PS6s-W08.doc

# C same as a except after tax interest rate 1r1 t 1101

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c) same as a, except after-tax interest rate = 1+r*(1-t) = 1+.10*(1-.2) = 1.08 Max log C1 + log (1.08*(100-C1)) FOC: 1/C1 – 1.08/(1.08*(100-C1)) = 0, so C1=100-C1 C1=50, S=50, C2=54 Same as a! Why? Income effect: drop in interest rate has made you poorer; must save more to have same amount of consumption next year, so S increases. Substitution effect: consumption in period 2 has become relatively more expensive, so shift towards more C1 and less C2; S decreases. Net effect is ambiguous; with log utility, two effects exactly offset, so net effect on S is zero. d) Part c showed that a decrease in r does not affect the optimal S. The same is true if government increases r by subsidizing savings. So S=50, as in part a. Again there are income and substitution effects which offset exactly. Income effect: rise in interest rate has made you richer; must save less to have same amount of consumption next year, so S decreases. Substitution effect: consumption in period 2 has become relatively less expensive, so shift towards less C1 and more C2; S increases. 2. The government introduces a tax incentive program in which the first \$5,000 of savings can be tax-deferred. Discuss the effects on saving. 3

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In this budget constraint, the first \$5,000 saved gains more future-period consumption than does other savings, so the slope of that part of the budget constraint is steeper. Any tax that would have been paid on that amount can be invested by the taxpayer, increasing future consumption. Savings in excess of \$5,000 is taxed immediately, reducing future consumption. In the graph below, Y denotes current income. Tax1 denotes tax assessed on the undeferred income; Tax2 is the tax paid on the amount deferred. The bolded kinked line illustrates the tax-deferred budget constraint. 3. Gale and Scholz (1994) estimate that increasing the contribution limits for Individual Retirement Accounts would have little effect on the overall rates of savings. Why do you think this might be the case? Overall savings rates only increase when people take money from current consumption and invest it in savings. When people merely switch from non- IRA savings to IRA savings, the total savings rate is unaffected. One reason for Gale and Scholz’s finding may be that the current IRA limits are so high that most people could not afford to reduce their current consumption further to invest more in retirement savings. Perhaps the only people who could or would increase IRA savings are the wealthy, who already have substantial savings that could be moved to this less-liquid, but tax-favored, form of savings. 4. Suppose that the government proposes to eliminate unemployment insurance. Which  model - the intertemporal choice model of saving or the precautionary saving model -  would predict that this policy change would affect savings the most? Explain your answer  and be sure to note any empirical evidence that might be relevant.
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• Spring '16
• Taxation in the United States

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