ARE100ASP08HW2KEY

ARE100ASP08HW2KEY - 1 Managerial Economics (ARE) 100A...

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1 Managerial Economics (ARE) 100A University of California, Davis Spring Quarter, 2008 Instructor: John H. Constantine KEY —Homework 2: Due Friday April 11, 2008 Problem 1 : (a) Why are standard indifference curves downward sloping? (b) Why are standard indifference curves convex to the origin? (c) Explain why two standard indifference curves cannot intersect. (d) What is meant by the transitivity of preferences ? Draw a set of indifference curves that violate this assumption. (e) What is non-satiation ? Draw a set of indifference curves that violate this assumption. (f) Why is the standard budget constraint downward sloping? (g) Why is the standard budget constraint linear? See text and notes for answers to problem 1.
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2 Problem 2 : Draw the indifference curves for the following individuals’ preferences for two goods: hamburgers and beer. (a) Al likes beer but hates hamburgers. He always prefers more beer no matter how many hamburgers he has. For Al, hamburgers are a “bad.” His indifference curves slope upward and to the right rather than downward and to the left. For Al, U 1 is preferred to U 2 and U 2 is preferred to U 3 . If you instead assumed that hamburgers were a neutral good, then the indifference curves would be vertical and utility is increasing to the right as more beer is consumed. (b) Betty is indifferent between bundles of either three beers or two hamburgers. Her preferences do not change as she consumes any more of either food. Since Betty is indifferent between three beers and two burgers, an indifference curve connects these two points. Betty’s indifference curves are a series of parallel lines with slope of –(2/3). (c) Chris eats one hamburger and washes it down with one beer. He will not consume an additional unit of one item without an additional unit of the other. For Chris, hamburgers and beer are perfect complements, i.e., he always wants to consume the goods in fixed proportions to each other. The indifference curves are L -shaped, with corners on a 45-degree line out of the origin. Hamburgers Beer U 3 U 2 U 1 U 1 U 2 U 3 1 2 3 4 5 6 7 8 9 369 U 1 U 2 U 3 1 2 3 12 3
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3 Problem 3 : (a) On two graphs (top and bottom), graph (i) the total utility function and (ii) the marginal utility function for the following. (i) TU X = 10,000X – 0.2X 2 (ii) TU X = 4X 1/2 (iii) TU X = 8X (b) Do these utility functions exhibit diminishing MU X ? If not, briefly explain what the given utility function implies about consumer tastes and preferences for X. (c) For each utility function, find the satiation values of X and TU, that is, the point where TU is maximized. (i) TU X = 10,000X – 0.2X 2 : MU X = 5,000 – 0.2X. TU increases at an decreasing rate until X = 25,000, at which point TU begins to decrease. MU is downward-sloping and linear; it takes on positive values until it crosses the X-axis at X = 25,000. Maximum utility is reached at X = 25,000 where TU = 1250,00,000. For values of X 25,000, this utility function is consistent with our beliefs about diminishing MU X ; beyond X = 25,000 the implication is that as we consume more X our satisfaction decreases which violates the assumption that more is better.
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ARE100ASP08HW2KEY - 1 Managerial Economics (ARE) 100A...

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