Question

Suppose that you initially have \(\$ 100\) to spend on books or movic tickets. The books start off costing \(\$ 25\) cach and the movic tickets start off costing \(\$ 10\) cach. For cach of the following situations, would the attainable set of combinations that you can afford increase or decrease? a. Your budget increases from \(\$ 100\) to \(\$ 150\) while the prices stay the same. b. Your budget remains \(\$ 100,\) the price of books remains S25, but the price of movie tickets rises to S20. c. Your budget remains \(S 100,\) the price of movie tickets remains \(\$ 10,\) but the price of a book falls to \(\$ 15\).

Short answer

(a) Increase; (b) Decrease; (c) Increase.

Step-by-step solution

Get the Initial Attainable Set

Initially, with a budget of $100, the possible combinations of books (B) and movie tickets (M) are given by the equation: \(25B + 10M \leq 100\). This means you can buy 4 books (if only books are bought) or 10 movie tickets (if only tickets are bought), or a mix of both.

Situation (a): Increase in Budget

When the budget increases to $150, the equation becomes \(25B + 10M \leq 150\). You can now buy 6 books or 15 movie tickets, or a combination that fits these totals. This increase in budget expands your attainable set of combinations.

Situation (b): Increase in Movie Ticket Price

With the price of movie tickets rising to \(20 while keeping the budget fixed at \)100, the equation changes to \(25B + 20M \leq 100\). This restricts the number of movie tickets you can buy to a maximum of 5. The attainable set of combinations decreases since purchasing movie tickets becomes more expensive.

Situation (c): Decrease in Book Price

When the price of books falls to \(15 with the budget staying at \)100, the equation is \(15B + 10M \leq 100\). You can buy up to 6 books instead of 4, increasing your attainable set of combinations since books are cheaper.

Key concepts

Consumer Choice

Consumer choice is at the heart of budgeting in economics. It revolves around how individuals decide to spend their limited resources to maximize their satisfaction. Imagine you have a budget of $100, and you have to choose between buying books and movie tickets. Every decision you make involves trade-offs, which means choosing more of one good results in choosing less of another. This principle is known as the opportunity cost. When you buy a book, you might have less money to spend on movie tickets, and vice versa. The choice depends not only on your budget but also on your preferences and the prices of the goods in question. By doing this, you aim to reach the most satisfying combination of goods within your budget. Consumer choice is influenced by the desire to achieve maximum utility, which is the satisfaction or pleasure derived from consuming goods.

Price Changes

Prices play a crucial role in consumer decision-making. A change in the price of goods can significantly alter your purchasing decisions. Let's explore how price changes impact what you can afford. Consider two scenarios:

• The price of movie tickets goes up to $20. With a fixed $100 budget, you can now buy fewer tickets than before. Thus, your set of possible combinations is reduced.
• If books become cheaper at $15 each, you can afford more books without having to sacrifice movie tickets. Hence, cheaper books expand your attainable combinations.

While price increases shrink your purchasing options, a decrease can do the opposite, broadening what you can buy within a fixed income. These fluctuations force consumers to continually reassess their purchasing strategies, aligning desires with real possibilities.

Attainable Combinations

In economic terms, attainable combinations are the various mixtures of goods you can buy, given your budget and the prices of these goods.Imagine you have \(100 to spend, and books cost \)25, while movie tickets are $10. You can mix and match these options within your budget. The formula used to describe attainable combinations is: \[25B + 10M \leq 100\]With this, you could buy up to 4 books, or 10 tickets, or a blend of both.When your budget increases or prices decrease, your set of attainable combinations grows. Conversely, if prices rise, your purchasing power diminishes, reducing these options.Consider attainable combinations as a map of possibilities that shift and change with your financial situation and market conditions. It highlights the balance between your financial limitations and your preferences.