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 peoples willingness to work as we switch from one system to another.