Question

Frank spends 75 dollar on 10 magazines and 25 newspapers. The magazines cost \(\$ 5\) each and the newspapers cost \(\$ 2.50\) each. Suppose that his \(M U\) from the final magazine is 10 utils while his MU from the final newspaper is also 10 utils. According to the utility-maximizing rule, Frank should: a. Reallocate spending from magazines to newspapers. b. Reallocate spending from newspapers to magazines. c. Be satisfied because he is already maximizing his total utility. d. None of the above.

Short answer

b: Reallocate spending from newspapers to magazines.

Step-by-step solution

Calculate Total Spending on Magazines

Frank spends 75 dollars on 10 magazines. Since each magazine costs \(\\( 5\), the total spending on magazines is calculated as follows:\[ \text{Total cost of magazines} = 10 \times \\) 5 = \$ 50 \]

Calculate Total Spending on Newspapers

Frank also purchases newspapers with the remaining amount. He buys 25 newspapers, each costing \(\\( 2.50\). The total spending on newspapers is calculated as follows:\[ \text{Total cost of newspapers} = 25 \times \\) 2.50 = \\( 62.50 \]However, the problem statement indicates that Frank spends exactly \\) 75 in total, suggesting there may be an oversight or simplification in the given information. Let's proceed assuming the spending is divided into these given quantities.

Determine Marginal Utility per Dollar for Magazines

The utility-maximizing rule requires us to find the marginal utility per dollar spent. For the magazines:\[ MU_m = 10, \text{ Price per magazine} = \$ 5 \]\[ \text{Marginal utility per dollar for magazines} = \frac{MU_m}{\text{Price}} = \frac{10}{5} = 2 \text{ utils per dollar} \]

Determine Marginal Utility per Dollar for Newspapers

Similarly, calculate the marginal utility per dollar for newspapers:\[ MU_n = 10, \text{ Price per newspaper} = \$ 2.50 \]\[ \text{Marginal utility per dollar for newspapers} = \frac{MU_n}{\text{Price}} = \frac{10}{2.50} = 4 \text{ utils per dollar} \]

Compare Utilities per Dollar and Decide Action

According to the utility-maximizing rule, Frank should allocate more spending towards the good that provides higher marginal utility per dollar. Comparing the results: - Magazines: 2 utils per dollar - Newspapers: 4 utils per dollar Frank gets more utility per dollar from newspapers, so he should reallocate spending from magazines to newspapers.

Key concepts

Understanding Marginal Utility

Marginal utility is a critical concept in consumer choice theory. It describes the additional satisfaction or benefit a consumer gets from consuming one more unit of a good. Imagine you are eating slices of pizza. The first slice might bring you immense joy, but by the fourth or fifth slice, that extra joy (or utility) starts decreasing. This decrease is known as diminishing marginal utility.

In Frank's case, both the magazine and the newspaper offer him a marginal utility of 10 utils. However, the crucial point lies in how much utility Frank gains per dollar spent on each. Calculating marginal utility per dollar helps to determine an efficient budget allocation. For magazines, he receives 2 utils per dollar, while for newspapers, he obtains 4 utils per dollar.

• Marginal utility helps in measuring satisfaction from each additional unit.
• It diminishes as more units are consumed, a phenomenon crucial for budget decisions.
• Evaluating marginal utility per dollar helps in maximizing total satisfaction or utility.

Consumer Choice Theory Explained

Consumer choice theory examines how people make decisions about spending their limited resources, such as time and money, to maximize their satisfaction or utility. Frank's decision about whether to buy magazines or newspapers falls under this framework. The goal for Frank, as a rational consumer, is to maximize his total utility given his budget constraints.

When faced with several choices, consumers like Frank assess the utility they will gain from each option. By comparing the marginal utility per dollar of different goods, Frank can determine which choice will bring him the most satisfaction for every dollar spent.

• This theory helps in understanding and predicting consumer behavior.
• Factors such as budgetary constraints, available choices, prices, and personal preferences come into play.
• Consumers aim to distribute their spending to equalize the marginal utility per dollar across all goods.

Optimizing Budget Allocation

Budget allocation involves planning out how to distribute one's available funds across different goods and services to achieve the highest possible utility. Frank wants to optimize his spending by making sure each dollar he spends results in the maximum satisfaction.

In his case, maximizing satisfaction means reallocating the budget from magazines to newspapers since newspapers offer higher utility per dollar. This approach ensures that every dollar goes to the good that adds the most value to Frank's personal satisfaction. The idea is to align one's spending habits in such a way that the last dollar spent on each good provides the same level of marginal utility.

• Effective budget planning ensures efficient use of available resources.
• Decisions should lead to the maximization of total utility given personal preferences.
• Reallocation should shift funds to goods with higher marginal utility per dollar.

Economic Decision Making

Economic decision making involves evaluating different options and choosing the one that provides the greatest benefit or least cost. This includes analyzing trade-offs where selecting one alternative may mean giving up something else. Frank's decision about buying magazines and newspapers is an example of such trade-offs.

In economic terms, Frank needs to decide between spending on magazines or newspapers, each offering different levels of satisfaction per dollar. His aim is to maximize his utility based on the information he has. By understanding where he gets more value for his money, he can make informed economic decisions that serve his best interest.

• Economic decisions often require considering both implicit and explicit costs.
• Rational choices involve maximizing utility while minimizing unnecessary expenditures.
• Trade-offs entail potential benefits forgone from non-chosen alternatives.