5. Suppose that a consumer's preferences are represented by u(x,y) = xy. A positive monotonic transformation of this function would also represent this consumer's preferences. Which of the following functions also represent this consumer's preferences? And for those that do, show the monotonic transformation that describes this equivalence. a. x²y² b. x²y5 c. x²y² + 100 d. In x + Iny + ln 3

5. Suppose that a consumer's preferences are represented by u(x,y) = xy. A positive monotonic transformation of this function would also represent this consumer's preferences. Which of the following functions also represent this consumer's preferences? And for those that do, show the monotonic transformation that describes this equivalence. a. x²y² b. x²y5 c. x²y² + 100 d. In x + Iny + ln 3

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…
5) Consider indifference curves for the consumption of milk and chocolates (you may assume that both are 'goods'). The indifference curves are drawn with the number of chocolate bars on the horizontal axis and pints of milk on the vertical axis. Suppose that at every point, consumer A's indifference curve is flatter than consumer B's. What can you conclude about consumers A and B tastes and preferences?
7) A consumer has to choose the optimal amount of cheese and crackers to purchase. He or she has drawn his or her budget constraint (BC) and indifference curves on a graph with the amount of cheese (in ounces) on the horizontal axis and the amount of crackers (in packages) on the vertical axis. Which of the following statements is true if the price of crackers declines? The BC shifts to the left (down). The BC shifts to the right (up). The BC rotates such that it intersects the horizontal axis at the same point as before and intersects the vertical axis at a lower point. The BC rotates such that it intersects the horizontal axis at the same point as before and intersects the vertical axis at a higher point.
4. Suppose the consumer's utility u: X → R is strictly conver-i.e. such that any x, y EX with ry and any 0 u(λx + (1 − A)y). (a) Show that the consumer will do one of the following: . Buy nothing. . Spend all their money on good 1. • Spend all their money on good 2. [Hint: The previous question could be helpful.] (b) Suppose that, in addition to behig strictly convex, u is increasing. Explain why the consumer will spend all their money on one good.
3. [In class, we noted that the consumer will spend all their money if they have in- creasing preferences. Here, we give a calculus-based condition for the consumer to spend all their money, that doesn't assume more is always better. The con- dition is a stronger version of what is sometimes called "local non-satiation".] Let E X, and let MU, denote the marginal utility for good i € {1,2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is pr 0 if MU; <0. Argue that the consumer would not optimally choose r. x (b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and u is concave. Explain why r is optimal.
Consumer Theory Daniel spends all his money on only two goods: chocolates (good 1) and milkshakes (good 2). We have information about his purchases, income and prices for 4 weeks: A, B, C and D. For each week, the budget line and the goods bought are shown on the graph below. a) Suppose that Daniel’s preferences are transitive and satisfy "more is better". Shade all the bundles that you are certain are worse for Daniel than bundle A in one colour, and all the bundles that you are certain are better for Daniel than bundle A in a different colour. (You can use different patterns instead of colours.) Indicate which is which. Explain.
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