ECON
PS6s-W08.doc

# Any change in the labor supply of married women in

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Any change in the labor supply of married women in Fligrenia in excess of (or less than) the change in the control location can be attributed to the change in the tax system. b. Which families do you expect to be most affected by this tax change, and why? The tax change would most affect couples with disparate incomes . The current system results in a high tax being paid by the secondary worker, because the primary worker’s earnings “use up” the lower tax rates charged on the first brackets of income. If the primary worker has a very high income relative to the secondary earner, the secondary earner (under the first system) would face high disincentives to working. Under the original tax system, that secondary earner might not work at all. Under the new system, a high-earning primary worker would benefit from having a low-earning spouse, because those low earnings would bring down the couple’s average incomes, possibly placing them in a lower tax bracket. Taxation and Savings 1. Consider a model where individuals live for two periods and have utility functions of the form: U = log (C 1 ) + log (C 2 ). They earn income of \$100 in the first period. They save S to finance consumption in the second period. The interest rate, r, is 10%. a) Set up the individual’s lifetime utility maximization problem. Solve for the optimal C 1 , C 2 , and S. [Hint: rewrite C 2 in terms of income, C 1 , and r.] Draw a graph showing the opportunity set. b) The government imposes a 20% tax on labor income. Solve for the new optimal levels of C 1 , C 2 , and S. Explain any differences between 2

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the new level of savings and the level in part a, paying attention to any income and substitution effects. c) Instead of the labor income tax, the government imposes a 20% tax on interest income. Solve for the new optimal levels of C 1 , C 2 , and S. [Hint: what is the new after-tax interest rate?] Explain any differences between the new level of savings and the level in part a, paying attention to any income and substitution effects. d) Suppose now that the government decides it wants to encourage savings for retirement and decides to subsidize savings instead of taxing it. Specifically, the government now offers a one-to-one match of interest income (for every dollar of interest income that you earn, the government gives you another dollar). Based on your answer to c, how do you think this will affect the level of savings? Why? You need not solve for the new level of S—just explain your answer intuitively. 1. a) Rewrite C2 = (1+r)*S = (1.1)*(100-C1) Max log C1 + log (1.1*(100-C1)) FOC: 1/C1 – 1.1/(1.1*(100-C1)) = 0, so C1=100-C1 C1=50, S=50, C2=55 b) same as a, except income = 100*(1-t) = 100*(1-.2) = 80 Max log C1 + log (1.1*(80-C1)) FOC: 1/C1 – 1.1/(1.1*(80-C1)) = 0, so C1=80-C1 C1=40, S=40, C2=44 Income effect: you are poorer, so you consume less in both periods; you still divide income evenly between C1 and S as in part a.
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• Spring '16
• Taxation in the United States

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