Problem 1 bob and bette rhymes with jetty each have

Assignment Help Microeconomics
Reference no: EM13371155

Problem 1. Bob and Bette (rhymes with \jetty") each have Cobb-Douglas preferences for cheese, C, and peanut butter, P (each of which will be measured in ounces1), de ned by the utility function U(C; P) = C P(1 ). However, their preferences are not identical, because
they have di erent values of . Bob's preferences are de ned by Bob = 23 , while Bette has Bette = 13 .

(a) Let's begin by getting a graphical picture of their preferences by plotting their indifference curves.

(i) Compute the formula for Bob's indi erence curves by setting U(C; P) = k for some constant, k, and solving for P as a function of C. [Remember that indi erence curves are just sets of all bundles of cheese and peanut butter that give the same constant|utility.

(ii) Plot two or three of Bob's indi erence curves for di erent values of k on a neat and clear graph. [Your graph does not need to be perfectly precise, but it should be as neat as possible, and it should give a reasonably accurate representation of the shapes of the indi erence curves. For a free, online graphing tool

(iii) Repeat steps (i) and (ii) for Bette's indi erence curves, plotting them on a separate graph.

(iv) Who likes cheese better, and who likes peanut butter better? Explain how you can determine this by looking at the indi erence curves. Also explain how you could have determined it just by looking at their utility functions.

(b) Now let's get more precise about Bob and Bette's likes and dislikes by looking at their MRS's.

(i) Compute Bob's MRS as a function of C and P. Explain what this term means economically, and what it tells us about Bob's preferences, and about his willingness to trade peanut butter for cheese and vice versa.

(ii) Do the same for Bette.

(iii) For any given bundle of cheese and peanut butter, how much more willing is Bob to trade peanut butter for cheese than Bette? How much more willing is Bette to trade cheese for peanut butter than Bob?

(c) Now suppose that Bob has three ounces of cheese and three ounces of peanut butter, and Bette has exactly the same bundle. (We'll assume they both have plenty of crackers.)

(i) How much peanut butter would Bob be willing to give up for one more ounce of cheese, starting from this bundle? Would he be willing to make a one-for-one trade where he gave up one ounce of peanut butter for one ounce of cheese?

(ii) How much cheese would Bette be willing to give up for one more ounce of peanut butter? Would she be willing to make a one-for-one trade where she gave up one ounce of cheese for one ounce of peanut butter?

(iii) Show that both Bob and Bette would be made better o in terms of utility if they made a one-for-one trade in which Bob gave Bette one ounce of peanut butter and Bette gave Bob one ounce of cheese. [Hint: you will need to compute their actual utility.]

(iv) Compute Bob and Bette's MRS's at their new bundles. Could both of them be made any better o if they continued to trade? Explain what economists mean when they say that free trade can make both parties better.

Problem 2. Let's take a look at how we might model the e ect of increased income (or wealth) on people's preferences for di erent kinds of goods. We'll start with a consumer named Florence, and we'll investigate her preferences for food versus all other goods, and her preferences for vacation travel versus all other goods. In other words, we are going to separately look at how Florence feels about trade-o s between food and money, and how she feels about trade-o s between travel and money, but not directly at how she feels about trade-o s between food and travel. This is obviously somewhat unrealistic, because most people probably take their food expenditures into account when deciding how much travel they can a ord, but this is the kind of simpli cation that economic analysts make all the time, and in many cases it is \good enough".

(a) Suppose Florence has Cobb-Douglas preferences over travel, T, measured in weekend trips, and all other goods, Y , measured in thousands of dollars, represented by the utility function U(T; Y ) = T

(i) Compute Florence's MRS of all other goods for travel. (In other words, compute her MRS with travel on the horizontal axis.

(ii) Let's look at a single year in Florence's life. Suppose that her current plan is to consume ve weekend trips and fty thousand dollars worth of other goods this year. What is her willingness to pay for additional units of travel?

(iii) Now, suppose we gave Florence $20,000 worth of non-travel goods, so that her new consumption bundle is ve weekend trips and seventy thousand dollars worth of other goods. This is e ectively the same thing as increasing her income. What is her willingness to pay for additional units of travel now? Compare it to her original willingness to pay. Has it gone up, gone down, or stayed the same?

(iv) Does the e ect of increased income on Florence's willingness to pay for travel seem realistic? Comment on the appropriateness of using a Cobb-Douglas utility function to analyze her travel decisions.

(b) Next, suppose Florence has quasilinear preferences over food, F, measured in pounds of food2, and all other goods, Y , measured in thousands of dollars, represented by the utility function U(F; Y ) = ln F + Y .

(i) Compute Florence's MRS of money for food. (In other words, compute her MRS with food on the horizontal axis.)

(ii) Once again, let's look at a single year in Florence's life. Suppose that she is currently planning to consume two thousand pounds of food and fty thousand dollars worth of other goods. What is her willingness to pay for additional units of food?

