## Economics 101

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Economics 101

Summer 2012

Answers to Homework #5

Due 6/20/12

Directions: The homework will be collected in a box before the lecture. Please place your name, TA

name and section number on top of the homework (legibly). Make sure you write your name as it appears

on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans

ahead of time. Please show your work. Good luck!

Please realize that you are essentially creating “your brand” when you submit this homework. Do

you want your homework to convey that you are competent, careful, professional? Or, do you want

to convey the image that you are careless, sloppy, and less than professional. For the rest of your life

you will be creating your brand: please think about what you are saying about yourself when you

do any work for someone else!

1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This

monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be

expressed as TC = 100Q + Q2 + 50.

a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges

a single price?

Answer:

MR = 520 – 4Q

MC = 100 + 2Q

520 – 4Q = 100 + 2Q

Q = 70 units of output

P = 520 – 2Q = 520 – 2(70) = $380 per unit of output

b. Given the above information, calculate this single price monopolist’s profit.

Answer:

Profit = TR – TC

TR = P*Q = ($380 per unit)(70 units) = $26,600

TC = 100Q + Q2 + 50 = 100(70) + (70)(70) + 50 = $11,950

Profit = $14650

c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?

Answer:

To answer this question we first need to write an expression for ATC.

ATC = TC/Q = 100 + Q + (50/Q)

Then replace Q with 70 to find the average total cost of producing 70 units of output.

ATC= 100 + 70 + (50/70) = $170.71 per unit

d. At the profit maximizing quantity, what is the profit per unit for this single price monopolist?

Answer:

Profit per unit = Price per unit – ATC per unit when producing 70 units of output

1

Profit per unit = 380 –170.71 = $209.29 per unit

To verify your answer, check that profit per unit times number of units yields the same profit as you got

initially. Thus, Profit = (profit per unit)(number of units produced) = ($209.29)(70) = $14650

2. Consider a monopolist described by the following equations:

Market demand for monopolist’s product: P = 100 – Q

ATC for monopolist: ATC = 20 +(3/10) Q

MC for monopolist: MC = 20 + (3/5)Q

In this question we will use the above data to compare a single price monopolist to the same monopolist

that is regulated either with average cost regulation or marginal cost regulation. At the end of the question

you will fill out a table to compare your results.

a. Given the above information, what is the profit maximizing price and quantity for the single price

monopolist? You should round your answers to the nearest whole number.

Answer:

To find the profit maximizing quantity for a single price monopolist you want to equate MR to MC. MR =

100 – 2Q. So,

100 – 2Q = 20 + (3/5)Q

400/13 = Q

Q = 30.8 or approximately 31 units

P = 100 – 31 = $69

b. Given the above information, what is the level of profit for this single price monopolist?

Answer:

To find the firm’s profit you will need to have TR and TC.

TR = P*Q = (69)(31) = $2139

TC = 20Q + (3/10)Q2 = (20)(31) +(3/10) (31)(31) =908.3

Profit = TR – TC = $1230.7

c. Suppose this monopolist is regulated to produce at that quantity where price equals average total cost.

Calculate the quantity the monopolist will produce and the price it will charge given this regulatory

scenario.

Answer:

To find the quantity where price equals average total cost use the demand curve and the average total cost

curve. Hence, 100 – Q = 20 +(3/10) Q or Q = 800/13 units=61.5units. Use the demand curve to find the

price associated with 40 units of output. Thus, P = 100 – Q = 100 – 800/13 = $500/13=38.5.

d. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price

equals average total cost. Explain how you got your answer.

Answer:

To find the firm’s profit you will need to have TR and TC.

TR = (800/13)(500/13) = $2367

TC = (20)(800/13) +(3/10) (800/13)(800/13) = $2367

Profit = TR – TC = $0

2

e. Suppose this monopolist is regulated to produce at that quantity where price equals marginal cost.

Calculate the quantity the monopolist will produce and the price it will charge given this regulatory

scenario.

Answer:

Use the demand curve and the MC curve to solve for the quantity.

100 – Q = 20 + (3/5)Q

500 – 5Q = 100 + 3Q

400 = 8Q

Q = 50 units

P = 100 – 50 = $50

f. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price

equals marginal cost.

Answer:

Profit = TR – TC

TR = (50)(50) = $2500

TC = (20)(50) +(3/10) (50)(50) = $1750

Profit = $2500 - $1750 = $750

g. How big a subsidy will the monopoly require in order to be willing to produce at the price and quantity

you calculated in part (e)? Explain your answer.

