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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

Debra usually buys a soft drink when she goes to a movie theater, where she has a choice of three sizes: the 8-ounce drink costs \(1.50, the 12-ounce drink \)2.00, and the 16-ounce drink $2.25. Describe the budget constraint that Debra faces when deciding how many ounces of the drink to purchase. (Assume that Debra can costlessly dispose of any of the soft drink that she does not want.

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?

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鈥檚 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鈥檚 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鈥檚 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?

Antonio buys five new college textbooks during his first year at school at a cost of \(80 each. Used books cost only \)50 each. When the bookstore announces that there will be a 10 percent increase in the price of new books and a 5 percent increase in the price of used books, Antonio鈥檚 father offers him $40 extra.

a. What happens to Antonio鈥檚 budget line? Illustrate the change with new books on the vertical axis.

b. Is Antonio worse or better off after the price change? Explain.

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