Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 10

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's father offers him \(\$ 40\) extra. a. What happens to Antonio's budget line? Illustrate the change with new books on the vertical axis. b. Is Antonio worse or better off after the price change? Explain.

Short Answer

Expert verified
Antonio's budget line for used books shifts outward along the x-axis (horizontal), showing he can afford more used books. However, the budget line for new books remains constant, showing he cannot afford additional new books. Despite the increase in his budget, Antonio is worse off after the price change, as his purchasing power decreased, particularly for new books.

Step by step solution

01

Calculate New Prices

First, calculate the new prices of both new and used books after their respective price increases. A 10% increase on the price of new books which cost $80 gives \(80 * 0.10 = \$8\). The new price for new books is thus \(80 + 8 = \$88\). A 5% increase on the price of used books which cost $50 gives \(50 * 0.05 = \$2.5\). Thus, the new price for used books is \(50 + 2.5 = \$52.5\).
02

Calculate Antonio's New Budget

Next, calculate Antonio's new budget. Initially, Antonio could afford five new textbooks at $80 a piece, thus his initial budget was \(5 * 80 = \$400\). After his father gave him extra $40, Antonio's new budget is \(400 + 40 = \$440\).
03

Construct Initial and New Budget Lines

A budget line represents the number of goods a consumer can afford given the price of goods and their budget. The quantity of a good (in this case, new textbooks) the consumer can afford is found by dividing their budget by the price of the good. The initial quantity of new textbooks Antonio could afford was \(400 / 80 = 5\), and the new quantity is \(440 / 88 \approx 5\). This remains constant on the vertical axis (y-axis). The quantity of used books Antonio could initially afford was \(400 / 50 = 8\) and the new quantity is \(440 / 52.5 \approx 8.38\). This increases on the horizontal axis (x-axis). Thus Antonio's budget line shifts outward along the x-axis.
04

Determine Antonio's Position After the Price Change

Since the price of new books increased more than the price of used books, and Antonio could not get more of the former, but he can afford more of the latter, his purchasing power, especially towards new books has decreased. Therefore, Antonio is worse off after the price change, despite the increase in his budget.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

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.)

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.

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 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?

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 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.

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.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free