Answer:

The monopolist will not need to receive a subsidy since when he produces where MR = P in this example

Economics 101
Summer 2012
Answers to Homework #5
Due 6/20/12
Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck!
Please realize that you are essentially creating “your brand” when you submit this homework. Do you want your homework to convey that you are competent, careful, professional? Or, do you want to convey the image that you are careless, sloppy, and less than professional. For the rest of your life you will be creating your brand: please think about what you are saying about yourself when you do any work for someone else!
1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be expressed as TC = 100Q + Q2 + 50.
a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges a single price?
b. Given the above information, calculate this single price monopolist’s profit.
c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?
d. At the profit maximizing quantity, what is the profit per unit for this single price monopolist?
2. Consider a monopolist described by the following equations:
Market demand for monopolist’s product: P = 100 – Q
ATC for monopolist: ATC = 20 +(3/10) Q
MC for monopolist: MC = 20 + (3/5)Q
In this question we will use the above data to compare a single price monopolist to the same monopolist that is regulated either with average cost regulation or marginal cost regulation. At the end of the question you will fill out a table to compare your results.
a. Given the above information, what is the profit maximizing price and quantity for the single price monopolist? You should round your answers to the nearest whole number.
b. Given the above information, what is the level of profit for this single price monopolist?
c. Suppose this monopolist is regulated to produce at that quantity where price equals average total cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario.
d. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price equals average total cost. Explain how you got your answer.
e. Suppose this monopolist is regulated to produce at that quantity where price equals marginal cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario.
f. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price equals marginal cost.
g. How big a subsidy will the monopoly require in order to be willing to produce at the price and quantity you calculated in part (e)? Explain your answer.
h. Fill in the table below with your findings. Remember that a firm is allocatively efficient if price is equal to marginal cost for the last unit of the good produced by the firm.
Single Price Monopolist Monopolist regulated with Average Cost Regulation Monopolist regulated with Marginal Cost Regulation
Price
Quantity
Profits
Subsidy Needed to Produce
Allocatively Efficient?
3. Consider two students, Jaeho and Lawrence. Both students are taking an exam in their math class this week and they are both, independently, trying to decide whether they will conceal their answers or reveal their answers while working on the exam. It takes time and effort to conceal answers so both students realize that revealing their answers will allow them to concentrate more fully on the exam. In addition, they both realize that if the other student reveals their answers they may potentially improve their scores. Jaeho knows that he is conceals his answers he will get a 60 on the exam and if he does not conceal his answers he will get a 65 provided that Lawrence conceals his answers. Jaeho knows that he will make a 75 on the exam if he conceals his answers while Lawrence reveals his answers; Jaeho will make an 80 on the exam if both Jaeho and Lawrence do not conceal their answers. Lawrence believes he will make an 80 on the exam he both students conceal their answers, an 85 on the exam if he conceals his answers while Jaeho reveals his answers, an 85 on the exam if he reveals his answers while Jaeho does not reveal his answers, and an 87 on the exam if both students do not conceal their answers.
a. Construct a payoff matrix for Jaeho and Lawrence. In the payoff matrix identify the two strategies that both students face and then enter their payoffs with Jaeho’s payoff the first number and Lawrence’s payoff the second number. Label this payoff matrix fully and completely.
b. Does Jaeho have a dominant strategy with regard to concealing or revealing his answers? Explain your answer.
c. Does Lawrence have a dominant strategy with regard to concealing or revealing his answers? Explain your answer.
d. What do you predict will be Jaeho’s and Lawrence’s scores on the exam? Explain your answer.
4. Consider a monopoly that faces a market demand curve given as P = 100 – Q. The marginal cost of production for this monopolist is MC = 10 and the monopolist has fixed costs equal to zero. The monopolist has asked you to compare what happens if the monopolist is a single-price monopolist, a second degree price discriminating monopolist, and a perfect price discriminating monopolist. At the end of this question you will be asked to fill out a table to summarize your findings.
i) Single-price monopolist:
Suppose the monopolist charges a single-price for its product. Given this assumption, find the answers to the following questions:
a. What is the profit maximizing quantity and price for this single-price monopolist?
b. What is total revenue (TR) equal to for this monopolist?
c. What is total cost (TC) equal to for this monopolist?
d. What are the economic profits for this single-price monopolist?
e. What is the value of consumer surplus (CSm) for this monopolist?
f. What is the value of producer surplus (PSm) for this monopolist?
g. What is the deadweight loss (DWLm) equal to for this monopolist?
h. Provide a graph of this single-price monopolist indicating CSm, PSm, DWLm, the profit maximizing quantity, and the profit maximizing price.
Suppose the monopolist charges two different prices: $80 and $55. Given this assumption, find the answers to the following questions:
i. How many units of the good will the monopolist sell at $80 per unit?
j. How many units of the good will the monopolist sell at $55 per unit?
k. What is total revenue (TR) for this monopolist when he practices second degree price discrimination as described?
