Q1. For each of the utility functions below, show whether the indifferencecurve for U = 8 is convex or not by showing whether the MRS is diminishingor not as x increases.a. U (x, y) = x + 2yb. U (x, y) = x³y²1c. U (x, y) = x² + 2yd. U (x, y)x² + y²=

Marginal Rate of substitution is the capability of the consumer to give up on a particular good and…

Answered: Q1. For each of the utility functions…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Since the consumer is indifferent between all points on an indifference curve, no point is preferred. True False
Q5. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has an income of $120; novels cost $5 each, while DVDs are priced at $15 each. [Hint: MUx=2xy2, MUy=2x2y] a) Sketch Jason's budget constraint, indifference curves and the interior solution in a graph. b) Calculate Jason's optimal consumption bundle, and his maximized utility level. Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. c) Calculate his new optimal bundle, show it in the same graph from a), and interpret the Marginal Rate of Substitution (MRS) at this new optional bundle (point).
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Emily is a utility maximizer. Her income is $100, which she can spend on cafeteria meals and on notepads. Each meal costs $5 and each notepad costs $2. At these prices Emily chooses to buy 16 cafeteria meals and 10 notepads. a) Draw a diagram that shows Emily’s choice using an indifference curve and her budget line, placing notepads on the vertical axis and cafeteria meals on the horizontal axis. Label the indifference curve, I1, and the budget line BL1. Make sure you calculate the endpoints of the budget constraint. b) The price of notepads falls to $1; the price of cafeteria meals remains the same. On the same diagram, draw Emily’s budget line with the new prices and label it BL2. c) Lastly, Emily’s income falls to $90. On the same diagram, draw his budget line with this income and the new prices and label it BL3. Is she worse off, better off, or equally as well off with these new prices and lower income than compared to the original prices and higher income?
Amy consumes x and y and her preferences can be represented by the following utility function U(x,y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 6- 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain
Consider a consumer with utility function u(x1, x2) = min{4 min{x1, x2}, x1 + x2} (a) Draw indifference curves passing through points (2, 2), (1, 2) and (4, 2). Make sure you correctly determine kink points. What properties of the preferences can you deduce from the shape of indifference curves? (b) When X = R2 +, does UMP have a solution when p1 = p2 = 0? What property of the preference relation did you use to get your answer? (c) Assume that prices are such that p1, p2 2 0 and that p` > 0 for some `e {1, 2} (i.e. the price of at least one good is positive). Derive Walrasian demand. What are the prices for which Walrasian demand is single-valued?
Given that utility function for a consumer is given by u = (x-3)2 + (y-4)2, draw any twoindifference curves for this consumer while clearly labelling the higher one as ‘H’ and lower oneas ‘L’. Does he prefer more of a good to less of it? Does he prefer averages to extremebundles? Explain.
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Q1. For each of the utility functions below, show whether the indifference curve for U = 8 is convex or not by showing whether the MRS is diminishing or not as x increases. a. U (x, y) = x + 2y b. U(x, y) = x³y² c. U(x, y) = x² + 2y d. U(x, y) = x² + y²