Consider an income guarantee (traditional means–tested) program with an income guarantee of $5,000 and a phase out rate of 25%. This means that individuals always have at least $5,000 in disposable income but lose 25 cents of the income guarantee for each $1 that they earn in the market. A person can work up to 5,000 hours per year at $10 per hour. Bruno, Damien, and Raja work for 400, 800, and 1500 hours, respectively, under this program. The government is considering altering the program to improve work incentives. Its proposal has three pieces. First, it will lower the guarantee to $2,500. Second, it will introduce an earnings subsidy of 25 cents for each $1 earned up to $10000. So benefits for individuals earning up to $10000 include both the new income guarantee and the earnings subsidy. Then, the benefits will finally be reduced at a phase out rate of 50%, so the individual loses 50 cents of the maximum benefits (which is maximized at $10000) for each $1 that they earn above $10000.

a. Draw the budget constraint facing any individual under the original program in a similar leisure–consumption diagram as in the “optimal labor income taxation” lecture. Assume that leisure is simply 5,000 if the individual does not work and 0 if the individual works 5,000 hours. Also assume that consumption is equal to disposable income. Indicate the choice of each individual on the budget constraint.

b. Draw the budget constraint facing any individual under the proposed new program.

c. For each of the three individuals, explain the impact of the new program in terms of income and substitution effects. Which of the three individuals do you expect to work more under the new program? Who do you expect to work less? Are there any individuals for whom you cannot tell if they will work more or less?