Consider two competitive consumers who have the same endowment, with positive current income plotted on the horizontal axis and positive future income on the vertical axis. Each consumer’s current income is taxed at the rate t1 and future income is taxed at the rate t2. The ?rst consumer becomes eligible in the current period to save up to $5000 in a traditional IRA, but there is no change in the consumer’s endowment and no change in the pretax market rate of return on saving, r. The second consumer becomes eligible in the current period to save up to $5000 in a Roth IRA. Again, there is no change in the consumer’s endowment and no change in the pretax market rate of return on saving. Money invested in a Roth IRA cannot be deducted from income tax, but the principal and return on the saving are not taxed.

a. Draw the e?ect on the consumers’ budget sets when they become eligible for the IRAs. Consider separately three cases in which t1 is greater than, less than or equal to t2. Assume that for both consumers borrowing is not tax deductible. Which type of IRA is more favorable for the consumers in each of these cases? Does the answer depend on the consumers’ preferences? If so, how? For each consumer, be as speci?c as possible, showing possible standard indi?erence curves and the slopes of all the segments of the consumers’ budget frontiers.

b. Use indi?erence curves to show that availability of each type of IRA could increase or decrease a consumer’s saving. Explain carefully how your graph(s) show this.