(iii) Once again, suppose we gave Florence $20,000 worth of non-food goods, so that her new consumption bundle is two thousand pounds of food and seventy thousand dollars worth of other goods. Again, we have e ectively increased her income. What is her willingness to pay for additional units of food now? Compare it to her original willingness to pay. Has it gone up, gone down, or stayed the same?

(iv) Does the e ect of increased income on Florence's willingness to pay for food seem realistic? Comment on the appropriateness of using a quasilinear utility function to analyze her food decisions.

(c) To convince yourself you fully understand what is going on here, a graph may be useful.

(i) Graph two or more of Florence's indi erence curves for travel and money. Draw a dashed vertical line at ve weekend trips. Graphically show her MRS at ve weekend trips on the two indi erence curves. What has happened to her MRS as she has gotten richer? [Your graph should be neat and clear, but does not need to be precise. There's a handy graph of Cobb-Douglas indi erence curves on page 64 of Varian.]

(ii) Graph two or more of Florence's indi erence curves for food and money. Draw a dashed vertical line at two thousand pounds of food. Graphically show her MRS at two thousand pounds of food on the two indi erence curves. What has happened to her MRS as she has gotten richer?

(iii) If you were a consultant, and a client asked you to analyze consumer decisions about di erent kinds of goods, for what kinds of goods might you choose to use a Cobb-Douglas model of preferences, and for what other kinds of goods might you choose to use a quasilinear model of preferences?

Reference no: EM13371155

Questions Cloud

An investor estimates that there is a 75 chance that a : an investor estimates that there is a 75 chance that a particular mutual funds price will increase to 100 per share
1 throughout history art has been used as propaganda to : 1. throughout history art has been used as propaganda to shape public opinion. propaganda takes many forms such as
As the owner of an independent firm you are looking to : as the owner of an independent firm you are looking to invest within the energy sector. you would like to purchase
Can a corporations annual profit be predicted from : can a corporations annual profit be predicted from information about the companys ceo? forbes may 1999 presented data
Problem 1 bob and bette rhymes with jetty each have : problem 1. bob and bette rhymes with jetty each have cobb-douglas preferences for cheese c and peanut butter p each of
Part i statistical measures statistics is a very powerful : part i statistical measures statistics is a very powerful topic that is used on a daily basis in many situations. for
Comparison between utility companies papercreate energy : comparison between utility companies papercreate energy profiles for two fortune 500 organizations that produce
1 how you will protect an underground pipe line from : 1. how you will protect an underground pipe line from corrosion?2. what are biodegradable polymers? give their
The following data summarize the results from an : the following data summarize the results from an independent-measures study comparing three treatment

Reviews

Write a Review

Microeconomics Questions & Answers

  The free rider problem

Question: Explain why the free rider problem makes it difficult for perfectly competitive markets to provide the Pareto efficient level of a public good.

  Failure of the super committee is good thing for economy

Some commentators have argued that the failure of the “Super committee” is good thing for the economy?  Do you agree?

  Case study analysis about optimum resource allocation

Case study analysis about optimum resource allocation: -  Why might you suspect (even without evidence) that the economy might not be able to produce all the schools and clinics the Ministers want? What constraints are there on an economy's productio..

  Fixed cost and vairiable cost

Questions:  :   Which of the following are likely to be fixed costs and which variable costs for a chocolate factory over the course of a month?  Explain your choice.

  Problem - total cost, average cost, marginal cost

Problem - Total Cost, Average Cost, Marginal Cost: -  Complete the following table of costs for a firm.  (Note: enter the figures in the  MC   column  between  outputs of  0 and 1, 1 and 2, 2 and 3, etc.)

  Oligopoly and demand curve problem

Problem based on Oligopoly and demand curve,  Draw and explain the demand curve facing each firm, and given this demand curve, does this mean that firms in the jeans industry do or do not compete against one another?

  Impact of external costs on resource allocation

Explain the impact of external costs and external benefits on resource allocation;  Why are public goods not produced in sufficient quantities by private markets?  Which of the following are examples of public goods (or services)? Delete the incorrec..

  Shifts in demand and movements along the demand curve

Describe the differences between shifts in demand and movements along the demand curve. What are the main factors which can shift the demand curve? Explain why they cause the demand curve to shift. Use examples and draw graphs to support your discuss..

  Article review question

Article Review Question: Read the following excerpts from the article "Fruit, veg costs surge' by Todd, Dagwell, published in the Herald on January 25th 2011 and answer questions below:

  Long-term growth, international trade & globalization

Long-term Growth, International Trade & Globalization:- This question deals with concepts such as long-term growth, international trade and globalization. Questions related to trade deficit, trade surplus, gains from trade, an international trade sce..

  European monetary union (emu) in crisis

"Does the economic bailout of Spain and Greece spell the beginning of the end for the European Monetary Union (EMU)?"

  Development game “settlers of catan”

Read the rules of the game, the overview and the almanac for the Development Game "Settlers of Catan"

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd