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Chapter 3: Problem 9

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
The budget constraint faced by Debra when deciding how many ounces of the drink to purchase at a movie theater is described by the equation \(1.5X + 2.0Y + 2.25Z = M\), where X, Y, Z denote the number of 8, 12, 16 ounces drinks she purchases and M denotes the total amount she is willing spend. This equation ensures that her total expenditure does not exceed her budget

Step by step solution

01

Define the Variables

Let X be the number of 8-ounce drinks, Y the number of 12-ounce drinks, and Z the number of 16-ounce drinks. Prices are expressed in dollars and ounces.
02

Formulate the budget constraint

Her budget constraint is determined by the number of ounces she wants to purchase and the cost of each size of a drink. Assuming she wants to buy a a total of N ounces and spends the entire amount on drinks, her budget constraint can be stated as: \(1.5X + 2.0Y + 2.25Z = M\), Where M is the total amount of money she is willing to spend.
03

Express individual consumption options

This equation represents her budget constraint. For each drink size, the amount spent buying each one (the price times the number purchased), should add up to her total spending M. For instance, if Debra want to buy 16 ounces, she could buy two 8-ounce drinks (\(2*1.5 = 3.00\)) or one 16-ounce drink (\(1*2.25 = 2.25\)). In selecting between these and possibly other choices, Debra maximizes her overall satisfaction given her consumption possibilities as defined by the budget constraint.

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Most popular questions from this chapter

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.

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 Bridget and Erin spend their incomes on two goods, food \((F)\) and clothing (C). Bridget's preferences are represented by the utility function \(U(F, C)=10 F C,\) while Erin's preferences are represented by the utility function \(U(F, C)=.20 F^{2} C^{2}\) 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.

Julio receives utility from consuming food and clothing (C) as given by the utility function \(U(F, C)=F C\) In addition, the price of food is \(\$ 2\) per unit, the price of clothing is \(\$ 10\) per unit, and Julio's weekly income is \(\$ 50\) a. What is Julio's marginal rate of substitution of food for clothing when utility is maximized? Explain. b. Suppose instead that Julio is consuming a bundle with more food and less clothing than his utility maximizing bundle. Would his marginal rate of substitution of food for clothing be greater than or less than your answer in part a? Explain.

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?
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