Question

Draw a graph with leisure on the horizontal axis and income on the vertical axis. Assume 320 discretionary hours in a month, that can be used for labor or leisure, and that the wage is $13 an hour. Draw the budget constraint, and an indifference curve corresponding to choosing a full time 160 hour a month job. Label earnings.

Assume the family would qualify for $785 in TANF benefits each month if hours of labor are zero. The program offers a $225 earned income disregard, and then a 50% benefit reduction rate. Add this TANF program to the budget constraint. Label kink points and the level of earnings at which TANF benefits are eliminated. Based on your graph, does the household choose to work a full time job, or opt for participation in the TANF program?

Answer 1

The graph is as shown

when leisure = 0 hours, then an individual can earn $4160 ( 320 x13).

when leisure = 320 hours, then an individual can earn $0.

Since utility function not given, assuming that it will have convex indifference curve.

If an individual doing work for 160 hours, then he will earn $2080 (160x13). Represented by point A in the diagram.

if labor income = 0, then the family can get TANF of $785. That is shown in the horizontal line which cuts original budget constraint at 259.62 hours ( 320 - 60.38 ) of leisure.

The program offers a $225 earned income disregard, and then a 50% benefit reduction rate.

That means it will increase the income at each point by $225 and also changes the slope by having 50% benefit reduction rate. So, the purple curve shows the budget constraint subject to these things.Because now, working for 50 hours could generate income of 1200 (because 50 hours * ($13 + $6.5) + 225).

There are 3 kink points in the model. And the last budget constraint after all these manipulations has been highlighted by green color.

At B kink point and the level of earnings= 945 at which TANF benefits are eliminated.

An optimal household would like to maximize their utility at Kink B, if they weigh leisure and labor equal. (Normally this factor depends on utility function)