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Let's break down and solve the given problem using the image provided.

### Part a: Finding the values of A and B

The worker views leisure and income as "goods" and has the opportunity to work at an hourly wage of **$10 per hour**.

- The horizontal axis represents **Leisure** (in hours).
- The vertical axis represents **Income** (in dollars).

#### To find A:
- **A** represents the maximum amount of income the worker could earn if they worked the entire day (i.e., 24 hours).
- The worker earns **$10 per hour**, so if they worked for **24 hours**, the maximum income is:
  \[
  A = 24 \times 10 = 240 \text{ dollars}.
  \]

#### To find B:
- **B** represents the maximum amount of leisure the worker could have in a 24-hour period, which is simply **24 hours** (since this is the total time available in a day).
  \[
  B = 24 \text{ hours}.
  \]

So:
- $ A = 240 \text{ dollars} $,
- $ B = 24 \text{ hours} $.

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### Part b: Choosing the number of hours to work

The worker is willing to give up **$12 of income** for each hour of leisure. This describes the worker's **marginal rate of substitution (MRS)** between income and leisure.

- The **wage rate** is **$10 per hour**, meaning the worker earns $10 for every hour worked.
- The worker's MRS is **$12 per hour of leisure**, which means the worker values leisure more than the wage they are being paid (since $12 > $10).

Because the worker values leisure more than what they can earn from working, they will prefer to work **0 hours** and enjoy the full **24 hours of leisure**.

#### Conclusion:
- The worker chooses **0 hours** of work.

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### Recap:
1. $ A = 240 \text{ dollars} $,
2. $ B = 24 \text{ hours} $,
3. The worker will work **0 hours**.

---

Do you want further clarification or have any questions?

Here are five related questions for deeper understanding:
1. How does a worker's marginal rate of substitution affect their work-leisure decision?
2. If the wage increased to $15 per hour, how would the worker's decision change?
3. What happens if the marginal rate of substitution equals the wage rate?
4. How would a diminishing marginal rate of substitution alter the outcome?
5. Could the worker's preferences be represented using indifference curves? If so, how?

**Tip**: The marginal rate of substitution (MRS) reflects how much of one good a person is willing to give up to gain more of another. It's crucial in decision-making involving trade-offs, like the work-leisure choice.

A worker views leisure and income as goods and has an opportunity to work at an hourly wage of $10 per hour. a. What are the values of A and B? b. Suppose the worker is always willing to give up $12 dollars of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?

This problem explores the trade-off between work and leisure. The worker has an hourly wage of $10 and a willingness to give up $12 of income for each hour of leisure. Learn how these rates affect the decision on how many hours to work per day. Suitable for high school students studying economics and mathematics.

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