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NEW06Answers - YORK UNIVERSITY Arts Economics 2300 D Barry...

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Unformatted text preview: YORK UNIVERSITY Arts Economics 2300 D: Barry Smith Final Exam December 12, 2006 Instructions. The exam consists of 2 parts: A and B. Part A contains choice and is worth 14 marks. Part B contains choice and is worth 36 points. You have 3 hours to complete this exam. You have approximately 40 minutes for part A and 14.0 minutes for part B. Write your answers in the exam booklets that have been supplied to you. Be sure to provide the information requested at the front of the exam booklets. Part A Answer 2 of the following 3 questions. Be sure to define any technical terms entering the questions. Each is worth 7 marks. Note: these questions require careful reasoned explanations. 1. What does it mean'for'c'oiisumerzlpreferences to be convex. Provide a practical explanation. Why is 'co‘nvexity important fo1 identifying the consumer optimum. ‘ \2./ Suppose that a government decides to raise $T by taxing a consumer. Demonstrate that an income tax of $T reduces the utility of a consumer le s than a specific tax on one of the goods. 9%:hat does it mean for a consumer to be risk—averse? Hint: prove that a consume1 who is risk averse will not accept a bet that an actuary would call fair. Part B Answer 4 of the following 57 questions. Each question is worth 9 ' marks 1. A consumer has inter temporal- preferences given by the utility function: U (01,02) — Ci5;0'25; The consumer has 1ncome in each period equal to $100 and can borrow at the interest rate r— — .1. The consumer gets no i erest on anything that is saved. Show the budget of the consumer with a carefully labelled dia— gram. Use this budget to prove that a consumer will never get better off as a result of an increase in the borrowing rate 7'. Show that this result does not depend upon whether the consumer is a saver or a borrower. 74:; (b) Solve for the intertemporal consumptions that maximize utility. Illustrate your results using a carefulity labelled diagram. U! Suppose there are two goods in the world: food and donations to char— ities. Let F stand for food and let the price of food he Pp. Let C stand for contributions to charity. Suppose that the income of the consumer is m. The government taxes income at the rate t. However, contribu— tions to charity are not taxed. Note: If C = 0 then after-tax income is — 15m : m(1 — t). M Figure out the budget constraint for a consumer in this world. Graph it with C on the horizontal axis. What happens to the bud 8t 0f the COIISUIDBI‘ lft I'lSGS. g ( Start from a consumer equilibrium and assume that C is a normal good. Show that (3' could increase or decrease as a result of an increase in 1.5. Explain this in terms of the appropriate Slutsky equation or in terms Q and F being complements or substitutes. ‘1 A consumer has preferences given by U(m1, $2)— — 531222. Prices and in— come are given by 191, p2 and m: p1w1+p2wg. The to ’s are endowments of the goods. (5{ Draw the budget constraint when: p1 2 pg : $1) cal : 4 and (.02 = 6. ()6 Derive the demand curves for the consumer and illustrate the C011— «fumer equilibrium on the budget diagram. Calculate the exact income and substitution effects for 591 when p1 rises to $2. Show all steps. Note: no marks will be given for a purely diagrammatic answer but your results must be illustrated with a carefully labelled diagram. 4. A consumer has preferences over wealth given by U(W) 2 W25 The consumer’s initial'wealth is $200 and she faces a loss of $100 with probability p = .25. {t6 Define the term risk aversion. Is this agent risk averse? Illustrate your results in a carefully laballed diagram. Show that, with these preferences the consumer will not accept a fair bet. :2 (b) What is the expected income of the consumer? {of ‘N hat is the largest premium that the consumer will pay to insure against the loss of $100? 5. Consider a standard labour supply model of an agent who has an en- dowment of time equal to E. There is a consumption good but the consumer has no endowment of this good. Suppose that the price of the consumption good is p and that the wage rate equals 10. (a) Derive the budget line of the consumer and plot it in a diagram with leisure on the horizontal axis. (b) Suppose that the preference of the consumer are given by: U (C, l) = Cl where 0 represents the consumption good and l represents leisure. Show that, regardless of the wage rate, the consumer will always choose leisure to be I = ill/2. (c) A University of Toronto student observed the result that 1 did not depend upon in and immediately concluded that the income and substitution effects of a wage increase must both he 0 for this consumer. Show that the UoiT student is wrong. Solve the following example. Let I, = 1, w = 11 p = 1 and then figure out the income and substitution effects assuming that it) increases to 2. AMW flair? 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