1. A government currently has a tax system such that it takes a fixed percentage (t) of any labor income. Consider an alternate proposal called a "negative income tax." You get a guaranteed income (x) even if you choose not to work (like a universal basic income). Then, for any income you earn in the labor market, the government takes a fixed percentage (k). Assume that k > t in order to finance the guaranteed income x. Also assume that the y intercept of the negative income tax plan is lower than the y-intercept of the current tax plan. a. Draw the budget constraint of the current tax system with Leisure (Hours) on the horizontal axis and Consumption ($) on the vertical axis. Assume that there is a total time endowment (E) (split into labor and leisure) and an hourly wage rate (w). Make sure to label the intercepts and calculate the slope of the budget line. b. On a similar (but separate) graph, draw the budget line and label the intercepts and slope of the budget constraint of the negative income tax. c. Say that an individual with typical convex preferences is completely indifferent between the two plans. Illustrate this situation on a new graph with both budget constraints. Do you know for certain under which plan they would work more (i.e. have less leisure). Describe your rationale using income and substitution effects. d. Could there be an individual that would not change their labor/leisure hours under either plan? What types of preferences would they exhibit? (HINT: what would indifference curves look like with no substitution effect?) e. True/False: The less substitutable leisure and consumption are, the less that policy makers have to worry about changes in people's willingness to work as we switch from one system to another.

2. An individual has $100000 in income today, but no income in the future, and we are considering the tradeoff between consumption now and consumption in the future. Assume that consumption now and the future can be considered "normal goods." Let savings be defined as any income not consumed today. a. Draw the budget constraints with a rate of return on savings (interest rate) of 10% and 20%. b. Suppose that indifference curves are perfect complements (L-shaped...with the "kink" occurring whenever consumption today is equal to consumption in the future. Can you tell whether the household will save more or less as a result of the rate increase? c. You are asked to advise Congress on a policy of subsidizing savings in order to increase the amount people save. Specifically, Congress proposes 5% in interest payments in addition to the regular market rate. Evaluate the following statement. "Assuming consumption is a normal good, small substitution effects make it likely that savings will actually decline as a result of this policy, but large substitution effects make it likely that savings will increase." d. True/False: If you only care about whether future consumption increases with this policy, then all you need to know is that consumption is a normal good.

3. Two students will have $210000(!) one year from now. Current borrowing rates are at 5%. Student 1 is a light borrower and borrows $50000 for consumption now. Student 2 is a heavy borrower and borrows $150000 for consumption now. Consumption now and in the future are normal goods, and preferences have our typical assumptions (convex, etc). a. Draw the budget line with intercepts and illustrate the two students' indifference curves at their chosen consumption bundles. b. Suppose the Biden administration drops borrowing rates to 2.5% for the first $100000 borrowed, after which rates go back to 5%. What would our models predict would happen to borrowing (present consumption) for both of these students and explain why? You don't need to draw a graph to answer this question but you could if you want. c. What would our models predict would happen to future consumption for both of these students and explain why? You don't need to draw a graph to answer this question but you could if you want.