Until the late 1990’s, one of the primary federal welfare programs was AFDC — or Aid to Families with Dependent Children. The program was structured roughly similarly to the following example: Suppose you can work any number of hours you choose at $5 per hour and you have no income other than that which you earn by working. If you have zero overall income, the government pays you a welfare payment of $25 per day. You can furthermore receive your full welfare benefits so long as you make no more than a total income of $5 per day. For every dollar you earn beyond $5, the government reduces your welfare benefits by exactly a dollar until your welfare benefits go to zero.
A: Suppose you have up to 8 hours of leisure per day that you can dedicate to work.
(a) Draw your budget constraint between daily leisure and daily consumption (measured in dollars).
(b) If you define marginal tax rates in this example as the fraction of additional dollars earned in the labor market that a worker does not get to keep, what is the marginal tax rate faced by this worker when he is working 1 hour per day? What if he is working 5 hours per day? What if he is working 6 hours a day?
(c) Without knowing anything about tastes, how many hours are you likely to work under these tradeoffs?
(d) The late Milton Friedman was critical of the incentives in the AFDC program and proposed a different mechanism for supporting the poor. He suggested a program, known as the negative income tax, that works something like this: Everyone is guaranteed $25 per day that he/she receives regardless of how much he/she works. Every dollar from working, starting with the first one earned, is then taxed at t = 0.2. Illustrate our worker’s budget constraint assuming
AFDC is replaced with such a negative income tax.
(e) Which of these systems will almost certainly cost the government more for this worker—the AFDC system or the negative income tax? Which does the worker most likely prefer? Explain. (f) What part of your negative income tax graph would be different for a worker who earns $10 per hour?
(g) Do marginal tax rates for an individual differ under the negative income tax depending on how much leisure he/she consumes? Do they differ across individuals?
B: Consider a more general version of the negative income tax, one that provides a guaranteed income y and then reduces this by some fraction t for every dollar earned — resulting eventually in individuals with sufficiently high income paying taxes.
(a) Derive a general expression for the budget constraint under a negative income tax, a constraint relating daily consumption c (in dollars) to daily leisure hours ℓ assuming that at most 8 hours of leisure are available.
(b) Derive an expression for how much the government will spend (or receive) for a given individual depending on how much leisure she takes.
(c) Derive expressions for marginal and average tax rates as a function of daily income I, the guaranteed income level y and the tax rate t. (d) On a graph with daily before-tax income on the horizontal axis and tax rates on the vertical, illustrate how marginal and average tax rates change as income rises.
(e) Is the negative income tax progressive?