Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 6

You are thinking about tutoring students in economics, and your research has convinced you that you face the following demand curve for your services: $$\begin{array}{cc} \begin{array}{c} \text { Price per Hour } \\ \text { of Tutoring } \end{array} & \begin{array}{c} \text { Number of Students } \\ \text { Tutored per Week } \end{array} \\ \hline>\$ 50 & 0 \\ \$ 40 & 1 \\ \$ 35 & 2 \\ \$ 27 & 3 \\ \$ 26 & 4 \\ \$ 20 & 5 \\ \$ 15 & 6 \\ <\$ 15 & 6 \end{array}$$ Each student who hires you gets one hour of tutoring per week. You have decided that your time and effort is worth \(\$ 25\) per hour and that you will not tutor anyone for less than that. a. Suppose you are wary that your students might talk to each other about the price you charge, so you decide to charge them all the same price. Determine (1) how many students you will tutor; (2) what price you will charge; and (3) your weekly earnings from tutoring. b. Now suppose you discover that your students don't know each other, and you decide to perfectly price discriminate. Once again, determine (1) how many students you will tutor; (2) what price you will charge; and (3) your weekly earnings from tutoring. Now suppose that your city requires all tutors to get a license, at a cost of \(\$ 1,300\) per year (\$25 per week). c. Does it make sense for you to buy this license and be a tutor if you must charge each student the same price? Explain. d. Does it make sense for you to buy the license and be a tutor if you can perfectly price discriminate? Explain.

Short Answer

Expert verified
a. You will tutor 5 students at a price of $25 and your weekly earnings will be $125. b. You will tutor 5 students, with individual prices adding up to $177 and your weekly earnings will be $177. c. It does make sense for you to buy the license if you charge each student the same price, as your weekly earnings after licensing cost are $100. d. It does make sense for you to buy the license if you can perfectly price discriminate, as your weekly earnings after licensing cost are $152.

Step by step solution

01

Identify Relevant Values

First, express the demand curve and your minimum acceptable payment. The minimum price you are willing to take for your time is $25/hour. Now, create a list of prices and corresponding demand (students) by extracting from the table provided.
02

Determine the Price and Number of Students for Equal Pricing

Identify the number of students you can tutor and the price you can charge, given that every student pays the same price. Looking at the demand curve, you see that you can tutor five students at a price at or above $25. So if you decide to only tutor at a price of $25 or higher, you will tutor 5 students and the price you will charge will be $25.
03

Calculate Weekly Earnings With Equal Pricing

Calculate your total weekly earnings by multiplying the price charged with the number of students. So, if you tutor five students at $25 each, the total earnings would be $25 * 5 = $125.
04

Determine the Price and Number of Students for Price Discrimination

Now consider if you are capable of perfectly price discriminating. This implies that you can charge each student the maximum they are willing to pay. Add all the prices from $50 to $25 from the demand curve. The total is $50 + $40 +$35 + $27 + $25 = $177.
05

Calculate Weekly Earnings With Price Discrimination

As you still tutor 5 students, your weekly earnings from tutoring in this case would be $177.
06

Evaluate the Necessity of Tutoring License for Equal Pricing

If you have to pay $25 per week for a license, then your weekly profit with equal pricing will be $125 - $25 = $100. Thus, buying the license and being a tutor is profitable.
07

Evaluate the Necessity of Tutoring License for Price Discrimination

If you are considering the case of perfect price discrimination and still have to pay $25 per week for a license, then your weekly profit will be $177 - $25 = $152. Therefore, buying the license and being a tutor is still profitable.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose a single-price monopoly's demand curve is given by \(P=20-4 Q,\) where \(P\) is price and \(Q\) is quantity demanded. Marginal revenue is \(M R=20-\) 8Q. Marginal cost is \(M C=Q^{2} .\) How much should this firm produce in order to maximize profit?

