You have 75 minutes to complete the exam. The exam is worth 75 points: keep track of time.

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1 Midterm Eam #1, brief solutions; Page 1 of 6 Economics 441 Professor Scholz Midterm #1, Version #1 October 11, 2006 You have 75 minutes to complete the eam. The eam is worth 75 points: keep track of time. If ou have a question during the eam, sta seated and please raise our hand. To show respect to our fellow students, please sta seated in our eam seat for the full 75 minutes. Rela, take a deep breath, and think carefull before ou answer an questions. Good luck! 1, 5 points): A member of Congress proposes a new ta schedule for U.S. citizens. The marginal ta schedule would look like: $0 - $20,000-20% $20, % What is the ta liabilit of a household with $100,000 of income? -20% indicates that the Congressperson is proposing a subsid (not a ta) on low incomes. This is similar to the earned income ta credit that is part of the U.S. ta code. A correct answer would make the following calculation: -.2(20,000)+.5(80,000)=$36,000. For what it s worth, under a ta sstem like this, a household would not begin to pa a positive income ta until their income eceeds $28,000. 2, 5 points): Suppose the paroll ta rate on labor is lowered. Which of the following statements is true for everone who had been working before the ta rate change? a) The income effect of the ta rate change induces them to work less. b) The substitution effect of the ta rate change induces them to work more. c) The income effect eceeds the substitution effect. d) All of the above statements are true. e) Both a) and b) are true. A reduction in paroll taes will pivot outward the budget set in the tpical labor suppl diagram (where leisure is on the horizontal ais and dollars are on the vertical ais). With higher after-ta wage rates, the household will take less leisure (and therefore work more), Thus, the substitution effect implies the will work more. With higher income, the household bus more of everthing the like, including leisure, so the both a) and b) are true. 3, 5 points): What is the difference between a ta credit and a ta deduction? A ta credit reduces the ta that is owed directl. As long as a person has a positive ta liabilit, the value of the credit does not depend on the tapaer s marginal ta rate. Put differentl, if a poor person has a ta liabilit of $750 and a rich person has a ta liabilit of $75,000, a $500 ta credit reduces their ta liabilit b the same amount, namel $500. A ta deduction reduces taable income. Ta liabilit is determined b multipling taable income b the average ta rate. Consequentl, the value of a deduction depends on the tapaer s marginal ta rate. A deduction, therefore, is worth more to a tapaer with a high marginal ta rate than it is for a tapaer

2 Midterm Eam #1, brief solutions, Page 2 of 6 with a low marginal ta rate. In t he above eample, suppose the $500 item was instead a deduction and the poor tapaer has an average rate of 10% and the rich tapaer has an average rate of 30%. The deduction would be worth $50 to the poor person and $150 to the rich person. 4, 5 points): True, false or uncertain. Your mark will depend solel on the qualit of our eplanation. There is deadweight loss associated with taes. Therefore, there are no deadweight losses associated with subsidies. Problem set #1 clearl shows (in problem 4) that there are deadweight losses associated with subsidies. The subsid (given no other market distortions) will increase the sum of consumer and producer surplus. This would seem to improve (not reduce) welfare. The deadweight loss arises because the increase in the sum of consumer and producer surplus will be less than the cost of the subsid to the government. Hence, subsidies create deadweight loss. You further know this since ou learned in Econ 301 (and in the first week of Econ 441) that perfectl competitive markets maimize well-being. A subsid drives a wedge between the prices consumers pa and producers receive. Consequentl, the reduce welfare. 5, 5 points): What is the deadweight loss associated with gift giving? Please look at the reading for 9/18 Santa and Deadweight Loss. The inefficienc arises because gifts often are worth less to the recipient than the cost the giver. 6, 5 points): All other things equal, the deadweight loss of a ta on producers is higher when suppl is. All other things equal, the deadweight loss of a ta on producers is higher when demand is. a) elastic; elastic b) unit elastic; elastic c) inelastic; inelastic d) elastic; inelastic e) none of the above. Deadweight loss arises from distortions in the quantities consumed (incidence depends solel on prices, and not quantities). The deadweight loss of a ta is larger the more elastic is demand, and the more elastic is suppl. Absent market frictions, it does not matter whether the ta is levied on consumers or producers. The general formula for deadweight loss is given on page 580 (Megan, let s double check that the DWL is everwhere increasing in the suppl elasticit, since it appears in both the numerator and denominator of the epression). 7, 5 points): Suppose that a person bus a share of stock for $10. The rate of taation on accrual is 50 percent, as is the rate of taation on realization. The da before the person dies, the stock is worth $20, as it is the da after the person dies. If the stock were sold the da before the person died, the government would receive in taes. If the stock were sold the da after the person died, the government would receive in taes. Assume that earnings on assets are taed as the are in the current U.S. sstem. a) $5; $5 b) $0; $5 c) $2.50; $0 d) $5; $2.50

