Question

Suppose a single parent can work up to 16 hours per day at a wage rate of $10 per hour. Various income maintenance programs have been developed to assure a minimum level of income for low-income families. Aid to Families with Dependent Children (AFDC) was established with the Social Security Act of 1935. The family was given an income subsidy depending on fam-ily size. Under this program, the family’s benefi t was reduced by $1 for every dollar earned. Suppose the maximum daily subsidy for the single parent described in this problem is $40. a. Draw the daily budget constraint without program participation for the single parent described in this problem. b. On the same graph, draw the daily budget constraint under AFDC for the single parent described in this problem. c. What effect does this program have on the incentive to work? Explain.

Answer 1

a) A single parent has a total of 16 hours in a day to divide between leisure and labor. The wage rate is $10 per hour. This means the maximum amount that the single parent can earn is $160 (=$10*16).

The daily budget constraint of the single parent is required to be drawn. There is also a government subsidy program for single parents. But in part (a), the budget constraint is required to be drawn without taking the government subsidy program into account.

As shown in Figure,the vertical intercept of the daily budget constraint is $160,i.e. the maximum amount the single parent can earn.

b) Under the government subsidy program, each single parent is allowed a daily subsidy of $40.this means even if the single parent spends his/her entire time in leinsure, he/she will have an income of $40.

Under the program, the daily subsidy reduces by $1 for every dollar earned. This means even if the single parent spends equal to or less than four hours working. the income will remain $40, because the subsidy will reduce equivalent to the amount earned.

Since there is no subsidy when the single parent spends more than or equal to 4 hours working. we know that the maximum amount the single parent can earn is still $160.

The daily budget constraint with program participation is the red curve shown in figure 2.

c) If, Without the program, the optimal number of labor hours for the single parent is lessthan or equal to 4 hours, the single parent would be earning less than or equal to $40.

In that case, the single parent's incentive to work will decline due to the government's subsidy program because the single parent will be able to get an income of $40 regardless of whether the single parent works or not.