**Unformatted text preview: **University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 5 Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. 1 Note: In some questions I've given guidance on how to derive the demand curve from indifference curve map. In other questions, I have given the demand curve in these questions, it would behoove you to figure out how to get the result. If you get stuck, please do see me or Asad. Question 1 (Based on 20072008 Final Exam Question) In a marketing survey, customers were asked about their preferences over cigarettes and coffee. The results indicate that customers perceive cigarettes and coffee to be pleasurable (`good' goods) and have increasing marginal rate of substitution. (a) Will consumers engage in "addictive" behavior? If so, when will they consume coffee only? (b) In part (a), what happens to coffee consumption as the price of coffee decreases? (c) In part (a), what happens to cigarettes consumption as the price of coffee decreases? (d) In part (a), what happens to coffee and cigarettes consumption as income increases? (e) Will consumers engage in addictive behavior if coffee prices decrease with volume? 1 Note for book: These figures created for HW 2 (20082009). 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 2 (Based on Summer 2008 Final Exam Question) If Ajax if doesn't have at least 5 pounds of food a day, he will die. In fact, with less than 5 pounds of food a day, he doesn't care about anything else. Suppose that once he has the threshold level of food: (a) He prefers food and everything else as perfect complements. Characterize Ajax's optimal choice. In particular is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? (b) He prefers food and everything else as imperfect substitutes with decreasing MRS. Characterize Ajax's optimal choice in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? (c) He prefers food and everything else as perfect substitutes with MRS of 1. Characterize Ajax's optimal choice. In particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? (d) He prefers food and everything else as perfect substitutes with MRS of 1/2. Characterize Ajax's optimal choice. In particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? (e) He only cares about everything else. Characterize Ajax's optimal choice. In particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? (f) He reaches a "bliss point" at 10 lbs of food a day and 5 units of everything else. Characterize Ajax's optimal choice. In particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Question 3 (Summer 2008 Final Exam Question) Meredith has preferences over wine and cheese represented by concentric circles centered around 10 units of cheese and wine. (a) Suppose her felicity is greatest at the center. What happens to Meredith's consumption of cheese as the price of cheese decreases? (b) Suppose her felicity is lowest at the center. What happens to Meredith's consumption of cheese as the price of cheese decreases? 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 4 In this question, you will go over the discussion about subsidizing education. This figure depicts a program in which the government provides a specific level of education for free: it depicts the private budget line and public budget point: In this question, you will analyze two variations of that question: (a) "coupons" that can only be used for education (exactly like gift certificates that can be spent only a certain store) and (b) a cash subsidy. Assume consumer has "imperfect substitutes" preferences over education and everything else, which are each good goods. (a) Suppose the government gives everyone a coupon (voucher) which can be used to obtain the up to 12 years of education for free. Analyze the impact of this policy on optimal choice, "happiness" and education levels. Note: in this question, the consumer will have the option of 12 years of education for free and if she wants more than 12 years of education to pay for additional years of schooling. In the lecture question you had to either go to free public schools for 12 years or go to private schooling for any number of years. (b) Suppose the government gives a cash payment guaranteeing 12 years of education which the consumer can spend however she wishes. Analyze the impact of this policy on optimal choice, "happiness" and education levels. In particular, compare the optimal choices in the coupon versus subsidy programs. Question 5 In this question, you will practice the intertemporal consumption model. Let's use the 2 periods, noinflation, and capital markets model. A consumer has income Y1 and Y2 in T = 1, 2 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain respectively. The consumer can borrow or lend at nominal interest rate i. For simplicity, assume P1 = P2 = 1 (i.e. no inflation). (a) Suppose the consumer has the utility function U = min (C1, C2). Solve for the optimal consumption in T = 1, 2. (b) Interpret your answer for the case when i = 0 (i.e. nominal interest rates are nil). (c) Interpret your answer for the case when i = 1 (i.e. nominal interest rates are 100%). (d) Use the results for C1 = C2 from part (a). When will this consumer be a borrower (lender) in T = 1? Question 6 In this question consider once again the intertemporal consumption, 2 periods, noinflation, and capital markets model, where the consumer has income Y1 and Y2 in T = 1, 2 respectively. The consumer can borrow or lend at nominal interest rate i. You will investigate the effect of higher nominal interest rates on whether someone who is a lender (borrower) continues to be a lender (borrower), and, the impact on utility. You will show: If the consumer is a lender at T = 1, then as nominal interest rates rise, she will continue to be a lender. This should be intuitive: at the current interest rates, if I am lending money, then as interest rates rise, lending becomes even more attractive and so I will continue to be a lender. The impact of rising interest rates on the lenders' utility is obvious: they will be "happier" If the consumer is a borrower at T = 1, then as nominal interest rates rise, she may switch to being a lender 2 . This should be intuitive: at the current interest rates, if I am borrowing money, then as interest rates rise slightly, I may continue borrowing. However, there may come a threshold interest rate, where borrowing becomes too expensive or put it another way, lending becomes more attractive so that I will switch from being a borrower to a lender. The impact of rising interest rates on the borrower's utility, if they continue to be a borrower, is obvious: they will be "sadder" For this question, assume the consumer has CobbDouglas utility function between C1 and C2: U = C1 C2 2 For the book: investigate general equilibrium effect: is it possible that everyone becomes a lender (which is impossible)? Or is there some market clearing condition that ensures that there will always be some lenders and borrowers may have implications for credit crunch and glut. Also investigate the threshold interest rate and the idea that borrower's utility goes down and when they switch to being a lender, their utility increases. Is there for example a "jump"? Actually, we have this result from the Lagrangian already. 4 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Intuitively, the consumer is willing to tradeoff consumption today against consumption tomorrow. She's not like the consumer with U = min (C1, C2) who will do consumption smoothing. In contrast the consumer U = C1 C2 won't necessarily smooth consumption she may or may not. For simplicity, assume P1 = P2 = 1 (i.e. no inflation). (a) Solve the consumer's intertemporal UMP. Hint: it's easier to work with the log transformation of the utility function. (b) When is the consumer a borrower in period 1? What about a lender in period 1? (c) Suppose this consumer is a lender in period 1. Show that if the nominal interest rate rises, she will continue to be a lender. If it helps you can assume that = = , Y1 = 10, Y2 = 5, i = 10%. (d) Suppose this consumer is a borrower in period 1. Show that if the nominal interest rate rises, she may become a lender. If it helps you can assume that = = , Y1 = 5, Y2 = 10, i = 10%. 5 ...

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