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Chapter 3: Problem 2

Draw indifference curves that represent the following individuals' preferences for hamburgers and soft drinks. Indicate the direction in which the individuals' satisfaction (or utility) is increasing. a. Joe has convex indifference curves and dislikes both hamburgers and soft drinks. b. Jane loves hamburgers and dislikes soft drinks. If she is served a soft drink, she will pour it down the drain rather than drink it. c. Bob loves hamburgers and dislikes soft drinks. If he is served a soft drink, he will drink it to be polite. d. Molly loves hamburgers and soft drinks, but insists on consuming exactly one soft drink for every two hamburgers that she eats. e. Bill likes hamburgers, but neither likes nor dislikes soft drinks. f. Mary always gets twice as much satisfaction from an extra hamburger as she does from an extra soft drink.

Short Answer

Expert verified
Joe has downward sloping convex curves; Jane has a vertical indifference curve; Bob has upward sloping curves; Molly has a line at 45 degrees; Bill has a horizontal curve; and Mary has steep curves.

Step by step solution

01

Analyzing each part

Divide the task into smaller parts, each case will be examined individually.
02

Drawing for Joe

Draw the quadrant with hamburgers on the x-axis and soft drinks on the y-axis. Draw a convex curve from the right corner of the x-axis. Convex curve shows decreasing marginal rate of substitution, which means Joe is willing to give up fewer and fewer hamburgers for each additional soft drink consumed. Also, his satisfaction level is decreasing in both goods.
03

Drawing for Jane

Jane's indifference curve will be a horizontal line on the x-axis. This line represents that she will only consume hamburgers and not consume any soft drinks.
04

Drawing for Bob

Bob's indifference curves will be similar to those of Jane but with a slight upward slope. This indicates that he will consume some soft drinks out of politeness but prefers hamburgers much more.
05

Drawing for Molly

Draw a line tilted 45 degrees from the origin. This reflects the preference of Molly to consume 2 hamburgers for each soft drink. At any point on the curve, the ratio of hamburgers to soft drinks is 2:1.
06

Drawing for Bill

Bill's indifference curve will be vertical on the x-axis. This line shows his preference for only hamburgers and neutrality to soft drinks.
07

Drawing for Mary

Finally, draw a curve which is twice as steep for a hamburger than a soft drink. This reflects Mary's marginal rate of substitution, she substitutes hamburgers for soft drinks at a 2:1 rate.

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Most popular questions from this chapter

Jane receives utility from days spent traveling on vacation domestically \((D)\) and days spent traveling on vacation in a foreign country ( \(F\) ), as given by the utility function \(U(D, F)=10 D F .\) In addition, the price of a day spent traveling domestically is \(\$ 100,\) the price of a day spent traveling in a foreign country is \(\$ 400,\) and Jane's annual travel budget is \(\$ 4000\). a. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200 b. Graph Jane's budget line on the same graph. c. Can Jane afford any of the bundles that give her a utility of \(800 ?\) What about a utility of \(1200 ?\) d. Find Jane's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country.

The utility that Meredith receives by consuming food \(F\) and clothing \(C\) is given by \(U(F, C)=F C\). Suppose that Meredith's income in 1990 is \(\$ 1200\) and that the prices of food and clothing are \(\$ 1\) per unit for each. By \(2000,\) however, the price of food has increased to \(\$ 2\) and the price of clothing to \(\$ 3 .\) Let 100 represent the cost of living index for \(1990 .\) Calculate the ideal and the Laspeyres cost-of-living index for Meredith for 2000 . (Hint: Meredith will spend equal amounts on food and clothing with these preferences.)

Connie has a monthly income of \(\$ 200\) that she allocates between two goods: meat and potatoes. a. Suppose meat costs \(\$ 4\) per pound and potatoes \(\$ 2\) per pound. Draw her budget constraint. b. Suppose also that her utility function is given by the equation \(U(M, P)=2 M+P .\) What combination of meat and potatoes should she buy to maximize her utility? (Hint: Meat and potatoes are perfect substitutes.) c. Connie's supermarket has a special promotion. If she buys 20 pounds of potatoes (at \(\$ 2\) per pound), she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes) are still \(\$ 2\) per pound. Draw her budget constraint. d. An outbreak of potato rot raises the price of \(\mathrm{po}\) tatoes to \(\$ 4\) per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility?

Ben allocates his lunch budget between two goods, pizza and burritos. a. Illustrate Ben's optimal bundle on a graph with pizza on the horizontal axis. b. Suppose now that pizza is taxed, causing the price to increase by 20 percent. Illustrate Ben's new optimal bundle. c. Suppose instead that pizza is rationed at a quantity less than Ben's desired quantity. Illustrate Ben's new optimal bundle.

In this chapter, consumer preferences for various commodities did not change during the analysis. In some situations, however, preferences do change as consumption occurs. Discuss why and how preferences might change over time with consumption of these two commodities: a. cigarettes. b. dinner for the first time at a restaurant with a special cuisine.
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