Suppose the consumer's utility u: X → R is strictly conver i.e. such that any x,y EX with r y and any 0 < X < 1 have Au(x) + (1 − λ)u(y) > u(λx + (1 − X)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 benig strictly convex, u is increasing. Explain why the consumer will spend all their money on one good.

Suppose the consumer's utility u: X → R is strictly conver i.e. such that any x,y EX with r y and any 0 < X < 1 have Au(x) + (1 − λ)u(y) > u(λx + (1 − X)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 benig strictly convex, u is increasing. Explain why the consumer will spend all their money on one good.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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I need help checkin my own answers to this homework question as im not sure of my own answers. The info for the question is attached the question: How much X and Y should the consumer purchase in order to maximize her utility? i got x =4.5 and y =18. is that correct?
U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
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21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =
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