In a certain large city, hot dog vendors are perfectly competitive, and face a market price of \(\$ 1.00\) per hot dog. Each hot dog vendor has the following total cost schedule: $$\begin{array}{cc} \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} & \text { Total cost } \\ \hline 0 & \$ 63 \\ 25 & 73 \\ 50 & 78 \\ 75 & 88 \\ 100 & 103 \\ 125 & 125 \\ 150 & 153 \\ 175 & 188 \\ 200 & 233 \end{array}$$ a. Add a marginal cost column to the right of the total cost column. (Hint: Don't forget to divide by the change in quantity when calculating \(M C .)\) b. What is the profit-maximizing quantity of hot dogs for the typical vendor, and what profit (loss) will he earn (suffer)? Give your answer to the nearest 25 hot dogs. One day, Zeke, a typical vendor, figures out that if he were the only seller in town, he would no longer have to sell his hot dogs at the market price of \(\$ 1.00\). Instead, he'd face the following demand schedule: $$\begin{array}{cc} \text { Price per Hot Dog } & \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} \\ \hline>\$ 6.00 & 0 \\ 6.00 & 25 \\ 5.00 & 50 \\ 4.00 & 75 \\ 3.25 & 100 \\ 2.75 & 125 \\ 2.25 & 150 \\ 1.75 & 175 \\ 1.25 & 200 \end{array}$$ c. Add total revenue and marginal revenue columns to the table above. (Hint: Once again, don't forget to divide by the change in quantity when calculating MR.) d. As a monopolist with the cost schedule given in the first table, how many hot dogs would Zeke choose to sell each day? What price would he charge? e. A lobbyist has approached Zeke, proposing to form a new organization called "Citizens to Eliminate Chaos in Hot Dog Sales." The organization will lobby the city council to grant Zeke the only hot dog license in town, and it is guaranteed to succeed. The only problem is, the lobbyist is asking for a payment that amounts to \(\$ 200\) per business day as long as Zeke stays in business. On purely economic grounds, should Zeke go for it? (Hint: If you're stumped, re-read the section on rent-seeking activity.)

A doctor in a rural area faces the following demand schedule: $$\begin{array}{cc} \begin{array}{c} \text { Price per } \\ \text { Office Visit } \end{array} & \begin{array}{c} \text { Number of Office } \\ \text { Visits per Day } \end{array} \\ \hline \$ 200 & 2 \\ \$ 175 & 3 \\ \$ 150 & 5 \\ \$ 125 & 8 \\ \$ 100 & 12 \\ \$ 75 & 18 \\ \$ 50 & 23 \\ \$ 25 & 25 \end{array}$$ The doctor's marginal cost of seeing patients is a constant \(\$ 50\) per patient. a. If the doctor must charge all patients the same price, what price will she charge, and how many patients will she see each day? b. If the doctor can perfectly price discriminate, how many patients will she see each day?

Below is demand and cost information for Warmfuzzy Press, which holds the copyright on the new best-seller, Burping Your Inner Child. $$\begin{array}{ccc} \begin{array}{c} Q \\ \text { (No. of Copies) } \end{array} & \begin{array}{c} P \\ \text { (per Book) } \end{array} & \begin{array}{c} A T C \\ \text { (per Book) } \end{array} \\ \hline 100,000 & \$ 100 & \$ 20 \\ 200,000 & \$ 80 & \$ 15 \\ 300,000 & \$ 60 & \$ 162 / 3 \\ 400,000 & \$ 40 & \$ 221 / 2 \\ 500,000 & \$ 20 & \$ 31 \end{array}$$ a. Determine what quantity of the book Warmfuzzy should print, and what price it should charge in order to maximize profit. b. What is Warmfuzzy's maximum profit? c. Prior to publication, the book's author renegotiates his contract with Warmfuzzy. He will receive a great big hug from the CEO, along with a onetime bonus of \(\$ 1,000,000,\) payable when the book is published. This payment was not part of Warmfuzzy's original cost calculations. How many copies should Warmfuzzy publish now? Explain your reasoning.

Draw demand, \(M R, M C, A V C,\) and \(A T C\) curves that show a monopolist operating at a loss that would cause it to stay open in the short run, but exit the industry in the long run. Then, show how a technological advance that lowers only the monopolist's fixed costs could cause a change in its long-run exit decision.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free