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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.

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?

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.

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.

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) = 2M + 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 potatoes 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?
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