l. What is total cost (TC) for this monopolist when he practices second degree price discrimination as described?
m. What are the economic profits for this second degree price discriminating monopolist?
n. What is the value of consumer surplus (CS2) for this monopolist?
o. What is the value of producer surplus (PS2) for this monopolist?
p. What is the deadweight loss (DWL2) equal to for this monopolist?
q. Provide a graph of this second degree price discriminating monopolist indicating CS2, PS2, DWL2, as well as the prices and quantities that the monopolist selects.
r. How many units will the perfect price discriminating monopolist produce?
s. Describe the price(s) the perfect price discriminating monopolist will charge.
t. What is the value of consumer surplus (CSppd) for this perfect price discriminating monopolist?
u. What is the value of producer surplus (PSppd) for this perfect price discriminating monopolist?
v. What is the value of deadweight loss (DWLppd) for this perfect price discriminating monopolist?
w. What do economic profits equal for this perfect price discriminating monopolist? Show your work to get this answer.
x. Draw a diagram graph of this perfect price discriminating monopolist indicating PSppd, DWLppd, as quantity that the monopolist selects.
y. Fill in the following summary table:
Single Price Monopolist Second Degree Price Discriminating Monopolist Perfect Price Discriminating Monopolist
Profit Maximizing Price
Profit Maximizing Quantity
Total Revenue
Total Cost
Economic Profit
Consumer Surplus
Producer Surplus
Deadweight Loss
5. Suppose a market is characterized as having two different classes of buyers: Class One and Class Two. Furthermore suppose there is only one producer serving this market and this producer has fixed costs equal to $20 and Marginal Cost equal to 1 (MC = 1). The two classes of buyers are described by the following demand curves:
Class One: P = 10 – Q
Class Two: P = 20 – Q
For each of the questions below show your work and reasoning.
Suppose that the monopolist decides to produce the good and sell it for a single price.
a. What is the market demand curve for this single price monopolist?
b. What is the marginal revenue curve for this single price monopolist?
c. What is the profit maximizing quantity for this single price monopolist to produce?
d. What is the profit maximizing price for this single price monopolist?
e. What is total revenue (TR) for this single price monopolist?
f. What is total cost (TC) for this single price monopolist?
g. What is the economic profit for this single price monopolist?
h. What is the marginal revenue curve for Class One and what is the marginal revenue curve for Class Two?
i. What is the profit maximizing quantity to sell to Class One? What price should this quantity be sold for?
j. What is the profit maximizing quantity to sell to Class Two? What price should this quantity be fold for?
k. Does the sum of the quantity sold to Class One plus the quantity sold to Class Two equal the profit maximizing amount you found in (c)?
l. Calculate the total revenue, total cost, and economic profit for Class One. Assume fixed cost is divided evenly between the two classes.
m. Calculate the total revenue, total cost, and economic profit for Class Two. Assume fixed cost is divided evenly between the two classes.
n. What do total profits equal for the monopolist when he practices third degree price discrimination?
o. Is it worth price discriminating for this monopolist? Explain your answer.
6. Consider the market for education. The marginal social cost of education (MSC) and the marginal private benefit of education (MPB) are given by the following equations where Q is the number of units of education provided per year.
MSC = 10 + Q
MPB = 100 – Q
You are also told that each unit of education provides an external benefit to society of $10 per unit. This external benefit is currently not being internalized in the market.
a. Given the MSC and MPB curves, what is the current number of education units being produced by the market?
b. Is the current level of market production for education the socially optimal amount of education? Explain your answer.
c. What is the value of consumer surplus (CS), the value of producer surplus (PS), and the value of the external benefits of the current level of production. Sum together (CS + PS + external benefits). Draw a diagram illustrating each of these concepts in the market for education.
d. Given the market level of production, what is the deadweight loss in this market?
e. Suppose that the external benefit is internalized in this market when the government provides a subsidy of $10 per educational unit to consumers. What will be the socially optimal amount of education to provide given this subsidy?
7. Consider a community that has two residents, Bill and Amanda. Bill and Amanda would both like to see streetlights installed in their community and they are busy trying to decide what the optimal amount of streetlights for their community is and what price they should each contribute for each streetlight installed. Luckily they are both willing to reveal their preferences and so we do not have to worry about the free rider problem. Bill’s demand for streetlights is given by the equation Q = 10 – P and Amanda’s demand for streetlights is given by the equation P = 5 – (1/2)Q. The marginal cost of providing a streetlight is $3.
a. On your homework paper draw three graphs vertically one above the other. The first graph should be labeled “Bill’s demand”; the second graph should be labeled “Amanda’s demand”; and the third graph should be labeled “market demand”. On each graph the horizontal axis should be labeled “Quantity of Streetlights” while the vertical axis should be labeled “Price of Streetlights”. Now in each graph draw in the demand curve corresponding to your label. Remember that the market demand curve will be a vertical summation of the individual demand curves since a public good is non-rival.
b. Write an equation for the market demand curve for the public good.
c. What is the optimal number of streetlights for this community? Show how you found this number.
d. What price per streetlight will Bill pay? What price per streetlight will Amanda pay? Why do Bill and Amanda pay different amounts for each streetlight that is produced?