A consumer has preferences over bundles of two goods with indifference curves defined by x2 = for k > 0. (a) Find a utility function representing these preferences assuming that the consumer's pref- erences are monotone. (b) Give an example of a utility function representing non-monotone preferences with the same indifference curves. (c) Show that indifference curves of the form x2 = x + k for k = R cannot arise from monotone preferences.

A consumer has preferences over bundles of two goods with indifference curves defined by x2 = for k > 0. (a) Find a utility function representing these preferences assuming that the consumer's pref- erences are monotone. (b) Give an example of a utility function representing non-monotone preferences with the same indifference curves. (c) Show that indifference curves of the form x2 = x + k for k = R cannot arise from monotone preferences.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.4P

See similar textbooks

Similar questions

2. A consumer has a utility fuinction given by a) Derive an expression for the two marginal utilities: MU (x1, 22) and MU2 (21, r2). Since AMRS = -YU use these marginal utilities to derive a simple expression for the MRS (r1, 22). b) Optimal choice on the part of the consumer implies MI RS = -. Suppose M 20, p1 = p2 = 1. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. c) Now keep income at 20, and pi = 1, but set p2 - 2. Show the optimal choice in this case on a well-labelled graplh of the budget set. Inclnde an indifference curve consistent with these preferences.
Question 3Draw indifference curves for the following sets of preferences and indicate the direction inwhich the individuals’ satisfaction (or utility) is increasing. Be specific about slopes when itis necessary. Assume for both parts (a) & (b) that soft drinks are measured on x-axis andhamburgers on the y-axis. (a) Mary always gets twice as much satisfaction from an extra hamburger as she does froman extra soft drink. (b) Bob loves soft drinks but dislikes hamburgers.
A4
Help me with this one
E2
Draw thes e utility functions a) u Cxiy) = 2. %3D
Hi, I need some help with the attached question. It is taken from an optimisation problem set in my intermediate maths for economists course.
1. Consider a utility maximizer with complete, transitive, and monotonic preferences. Sup- pose you have data on the pairs of choices made by the consumer at different times. The bundles comprising these pairs of choices are y = (x1, x2) and z = (21, 22). For each of the scenarios given below, make use of the axiomatic properties of the preferences to say whether y is >, <, 3, E, or incomparable t z. (a) y =(2,4) and z = (1, 4) (b) y =(0,4) and w 3 z, where w =(3, 6) (c) y =(2,4) and z = (6, 3)
3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?
. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.
Dear Expert hero pro Hand written solution is not allowed.
Give examples by drawing a graph of each of the following. Please draw your graphs neatly using a ruler to draw the axes and label your graphs completely. In each case draw ar least three indiffer- ence curves and indicate clearly the direction of increasing prefer- ence. (i) the preferences being convex but not strictly convex. (ii) the preferences being strictly increasing but not convex.