eco204_summer_2009_practice_problem_4

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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 4 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 (ECO 204 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. Let food be on the xaxis and everything else on the y axis. Answer the following questions: suppose that once he has the threshold level of food: (a) He prefers food and everything else as perfect complements. Graph Ajax's indifference curves. (b) He prefers food and everything else as imperfect substitutes with decreasing MRS. Graph Ajax's indifference curves. (c) He prefers food and everything else as perfect substitutes with MRS of 1. Graph Ajax's indifference curves. (d) He prefers food and everything else as perfect substitutes with MRS of 1/2. Graph Ajax's indifference curves. (e) He only cares about everything else. Graph Ajax's indifference curves. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 2 After giving really hard tests in his ECO 200 class, Carlos loves to go out and celebrate over dinner where he likes to have Porterhouse steaks with glasses of Chteau Mouton Rothschild 1986 wine as complements. Let wine be on the xaxis and steak on the yaxis. Draw Carlos' indifference curves given that as he has more steaks, he prefers to have more glasses of wine per steak at an increasing rate. For example, he may have a glass of wine with the first steak; more than 2 glasses of wine with the second steak and so on. There is no one right answer depending on the assumptions you make, there can be a range of correct answers. Question 3 In this question you will practice the CobbDouglas utility function. Ajax has utility function U = Q11/5Q24/5. (a) What are and in U = Q1Q2? (b) Does Ajax's utility function U = Q11/5Q24/5 represent monotone "more is better" preferences over Q1 and Q2? (b) Why does the utility function U = (1/5) log (Q1) + (4/5 log (Q2) also represent Ajax's preferences over Q1 and Q2? (c) Given an arbitrary level of utility, what is the equation of Ajax's indifference curve over Q1 and Q2? (d) Suppose all good are sold at uniform prices. Assume Ajax is a price taker. Show that Ajax will always spend 20% of his income Y on good 1 and the remainder on good 2. (e) Derive Ajax's demand equation for good 1. (f) What is Ajax's price elasticity of good 1? (g) What is Ajax's income elasticity of good 1? (h) What is Ajax's crossprice elasticity for good 1? Question 4 Jenn has utility function U = Q11/5. (a) What are and in U = Q1Q2? (b) Given an arbitrary level of utility, what is the equation of Jenn's indifference curve over Q1 and Q2? 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (c) Suppose all goods are sold at uniform prices. Assume Jenn is a price taker..Show that Jenn will always spend 100% of his income Y on good 1 and the nothing on good 2. Question 5 GIndart has utility function U = min(2Q1 , 4Q2) (a) What are and in U = min(Q1,Q2)? (b) Does GIndart's utility function U = min(2Q1 , 4Q2) represent monotone "more is better" preferences over Q1 and Q2? (c) Suppose GIndart purchases goods 1 and 2 for (uniform) prices P1 and P2. Assume GIndart is a price taker. Derive an expression for GIndart's expenditure on goods 1 and 2. (d) Derive GIndart's demand equation for good 1. (e) What is GIndart's price elasticity of good 1? (f) What is GIndart's income elasticity of good 1? Question 6 (ECO 204 2008 Final Exam Question) Alma's preferences over goods 1 and 2 are given by the utility function: U = Q1 Q2 where Q1 and Q2 are units of goods 1 and 2 respectively. Suppose + = 1. Denote Alma's weekly income by Y. Denote the price of good 1 by P1 and the price of good 2 by P2. (a) Derive Alma's demand functions for goods 1 and 2. Show your calculations. (b) True or false: for a company selling good 1 to Alma any price will maximize revenues. Show your reasoning. (c) True or false: a 10% increase in all prices and Alma's income will not change her optimal consumption of goods 1 and 2. Briefly explain your reasoning. (d) Suppose = 0.25 and = 0.75. Evaluate the statement: "a 100% increase in Alma's income leads to a 25% increase in the consumption of good 1 and a 75% increase in the consumption of good 2". 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 7 (ECO 204 2008 Final Exam Question) Your utility is a function of three goods: U = min(Q1 , Q2 , Q3 ) Denote income by Y and the price of good 1 by P1, the price of good 2 by P2 and the price of good 3 by P3. (a) Derive the demand equations for goods 1, 2 and 3. Explain your reasoning and show all calculations. (b) What is the income elasticity for good 1? Show your calculations. Question 8 In this question you will do a variation of a utility maximization problem (UMP) that we've seen before. Suppose a consumer's utility over 3 goods is given by: U = Q1 Q2 Q3 Denote the consumer's income by Y. Solve for the optimal demands for goods 1, 2 and 3. 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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