new equilibrium wage, total compensation for a worker, cost of employing a worker, and labor supplied? What is the DWL? Who bears more of the burden of the cost of the mandate?

(d) Suppose now that the workers value the beneÖt at $2 per hour. What is the new equilibrium wage, cost of employing a worker, and labor supplied? Are the disemployment e§ects of the policy bigger than if the workers did not value the beneÖt? Is the new DWL larger or smaller than with a payroll tax?

(e) Suppose the workers value the beneÖt at $3 per hour. What is the new equilibrium wage, total compensation for the worker, cost of employing a worker, and labor supplied? Are the disemployment e§ects of the policy bigger than if the workers valued the beneÖt at $0 or $2 an hour? What is the new DWL and is it larger or smaller than with a payroll tax, larger or smaller than if the workers value the beneÖt at $2 an hour? Who bears more of the burden of the mandate?

Need c,d,e please

Answer 1

(a) Labor demand function is Ld = 1000-25w and inverse demand-w= 40-L25 Labor supply function isLs-100+ 20w and inverse supply-: w-5-L20 So equilibrium is L -500,W -20 before the policy are implemented 40-5 25 20 =40__ L = 500, W = 20 (b) The new equilibrium is L- 466.66 and w- 18.34 Suppose the policy is implemented through a payroll tax then cost hiring for one labor is 25 20 w + 3. Now the new inverse demand is w+3 40- L/25, so w-37-L/25 So new equilibrium is し/20-5 = 37-L /25 9L 4200 L 4200/9 466.66 And W- 37- 466.66/25 37- 18.66 W 18.34 So the total compensation wage, cost of hiring one worker is 18.34 + 3 21.34 Tax revenue is L*3-466.66 3 1399.98 or 1400 approx. and

DWL= 3 * (500-466.66) * ½ = 50. Here labor demand is more elastic so the foirm will bear less tax burden and workers pay more tax burden. (c) Suppose the g compensation for a workers cost of employing worker is the same as in the part (b). The DWL is the same also as in the part (b). Thus, firm bear less of the cost of the mandate. t instead imposes a mandate. Then the new e

(d) Cost of hiring one worker is w 3 where it used to be w. New inverse demand: w + 3- 40 - Ld/25. The benefit of working is now w + 2 where it used to be w. New inverse supply: w+2--5 Ls/20. Therefore, the equilibrium is: 37 - L/25 7+L/20. Thus, L 4400/9 488.88, w 157,9 17.44 Total compensation for the worker is 17.44 2 19.44, and cost of hiring a worker is 20.44. The disemployment effect with the worker valuing the benefit at $2 is 500-488.88-11.11. The disemployment effect with the worker valuing the mandated benefit at S0 or with the payroll tax is 500 466.66 33.33. The disemployment effects are smaller if the workers value the benefit than with the payroll tax. DWL 3-2 (500-488.33)*1/2-5.55 The disemployment effects are smaller than with the payroll tax or with the worker valuing the mandated benefit at 0 and the DWL are smaller than with the payroll tax or with the worker valuing the mandated benefit at 0. Here, the money wage is lower but total compensation is higher. Firm pays (20.44 20)*488.88 and workers pay (20 the cost, but here the worker gets S2 in benefit. 17.44 )* 488.88. The firm pays less of