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
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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