Question

Assume the average worker has 100 hours of leisure and could earn $10 an hour. Suppose the Social Security disability insurance (DI) program was structured so that otherwise eligible recipients lost their entire disability benefit if they had any labor market earnings at all. Suppose, too, that Congress was concerned about the work disincentives inherent in this program, and that the relevant committee was studying two alternatives for increasing work incentives among those disabled enough to qualify for it. Alternative A was to reduce the benefits paid to all DI recipients (from $500 to $300) but make no other changes in the program.The other (alternative B) for reforming the disability system is to maintain the old benefit levels (for those who receive them) but allow workers to earn up to $300 a month and still keep their benefits. Those who earn over $300 per month would lose all DI benefits.

a) Draw the original budget constraint and the budget constraint under alternative B.

b) Can this program increase labor supply? Explain how it possible or impossible. If possible show how graphically.

c) Can this program have no effect on labor supply? If yes show how graphically.

d) Can this program decrease labor supply? (Hint some current workers are eligible for DI but choose to work instead) Explain how it possible or impossible. If possible show how graphically.

Answer 1

a) The original budget constraint and the budget constraint after alternative B are as follows:

Note that under the original budget constraint, when leisure is 100 (i.e. when labor supply is zero), then point A, not point B, is relevant. That is, when leisure is 100, income is 500. Similarly, in the case of budget constraint under alternative B, when leisure is 70, income is 800.

(b) The program can increase labor supply if the labor supply at the point where the worker attains the highest indifference curve after the program is introduced is higher than the labor supply at the point where the worker attains the highest indifference curve before the program is introduced. In other words, the program can increase labor supply if the labor supply at the point where the worker attains the highest indifference curve with the budget constraint AECD is higher than the labor supply at the point where the worker attains the highest indifference curve with the budget constraint ABCD. This is shown in the following figure, where the labor supply at point E is 30 (= 100 – 70) hours, which is higher than labor supply at point A. Labor supply at point A is 0.

(c) The program will have no impact on labor supply if the point where the worker attains the highest indifference curve after the program is introduced is the same as the point where the worker attains the highest indifference curve before the program is introduced. In other words, the program will have no impact on labor supply if the point where the worker attains the highest indifference curve with the budget constraint AECD is the same as the point where the worker attains the highest indifference curve with the budget constraint ABCD. This is shown in the following figure, where the point where the worker attains the highest indifference curve is point E, both before and after the program is introduced.

(d) The program can decrease labor supply if the labor supply at the point where the worker attains the highest indifference curve after the program is introduced is less than the labor supply at the point where the worker attains the highest indifference curve before the program is introduced. In other words, the program can decrease labor supply if the labor supply at the point where the worker attains the highest indifference curve with the budget constraint AECD is less than the labor supply at the point where the worker attains the highest indifference curve with the budget constraint ABCD. This is shown in the following figure, where the labor supply at point E is 30 (= 100 – 70) hours, which is less than labor supply at point F. Labor supply at point F is 70 (= 100 – 30).