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Chapter 3: Q9. (page 129)

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.

Short Answer

Expert verified

Debra’s budget constraint will be:

1.9x + 0.7y + 0.14z = 5.75

Step by step solution

01

Definition and equation of a budget line

The data in question suggest that as the size of soft drinks increases, the budget line becomes more inelastic. It can be verified from the following computation.

The per-unit cost for :

8ounces:1.508=1.912ounces:2.0012=0.716ounces:2.2516=0.14

When Debra buys 8-ounce, she pays $1.9 per ounce; when she buys 12-ounce, she pays $0.7 per ounce, and when she buys 16-ounce, she pays $0.14 per ounce.

02

Drawing the budget line

The budget constraint will be given by:

1.9x1 + 0.7x2 + 0.14x3 = 5.75

Where $5.75 is Debra’s income, and x1,x2, andx3 are the three consumption bundles.

The following figure shows Debra’s budget line.

The budget line has two kinks (at 8 & 12) showing different elasticities for different bundles.

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Most popular questions from this chapter

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?

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?

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.

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 the consumption of these two commodities:

a. cigarettes.

b. dinner for the first time at a restaurant with a special cuisine.
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