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Chapter 9: Problem 9

Patty delivers pizza using her own car, and she is paid according to the number of pizzas she delivers. The accompanying table shows Patty's total benefit and total cost when she works a specific number of hours. $$ \begin{array}{ccc} \begin{array}{c} \text { Quantity of } \\\ \text { hours worked } \end{array} & \text { Total benefit } & \text { Total cost } \\ \hline 0 & \$ 0 & \text { \$0 } \\\ 1 & 30 & 10 \\\ 2 & 55 & 21 \\\ 3 & 75 & 34 \\\ 4 & 90 & 50 \\\ 5 & 100 & 70 \end{array} $$ a. Use marginal analysis to determine Patty's optimal number of hours worked. b. Calculate the total profit to Patty from working 0 hours, 1 hour, 2 hours, and so on. Now suppose Patty chooses to work for 1 hour. Compare her total profit from working for 1 hour with her total profit from working the optimal number of hours. How much would she lose by working for only 1 hour?

Short Answer

Expert verified
Answer: To calculate the difference in total profit, we will subtract the total profit for working 1 hour from the total profit for working the optimal number of hours. This will give us the difference in total profit between these two options.

Step by step solution

01

Find the Marginal Benefit and Marginal Cost of each hour worked

First, we need to find the marginal benefit (MB) and marginal cost (MC) for each hour worked. The Marginal Benefit is the added benefit for each additional hour worked, and the Marginal Cost is the added cost for each additional hour worked. To find the MB and MC, we will calculate the difference between consecutive total benefits and total costs respectively.
02

Find the Optimal Number of Hours Worked

We will compare the marginal benefit (MB) and marginal cost (MC) for each hour worked to determine the optimal number of hours. The optimal number of hours is when the marginal benefit is equal to or greater than the marginal cost (MB >= MC).
03

Calculate Total Profit for each Hour Worked

The total profit is calculated as the total benefit minus the total cost for each hour worked. We can use the table to calculate the total profit for each hour worked (0, 1, 2, and so on).
04

Compare Total Profit of Working 1 hour with the Optimal Number of Hours Worked

Finally, we will compare the total profit of working for 1 hour with the total profit of working the optimal number of hours to find the difference. The difference will indicate how much Patty would lose by working only 1 hour instead of the optimal number of hours.

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Most popular questions from this chapter

Jackie owns and operates a website design business. To keep up with new technology, she spends \(\$ 5,000\) per year upgrading her computer equipment. She runs the business out of a room in her home. If she didn't use the room as her business office, she could rent it out for \(\$ 2,000\) per year. Jackie knows that if she didn't run her own business, she could return to her previous job at a large software company that would pay her a salary of $\$ 60,000$ per year. Jackie has no other expenses. a. How much total revenue does Jackie need to make in order to break even in the eyes of her accountant? That is, how much total revenue would give Jackie an accounting profit of just zero? b. How much total revenue does Jackie need to make in order for her to want to remain self-employed? That is, how much total revenue would give Jackie an economic profit of just zero?

Suppose you have just paid a nonrefundable fee of \(\$ 1,000\) for your meal plan for this academic term. This allows you to eat dinner in the cafeteria every evening. a. You are offered a part-time job in a restaurant where you can eat for free each evening. Your parents say that you should eat dinner in the cafeteria anyway, since you have already paid for those meals. Are your parents right? Explain why or why not. b. You are offered a part-time job in a different restaurant where, rather than being able to eat for free, you receive only a large discount on your meals. Each meal there will cost you \(\$ 2\); if you eat there each evening this semester, it will add up to \(\$ 200\). Your roommate says that you should eat in the restaurant since it costs less than the \(\$ 1,000\) that you paid for the meal plan. Is your roommate right? Explain why or why not.

You have bought a \(\$ 10\) ticket in advance for the college soccer game, a ticket that cannot be resold. You know that going to the soccer game will give you a benefit equal to \(\$ 20\). After you have bought the ticket, you hear that there will be a professional baseball post-season game at the same time. Tickets to the baseball game cost \(\$ 20\), and you know that going to the baseball game will give you a benefit equal to \(\$ 35\). You tell your friends the following: "If I had known about the baseball game before buying the ticket to the soccer game, I would have gone to the baseball game instead. But now that I already have the ticket to the soccer game, it's better for me to just go to the soccer game." Are you making the correct decision? Justify your answer by calculating the benefits and costs of your decision.

Hiro owns and operates a small business that provides economic consulting services. During the year he spends \(\$ 57,000\) on travel to clients and other expenses. In addition, he owns a computer that he uses for business. If he didn't use the computer, he could sell it and earn yearly interest of \(\$ 100\) on the money created through this sale. Hiro's total revenue for the year is \(\$ 100,000\). Instead of working as a consultant for the year, he could teach economics at a small local college and make a salary of \(\$ 50,000\). a. What is Hiro's accounting profit? b. What is Hiro's economic profit? c. Should Hiro continue working as a consultant, or should he teach economics instead?

Amy, Bill, and Carla all mow lawns for money. Each of them operates a different lawn mower. The accompanying table shows the total cost to Amy, Bill, and Carla of mowing lawns. $$ \begin{array}{cccc} \begin{array}{c} \text { Quantity of } \\\ \text { lawns mowed } \end{array} & \begin{array}{c} \text { Amy's } \\\ \text { total cost } \end{array} & \begin{array}{c} \text { Bill's } \\\ \text { total cost } \end{array} & \begin{array}{c} \text { Carla's } \\\ \text { total cost } \end{array} \\\ 0 & \$ 0 & \$ 0 & \$ 0 \\\ 1 & 20 & 10 & 2 \\\ 2 & 35 & 20 & 7 \\\ 3 & 45 & 30 & 17 \\\ 4 & 50 & 40 & 32 \\\ 5 & 52 & 50 & 52 \\\ 6 & 53 & 60 & 82 \end{array} $$ a. Calculate Amy's, Bill's, and Carla's marginal costs, and draw each of their marginal cost curves. b. Who has increasing marginal cost, who has decreasing marginal cost, and who has constant marginal cost?
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