REDISTRIBUTION: OKUN'S BUCKET When a worker works, she earns income but she gives up leisure. The benet lost on the leisure foregone is the private marginal cost (PMC) if the worker works an additional hour. In this problem, if the worker L (hours per week), the PMC associated with working an additional hour is: PMC = it. (3 per hour) This is drawn on the attached curve sheets. The government introduces a welfare program. The program is structured so that, if a worker earns no income, he receives a grant of 136 {3 per week) from the government. For each $ the worker earns in a week, the grant is reduced by .4 ($ per week). This process of withdrawal continues until the grant is exhausted. For example, If the worker earns 60 (5 per week), the grant is reduced by .4 (60) = 24 (3 per week); the worker earns 60 ($ per week) from the rm and gets a grant from the government of I36 - 24 = 112 (3 per week), giving a take-home income of 172 (3 per week) total. If the worker has productivity w (S per hour), under perfect competition a rm will pay the worker w (5 per hour). (1) If there is no welfare program, draw the curve which relates the worker's wage to its labor supply. Parts (2) - (5) - by considering a worker's wage w = 10 (5 per hour) - refer to the way the program changes the decisions made by a poor worker and to the welfare cost of the program. Using Curve Sheet A: (2) For a worker with w = 10 ($ per hour): If there is no welfare program, how many hours does the worker work? What is the worker's take-home income? (3) For a worker with w = 10 ($ per hour): If there is a welfare program, how many hours must the worker work if the grant is exhausted? (4) For a worker with w = 10 ($ per hour): If there is a welfare program, how many hours does the worker work? What is the worker's take-home income? (5) For a worker with w = 10 ($ per hour): What is the deadweight loss associated with providing the program to the worker? Part (6) - by considering a worker with wage w = 16 (3 per hour) - shows that the distortions introduced by the program are conned to workers with low wages. Using Curve Sheet B: (6) Show that a worker with w = 16 ($ per hour) is unaffected by the program. 24 CURVE SHEET A 22 20 18 S per hr 16 14 MC 12 101 8 a 2 10 20 30 40 L, hours per week