Question

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

The budget line of Antonio has shifted due to changes in prices and increase in his budget. Generally, he can now buy fewer new books, but more used books. Whether he is better or worse off depends on his preference for new versus used books.

Step-by-step solution

Determine the initial budget line

Initially, Antonio can buy several combinations of new and used books. Suppose he spends all his money on new books, the number of new books he could buy would be his total money divided by the price of new books, which is \(\frac{M}{P_{N}}\). Similarly, if he only buys used books, the number of used books would be \(\frac{M}{P_{U}}\). Therefore, the equation of the initial budget line would be \(P_{N}N + P_{U}U = M\) where \(N\) is the quantity of new books, \(P_{N}\) is the price of new books, \(U\) is the quantity of used books and \(P_{U}\) is the price of used books.

Determine the new budget line

After the price changes of the books and the extra money from Antonio's father, the budget line changes. The prices of the new books and used books increase by 10% and 5% respectively, and Antonio receives an extra \(40\) dollars. If he spends all his new money on new books, the number of new books he could buy would be \((M + 40) / (P_{N} · 1.1)\). Similarly, if he spends all his money on used books, the number of used books he could buy would be \((M + 40) / (P_{U} · 1.05)\). Thus, the equation for the new budget line would be \((P_{N} · 1.1)N + (P_{U} · 1.05)U = M + 40\).

Compare the initial and new budget line

Looking at the new budget line compared to the initial one, a couple of things stand out. In terms of new books, Antonio can now buy fewer than before due to the price increase, despite the extra money. But for used books, because the price increase is half as much as the new books, and with the extra money, Antonio can actually buy more used books than before, if he decides to spend all his money on them, potentially improving his ability to buy books overall.

Evaluate Antonio's situation

Whether Antonio is better or worse off depends on his preferences. If he strongly prefers new books, he might be worse off as he can buy fewer new books than before despite the extra money. If he is indifferent between new and used books, or prefers used books, he could be better off as he can now buy more used books than before.

Key concepts

Price Elasticity

Price elasticity measures how much the quantity demanded of a good changes when its price changes. It's a crucial concept in economic studies because it helps to understand consumer behavior when prices fluctuate. In the case of Antonio and his textbooks, the price elasticity will determine how sensitive his purchasing decisions are to the increased prices of new and used books.

When analyzing price elasticity, consider:

• **Elastic Demand:** If a 10% increase in price results in a more than 10% decrease in quantity demanded, the demand is considered elastic. Consumers change their buying behaviors significantly in response to price changes.
• **Inelastic Demand:** Conversely, if the quantity demanded changes little when prices change, the demand is inelastic. This might occur due to lack of substitutes or necessity of the product.

For Antonio, used textbooks might have more inelastic demand if they are seen as good substitutes for new ones or if budget constraints force him to prioritize cost over preference. Understanding how elastic the demand is for each type of textbook helps anticipate how Antonio will adjust his purchases after the price changes.

Consumer Choice Theory

Consumer choice theory explores how individuals decide to allocate their scarce resources among different goods and services to maximize their satisfaction. It involves understanding consumer's preferences, budget constraints, and the prices of goods.

For Antonio, the consumer choice comes down to how he values new versus used textbooks. His decision-making process after the price changes can be understood by:

• **Preferences:** If he prefers the quality or content of new textbooks, he might continue to buy them despite higher costs.
• **Budget Constraint:** Antonio's purchasing options are limited by his budget. With the price increases and additional $40, he needs to rethink how to maximize his book purchases within this altered budget.

Consumer choice theory emphasizes that each consumer makes decisions to obtain the highest satisfaction, known as 'utility,' given their financial limitations. Thus, analyzing Antonio's choice helps us understand his priority between new and used textbooks within his budget.

Indifference Curve Analysis

Indifference curve analysis is a graphical tool used in economics to understand consumer preferences and choices, showing combinations of goods to which a consumer is indifferent. In Antonio's case, it would help illustrate his preferences between new and used textbooks.

Key components of indifference curve analysis include:

• **Indifference Curves:** Each curve represents combinations of two products (e.g., new and used books) that provide the same level of utility or satisfaction to Antonio. If Antonio moves along an indifference curve, he would be equally happy with any combination of new and used books.
• **Budget Line:** This line shows all possible combinations of the goods that Antonio can afford. The intersection of the budget line and an indifference curve represents the optimal choice where Antonio maximizes his utility given his budget.

After the price changes, the budget line shifts, affecting Antonio's ability to reach the same indifference curve as before. If the optimal point moves to a lower indifference curve, it suggests that Antonio may be worse off unless his preferences align more within the affordable combinations.