eco204_HW_1_solution

eco204_HW_1_solution - 1 ECO 204 2008‐2009 Ajaz Hussain...

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Unformatted text preview: 1 ECO 204 2008‐2009 Ajaz Hussain HW 1 Solution Question 1 (Based on 2007‐2008 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 y‐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 “textbook” indifference curve depicted in Figure 1: observe how with each additional unit of good 1, the consumer makes a smaller tradeoff with good 2. Put simply, the marginal rate of substitution (MRS) is decreasing. The indifference curve in Figure 1 is “bowed in” to the origin. Thus, if we are top draw an indifference curve with increasing MRS, we would have it “bowed out” from the origin as in Figure 2 below. The indifference curve in Figure 1 is also known as “convex” and the one in Figure 2 is also known as “concave” and will be used later to analyze consumer choice when the consumer engages in “addictive” behavior. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 2 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 3 Question 2 (Based on Summer 2008 Final Exam) 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 (Let food be on the x‐axis and everything else on the y axis): (a) He prefers food and everything else as perfect complements. Graph Ajax’s indifference curves. Answer: Assume that once Ajax has 5 lbs of food, that he prefers food and everything else in 1:1 ratio. In this case, his indifference curves are in Figure 3: (b) He prefers food and everything else as imperfect substitutes with decreasing MRS. Graph Ajax’s indifference curves. Answer: Assume that once Ajax has 5 lbs of food, that he prefers food and everything else as imperfect substitutes. From lecture 1, recall that imperfect substitutes have “bowed in” (convex) shapes. In this case, Ajax’s indifference curves are depicted in ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 4 Figure 4: (c) He prefers food and everything else as perfect substitutes with MRS of ‐1. Graph Ajax’s indifference curves. Answer: Assume that once Ajax has 5 lbs of food, that he prefers food and everything else as perfect substitutes in 1:1 ratio. From lecture 1, recall that perfect substitutes are so called because the MRS is constant. In this case, after Ajax has had 5 lbs of food, the MRS is ‐1 and so Ajax’s indifference curves are depicted in Figure 5: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 5 (d) He prefers food and everything else as perfect substitutes with MRS of ‐1/2. Graph Ajax’s indifference curves. Answer: Assume that once Ajax has 5 lbs of food, that he prefers food and everything else as perfect substitutes in 2:1 ratio (i.e. 2 units of food are traded off for a unit of everything else). From lecture 1, recall that perfect substitutes are so called because the MRS is constant. In this case, after Ajax has had 5 lbs of food, the MRS is ‐1/2 and so Ajax’s indifference curves are depicted in Figure 6: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 6 (e) He only cares about everything else. Graph Ajax’s indifference curves. Answer: Assume that once Ajax has 5 lbs of food that he does not care about food anymore. Ajax’s indifference curves are depicted in Figure 7: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 7 (f) He reaches a “bliss point” at 10 lbs of food a day (Ajax needs to go on a diet!) and 5 units of everything else. Graph Ajax’s indifference curves. What assumption about preferences is being violated? Answer: From lecture 1, recall that the more is better preference assumption rules out “bliss points” (i.e., there can’t be a point where felicity is maximized). In this case, Ajax, by having a bliss point, is in violation of the more is better assumption. His indifference must show a bliss point at (10, 5). Since we don’t know the shape of Ajax’s indifference curves beyond 5 lbs of food, we can draw various shapes, as long as the bliss point is at (10,5). Figure 8 shows a bliss point with a upside down bowl felicity mountain while Figure 9 shows a bliss point with a pyramid felicity mountain: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 8 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 9 Question 3 After giving really hard tests in his ECO 200 class, Carlos loves to go out and celebrate. He likes Porterhouse steaks with Château Mouton Rothschild 1986 wine. Let wine be on the x‐axis and steak on the y‐axis. Draw Carlos’ indifference curves given that as he has more steaks, he prefers to have more glasses of wine per steak. Answer: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto ...
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