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 December 12, 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.) Solution 2 See class notes 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 1 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 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.) Solution 3 Optimality conditions for the 5th tax bracket 3C R = 67 C = 100 + 85 ∗ 5 + (15− 6) ∗ 75 + 15 ∗ 72 + 67(168− 30−R) Solution is: R = 17 289 134 = 129. 02, which falls into the range consistent with this tax bracket, [98, 138] .C = 5763 2 = 2881. 5 1. 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? Solution 4 2881. 5/3 = 960. 5, tax bracket 3. Problem 5 (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