3 Midterm Eam #1, brief solutions; Page 3 of 6 e) None of the above The capital gain on the stock is $10, the difference between the selling price and the buing price. If the stock were sold the da before the person dies, the ta would be $5 (or 50% of $10). If the stock were sold after the person dies, the basis of the stock (the purchase price of the stock) is stepped up to the value of the stock at the time the person dies. Consequentl, there would be no capital gains ta levied. Since $5, $0 is not an option, the correct answer is E. For those wanting to include the estate ta, the estate ta onl affects (roughl) 1% of the people who die in the U.S. in a given ear. Consequentl, the estate ta is irrelevant for the vast majorit of cases where someone dies. Given the magnitudes being discussed in this question, it s unlike that the estate ta would be a relevant consideration. 8, 10 points): With a clearl drawn graphical analsis, eplain how ou would epect IRAs to affect household saving for three cases: a) For a household that was borrowing prior to the introduction of the IRA, b) for a household that was saving less than the IRA contribution limit prior to the introduction of the IRA, and c) for a household that was saving more than the IRA contribution limit prior to the introduction of the IRA. See the attached figures. 9, 15 points): The annual chocolate consumption for our professor is characterized b demand, which equals P= Q d, and suppl, which equals P= Q s. Policmakers are worried about the contribution of chocolate to obesit, since obesit is thought to cost the nation s health care sstem billions of additional, (potentiall) preventable ependitures. Consequentl, the propose a $120 annual ta on chocolate consumption. For 3 points each, please (correctl) answer the following questions. a) What is the original equilibrium price and quantit? b) What is the new (post-ta) equilibrium price and quantit? c) How much revenue does the ta collect? d) Who bears the burden of the ta (what is the incidence of the ta)? e) What is the deadweight loss of the ta? 9a) Set S=D and solve to find Q=0, or Q=20, P=100 9b) The new demand curve is P=380-20Q. Set S=new D and find 360=24Q, or Q=15, P=80. 9c) Ta revenue equals the new quantit times the ta, or 15*120=$180. 9d) The ta is 120. The price producers receive is $80. Consumers are now paing $200: ou can see this b inserting Q=15 into the original demand curve. Therefore, consumers bear ( )/120=5/6 of the ta. Producers bear the remaining 1/6 of the ta. 9e) The deadweight loss is equal to.5*b*h of the welfare triangle. The height of the triangle is 5, the base is 120, so the deadweight loss is $300. The handwritten diagram gives details. 10, 15 points): Recall from the homework that the general formula for the deadweight loss of a s d 2 1 ε * ε τ Q commodit ta is DWL = * *. Suppose households care onl about 2 goods, X and Y, s d 2 ε ε P and their utilit function is U( X, Y) = X Y.

4 Midterm Eam #1, brief solutions, Page 4 of 6 What does the Ramse Rule suggest is the optimal ratio of commodit taes on X and Y if the following is true? For good X the suppl elasticit is 3, income is 50, the P = 1, and TR = 50τ. For good the 1 suppl elasticit is 1, income is 50, the P =, and TR = 200τ. 2 Recall the Ramse formula implies that the ratio of the marginal inefficienc associated with each commodit ta instrument (that is, the marginal deadweight loss) should be equal to the marginal benefit from each ta (that is, the marginal revenue). Hence, for this problem we need to compute the ratios of s d ε * ε τq MDWL/MR for each commodit, X and Y. The MDWL is simpl MDWL =. s d You know ε ε P from problem 5 in the first problem set that that demands from Cobb Douglas preferences are.5 Y P for i the given utilit function and the price elasticit of demand is -1. Therefore, for good X, Q=25 and for MDWL 3( 1) τ (25) 3τ good Y, Q=50. For good X the = =. For good Y, ou know MR MDWL MR 1( 1) τ (50) 2τ τ 2 = =. This implies =. 2(0.5) 8 τ 3 200

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