Download Econ 4211 Fall 2008 Homework Assignment 6: Budget Constraints and Taxes - Prof. Anna Rubin and more Assignments Economics in PDF only on Docsity! Econ 4211 Fall 2008 Homework Assignment 6 Due Fri Dec 5 November 19, 2008 Problem 1 A businessmen consumes all his earned income. His utility is u (R,C) = R3/4C1/4, where R is leisure in hours and C is consumption in dollars, so MRSR,C (R,C) = 3CR . He gets $100 per hour and has choose the time to devote to work every week. Assume that he faces the following tax schedule (on weekly earnings): Earnings, in $ Income tax rate, in % 1 0-100 0 2 100-600 15 3 600-1500 25 4 1500-3000 28 5 3000-7000 33 6 7000- 35 1. Draw the before and after tax budget constraint of the businessman. 2. Write down the budget constraint for each of the four cases correspond- ing to the four tax brackets (as he can choose to earn any amount.) 3. How many hours per week (out of 168) will the businessmen choose to work? (Hint: guess first that the businessman’s pre-tax earning will fall into, say, the second bracket. Write his utility maximization problem with the corresponding budget constraint you found in the previous question. Solve the problem, i.e., find C, R that will be optimal. Will the pre-tax earnings fall into the second bracket, i.e., is it true that 1 given the optimal R, the earnings, 100 (168−R) are above 100 and below 400? If yes, your guess was correct and you have found a solution, if not, continue with another guess, say, bracket 3, etc.) 4. The businessman faces retirement next year. He expects to receive a third of the after-tax income in the working years in retirement benefits next year. Assume for simplicity the answer you got in 3. is representa- tive for all his working years. Retirement benefits are taxed according to the same schedule (see the table above). Calculate the after-tax re- tirement benefit for the next (retirement) year. What is his tax bracket for the retirement year? Problem 2 (See chapter 22) Assume you start with an economy where any interest derived from savings is subject to tax (capital gains tax). Assume a retiree gets 1 3 of working age income when retired. Assume also, for simplic- ity, the interest payments on loans are not subject to tax deduction. 1. Draw a budget constraint of an individual with c1, consumption in the working years, on the vertical axis; and c2, consumption in the retirement years, on the horizontal axis. Assume an individual can borrow against future income. 2. Suggest a retirement savings plan that will encourage savings. Analyze a possible effect of introducing your plan on individual savings using its effect on the budget constraint in part 1. 3. Extra credit. Pick a utility function, say, u (c1, c2) = ln c1 + ln c2 and the level of earnings during the working years to calculate the effects of the suggested policy on the optimal consumption of such an individual. Problem 3 Assume Ceasar is facing a 31% federal income tax bracket on additional income and Brutus faces a 15% tax rate. The city of Happyville plans to issue bonds (borrow from the public) and the return on these bonds is not subject to income tax. The market rate of return on taxable bonds is 15%. What is the lowest rate of return that the city of Happyville should offer to induce both Ceasar and Brutus to buy its bonds? Assume the city borrows $100 from Brutus and Ceasar. How much will the city of Happyville gain from the tax exemption? (Hint: compare the in- terest payments of the city with and without the tax exemption.) 2
