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Chapter 3: Problem 7

The price of DVDs \((D)\) is \(\$ 20\) and the price of \(\operatorname{CDs}(C)\) is \(\$ 10 .\) Philip has a budget of \(\$ 100\) to spend on the two goods. Suppose that he has already bought one DVD and one \(\mathrm{CD}\). In addition, there are 3 more DVDs and 5 more CDs that he would really like to buy. a. Given the above prices and income, draw his budget line on a graph with CDs on the horizontal axis. b. Considering what he has already purchased and what he still wants to purchase, identify the three different bundles of CDs and DVDs that he could choose. For this part of the question, assume that he cannot purchase fractional units.

Short Answer

Expert verified
The budget line would have CD = 7 - 2D as equation and the possible bundles of goods that Philip could purchase with his remaining budget are (0,3), (5,0) and (2,2), representing the numbers of CDs and DVDs respectively.

Step by step solution

01

Drawing the Budget Line

The budget line can be drawn on a graph representing the number of CDs on x-axis and DVDs on the y-axis. The slope of the budget line will be -2, representing the price ratio of DVDs to CDs, i.e., -\($20/$10\). Philip has $100 to spend, already spent $30, so he has $70 left. A point on this line, thus, can be (7,0) when he buys 7 CDs and no DVDs or (0,3) when he buys no CDs and 3 DVDs. Connecting these two points would give the budget line.
02

Identifying Purchase Bundles

Three different bundles Philip can afford include: 1) Buying only more 3 DVDs and no CDs. This bundle will cost $60 exactly fitting his remaining budget. 2) Buying only more 5 CDs. This also exactly fits his budget costing $50. 3) He can purchase two more DVDs and two more CDs. This will cost him $60, leaving $10 within his budget.
03

No Fractional Units

For this exercise it’s assumed that Philip cannot buy fractional units of DVDs or CDs. Therefore, every potential bundle we consider must contain integer quantities of CDs and DVDs. The leftover money from the purchase of any of these bundles is either saved or considered as spent on other goods or services not considered in this exercise.

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Most popular questions from this chapter

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

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.

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.

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.)

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.
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