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Chapter 3: Q3. (page 128)

If Jane is currently willing to trade 4 movie tickets for 1 basketball ticket, then she must like basketball better than movies. True or false? Explain.

Short Answer

Expert verified

True, Jane likes basketball better than movies. This is evident because, despite costlier basketball tickets, she is willing to trade for movie tickets, which gives her the same level of satisfaction.

Step by step solution

01

Utility function and cardinal approach

The concept of utility refers to the numerical score representing a consumer's satisfaction from a market basket. A utility function is represented by a set of indifference curves that assigns a level of utility to each market basket.

A utility function that describes how much one market basket is preferred to another is called a cardinal utility function.

The cardinal utility function attaches numerical values to market baskets that cannot arbitrarily be doubled or tripled without altering the differences between the values of various market baskets.

02

Preference for basketball over movies

If Jane is willing to trade movie tickets for basketball tickets, she must like basketball over movies. The number of movie tickets exchanged for basketball is large, which means that basketball is costlier than movie tickets.

However, Jane is at the same level of satisfaction when she receives one basketball ticket in exchange for four movie tickets. This justifies her love for basketball.

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Most popular questions from this chapter

Consumers in Georgia pay twice as much for avocados as they do for peaches. However, avocados and peaches are the same price in California. If consumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher?

Suppose that Jones and Smith have each decided to allocate $1000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games.

a. Draw a set of indifference curves for Jones and a second set for Smith.

b. Using the concept of the marginal rate of substitution, explain why the two sets of curves are different from each other.

Brenda wants to buy a new car and has a budget of \(25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1 to 10, with 10 representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by \)5000. She also observes that as the gas-mileage index rises by one unit, the price of the car increases by \(2500.

a. Illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her \)25,000 budget. Place gas mileage on the horizontal axis.

b. Suppose Brenda’s preferences are such that she always receives three times as much satisfaction from an extra unit of styling as she does from gas mileage. What type of car will Brenda choose?

c. Suppose that Brenda’s marginal rate of substitution (of the gas mileage for styling) is equal to S/(4G). What value of each index would she like to have in her car?

d. Suppose that Brenda’s marginal rate of substitution (of the gas mileage for styling) is equal to (3S)/G. What value of each index would she like to have in her car?

The utility that Meredith receives by consuming food F and clothing C is given by U(F,C) = FC. 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.)

Suppose that Bridget and Erin spend their incomes on two goods, food (F) and clothing (C). Bridget’s preferences are represented by the utility function U(F, C) = 10FC, while Erin’s preferences are represented by the utility function U(F,C) = 0.20F2C2.

a. With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bridget the same level of utility as the bundle (10, 5). Do the same for Erin on a separate graph.

b. On the same two graphs, identify the set of bundles that give Bridget and Erin the same level of utility as the bundle (15, 8).

c. Do you think Bridget and Erin have the same preferences or different preferences? Explain.
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