Consider the following utility functions:Eleanor Rigby !" #, % = #%/10Father McKenzie !* #, % = 100#2%2;where # is one kilogram of apples and % one kilogram of bananas.1) Sketch all the bundles that Eleanor finds indifferent to having 8kg of apples and 2kg of bananas.2) Sketch all the bundles that Eleanor finds indifferent to having 6kg of apples and 4kg of bananas.3) Sketch all the bundles that Father McKenzie finds indifferent to having 8kg of apples and 2kg of bananas.

Consider the following utility functions:Eleanor Rigby !" #, % = #%/10Father McKenzie !* #, % = 100#2%2;where # is one kilogram of apples and % one kilogram of bananas.1) Sketch all the bundles that Eleanor finds indifferent to having 8kg of apples and 2kg of bananas.2) Sketch all the bundles that Eleanor finds indifferent to having 6kg of apples and 4kg of bananas.3) Sketch all the bundles that Father McKenzie finds indifferent to having 8kg of apples and 2kg of bananas.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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Consider the following utility functions: Eleanor Rigby !" #, % = #%/10 Father McKenzie !* #, % = 100#2%2; where # is one kilogram of apples and % one kilogram of bananas. 1) Sketch all the bundles that Eleanor finds indifferent to having 8kg of apples and 2kg of bananas. 2) Sketch all the bundles that Eleanor finds indifferent to having 6kg of apples and 4kg of bananas. 3) Sketch all the bundles that Father McKenzie finds indifferent to having 8kg of apples and 2kg of bananas.
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?
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…
Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Suppose that now Reese loses almost his entire income, so that he is left with only one dollar, i.e. his new income is I0 = 1. If prices are still px = 2, py = 4, what is his new optimal consumption of x and y (Hint: Remember that consumption of both goods must be weakly positive, i.e. x∗ ≥ 0 and y∗ ≥ 0) (a) x∗ = 0.5, y∗ = 0(b) x∗ = 0.25, y∗ = 0(c) x∗ = 0.75, y∗ = 0.25(d) x∗ = 0.75, y∗ = 0(e) x∗ = 0.5, y∗ = 1
Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.
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?
Assume an individual spends all of the their income on a bundle comprised of good #1 and good #2. In particular, their utility function is given by: U(q1,q2) = q12/3q21/3 Assume the price of good #1 is $1 (p1=1) and the price of good #2 is $3 (p2=3). What must the individual's income be if they maximize their utility by purchasing 10 units of good #1?
Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.
I. A)MRS=1/3, B)MRS=1/4, C)MRS=4/3, D)MRS=12 II. A)Rhea should buy more bread, less milk, B)Rhea should buy more milk, less bread, C) Rhea maximizes her utility at bundle A, so she should not change her consumptions of either good, D) Rhea cannot afford bundle A, so she should buy less of both goods III. A)Rhea's MRS at bundle A is greater than the price ratio (Pb/Pm), B)Changing her bundle moves Rhea to a higher indifference curve, C)The slope of the indifference curve (where bundle A is found) is not equal to the slope of Rhea's budget constraint, D)All of the above statements explain your answer to part II.
George has a fixed income and can afford at most 7 units of X if he spends his entire income on X. Alternatively, if he spends all his income on Y, he can afford at most 6 units of Y. Draw George's budget line and an indifference curve such that George chooses to buy 4 pieces of X. Martha has the same income and faces the same prices, yet she chooses to buy 2 pieces of X. In equilibrium, what is George's subjective value of X in terms of Y? What is Martha's? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Why the following variables (x1, x2 and x3) cannot be the Marshallian demandfunctions of a consumer with well–behaved preferences, even when pa ≥ pc.x1(p,y)= y/2pax2(p,y)= (pc y)/2pa pbx3(p,y)= (pa-pc)y/2pa pcHINT: Use properties of the Marshallian demand function to check this.
You have £20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs £2, and each cup of coffee costs £1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. Now suppose the price of telephone calls drops to £1 per hour. What are your optimal choices? What is the resulting utility level? How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Comment on your answer in the context of equivalent variation and compensating variation.