eco204_summer_2009_practice_problem_2_solution

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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 2 Solutions 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. Question 1 Recall that a consumer's consumption set shows the (physically) feasible combinations of goods available to the consumer. Suppose a consumer can only consume combinations in which Q2 Q1 that is, the amounts of good 2 must be less than or equal to the amounts of good 1. Graph the consumption set. Answer: The 45 degree line has equation Q2 = Q1 . Thus, Q2 Q1 is the region that includes the 45 degree line and the area below: The consumption set Q2 Q1 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 2 In a marketing survey, a consumer is asked about her preferences over goods A, B and C. Recall that the symbol f denotes "strictly prefers" and that the symbol ~ denotes "indifferent to". Suppose this consumer says A f B f C f A. (a) Are her preferences complete? Answer: Yes her preferences are complete. Recall that for any pair of goods (or bundles of goods), if someone is able to indicate that they prefer one over the other, or are indifferent between the two, their preferences are "complete". Put differently, if someone's preferences are complete they cannot say "I don't know". With complete preferences, they must say either whether they prefer one over the other or that they are indifferent. (b) Are her preferences transitive? Answer: No. Recall that if someone has transitive preferences then there are no "cycles" in preferences. Here: A f B f C f A so that A is preferred to B, B is preferred to C and C is preferred to A: the final link C f A violates transitivity. Question 3 Suppose 3 individuals, Britney, Jonas and Rihana are asked about their preferences over goods B, E and G. Their responses, in order of preference are: Order Britney Jonas Rihana 1 2 3 B E G E G B G B E That is, Britney's preferences are B f E f G, Jonas's preferences are E f G f B and Rihana's preferences are G f B f E. (a) Suppose Britney, Jonas and Rihana are on a committee and are asked to choose between goods B vs. E on the basis of a majority voting rule. What will be the committee's decision? 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: Britney will vote for B since B f E. Jonas will vote for E since E f B. Rihana will vote for B since B f E. The majority votes for B. (b) Suppose the three individuals are on a committee and are asked to choose between goods E vs. G on the basis of a majority voting rule. What will be the committee's decision? Answer: Britney will vote for E since E f G. Jonas will vote for E since E f G. Rihana will vote for G since G f E. The majority votes for E. (c) Suppose the three individuals are on a committee and are asked to choose between goods B vs. G on the basis of a majority voting rule. What will be the committee's decision? Answer: Britney will vote for B since B f G. Jonas will vote for G since G f B. Rihana will vote for G since G f B. The majority votes for G. (d) Now suppose the committee itself is interpreted as a single individual. Based on the answers in (a) through (c), are the committee's preferences complete? Transitive? Answer: The preferences are complete: in any pair wise comparison, the committee was able to indicate its preferences. In part (a) when asked to compare goods B and E the committee said B f E. In part (b), when asked to compare goods E and G, the committee said E f G. Now combine parts (a) and (b): B f E f G However, in part (c) when asked to compare goods B and G, the committee said G f B. Combining this with parts (a) and (b) yields: B f E f G f B, which violates transitivity. 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 4 (Based on 20072008 Final Exam) 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. Graph these customer's indifference curves. Answer: Let coffee be good 1 on the x axis and cigarettes be good 2 on the yaxis (it actually doesn't matter which good you put on an axis). We're told that consumers find these goods "good" and have increasing marginal rate of substitution. Before doing this, it's a good idea to review the imperfect substitute indifference curve depicted below. Observe how with each additional cup of coffee, the consumer makes a smaller tradeoff with cigarettes. Put simply, the marginal rate of substitution (MRS) is decreasing. Observe that the decreasing MRS indifference curve is "bowed" towards the origin. Thus, if we are top draw an indifference curve with increasing MRS, we would have to draw it "bowed out" from the origin (see below). What does an increasing rate of MRS mean? If the consumer is smoking a lot (and concomitantly having a few cups of coffee) she is willing to give up very few cigarettes for another cup. In a sense she is addicted to cigarettes. Alternatively, if she drinking a lot of coffee, to have another cup of coffee, she is willing to give up a lot of cigarettes. In a sense she is addicted to coffee. It is in this sense that an increasing MRS indifference curve captures "addictive" behavior. Which indifference curve you work with depends on the situation: some people don't get addicted and we should use a decreasing MRS indifference curve for them; others do get addicted and we should use an increasing MRS indifference curve for them. Left: Decreasing MRS indifference curve, Right: Increasing MRS indifference curve 4 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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