John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where I < B. The competitive equilibrium price ratio is p/py = C. Which of the following is true? a. C> B. b. C < J. c. C = J. d. C = B. e. J

John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where I < B. The competitive equilibrium price ratio is p/py = C. Which of the following is true? a. C> B. b. C < J. c. C = J. d. C = B. e. J

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

See similar textbooks

Similar questions

Pareto eliminated psychology from economics:a. by defining utility as ordinal, not cardinal utilityb. searching for secondary qualities of thingsc. defined rationality as consumer behavior only after they have bought something several timesd. by accepting revealed preference.
Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.
A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6y0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?
Continue to consider Ronald from Q1. Suppose that Ronald’s preferences over movies and climbing are such that he likes them exactly equally: he is always willing to trade one movie for one climbing session and remain exactly as well of as he was before. One valid utility representation of Ronald’s preferences is u(x, y) = x + y. (a) On the same picture as before, plot indifference curves for the utility levels u = 5.8, 10, 14.2, 18.4. (b) Compute Ronald’s marginal utilities for each good. Using the marginal utility formulas you have just computed, prove that Ronald’s preferences are strongly monotone. (c) i. Label three distinct bundles (x, y) on the indifference curve corresponding to a utility of 5.8. ii. Hence, or otherwise, argue that his preferences are not strictly convex. (d) i. Explain why Ronald’s optimal consumption bundle must lie on the outer boundary of his budget set. ii. Identify Ronald’s optimal bundle by visual inspection. Briefly explain what you did. iii. Find…
Student question Time Left :00:09:43Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = 2X + Y UB(X,Y) = Min(X,Y) The initial endowments are: A: X = 5; Y = 3 B: X = 2; Y = 2 a. Illustrate the initial endowments in an Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer’s indifference curve that runs through the initial endowments. Is this initial endowment Pareto Efficient? b. Now suppose Consumer A gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”) c. Now suppose Consumer B gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”)
Suppose pizza(P) and hamburger(H) are perfect substitutes for Andy. He is always willing to substitute two pizzas for one hamburge(b) The price of pizza is pP = $2 per pizza and the price of hamburger is pH = $2 per hamburger.What is Andy’s optimal consumption bundle if his income level is $30?(c) To promote the sale of pizza, now the owner of the pizza restaurant decides to give out the first two pizzas to every consumer for free, and af- terwards, if the consumer wants more, the consumer will still pay at the price of pP = $2 per pizza. If the price of hamburger and Andy’s income are same as before,draw Andy’s budget line. What is Andy’s optimal con- sumption bundle in this case?(d) Now,to promote the sale of pizza, instead of giving out the first two pizzas for free, the owner of the pizza restaurant decides to lower the price of pizza to $0.8 per pizza. Given price of hamburger and Andy’s income remain the same as before, what is Andy’s optimal consumption budle now? Compare with…
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)− according to the Cobb-Douglas utility function U(x,y,z)=x0.5y0.5(1+z)0.5. Suppose also that the prices for these goods are given by px=1,py=4, and pz=8 and that this consumer's income is given by I=8.a. Show that, for z=0, maximization of utility results in the same optimal choices as in Example 4.1 . Show also that any choice that results in z>0 (even for a fractionalz ) reduces utility from this optimum.b. How do you explain the fact that z=0 is optimal here?c. How high would this individual's income have to be for any z to be purchased?
Calculate the demand for goods for Mad HatterAssume Mad Hatter has utility U = q1M * (q2M)^2. He maximises his utility given his budget constraint. He does not have any income, but can sell his endowment (12 apples, 3 bananas) to get money to buy what he wants. Calculate his demand for apples and bananas.
Suppose there are two individuals, Jane and Keith. Jane's utility function is Uj = XY, while Keith’s is Uk = X^2 Y^2 . Where X and Y are two separate goods. a) Find the marginal utilities of the two goods for Jane and Keith. b) Sketch the marginal utilities for Jane and Keith. c) What do the marginal utilities tell us about their tastes? d) Show by implicit differentiation that, for any given combination of X and Y, Jane's indifference curve has the same slope as Keith's.
You are choosing between two goods, X and Y, and your marginal utility from each is shown in the following table. Units of X MUx Units of Y MUy 1 10 1 8 2 8 2 7 3 6 3 6 4 4 4 5 5 3 5 4 6 2 6 3 a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? ______units of X and ______units of Y b. What total utility will you realize? ______utils c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? _____units of X and ______units of Y d. Using the two prices and quantities for X, complete the table to derive the demand schedule (a table showing prices and quantities demanded) for X. Instructions: Start with the highest price first Price of X Quantity Demanded of X $ $
Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B, according to the utility functionU(C, D) = 25[C−3 +4D−3]−4 +25. While Lucas would like to consume as much as possiblehe is limited by his income. Maximize Lucas’ utility subject to the budget constraint usingthe Lagrangean method.
I need help with this question in my homework. Suppose a consumer’s utility function is given by U(X,Y) = MIN (5X, Y). Also, the consumer has $60 to spend, and the price of good X is P(x) = $5. Let good Y be a composite good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. What is the Indirect Utility Function? What is the Expenditure Function?