David Epstein
Yusuke Fujita
Michael W. Kim
Liana Kohn-Gardner
Alice Sheng
Brian White
Managerial Economics
Section E, Group 6
Problem Set 6
Problem 1.
A. Calculate the firm's optimal price in the US. Show your work.
Set MR=MC
Q = 2,000,000 – 20,000P
P = 100 – 0.00005Q
TR = P*Q = 100Q – 0.00005Q^2
MR = 100 - .0001Q
TC = 40,000,000 + 5Q
MC = 5
MR = MC is firm’s optimal price in the US.
MC = 5 = 100 – 0.0001Q
Q = 950,000
P = 100 – 0.00005*950,000
P = $52.50
B. What is the optimal price to charge in the Brazilian market? Show your work.
Set MR=MC
MC =5
P = (200/3)-(1/3,000)Q
TR = P*Q
TR = Q[(200/3)-(1/3,000)Q]
TR = 200/3Q-1/3,000Q^2
MR = (200/3)-(2/3,000)Q
5 = (200/3)-(2/3,000)Q
Q = 92,500
P = (200/3)-(1/3,000)*92,500
P = $35.83
C. Explain why the problem of parallel imports, a form of arbitrage, may result from the pricing
structure you have calculated in the previous questions.
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The issue of parallel imports is if American importers go to Brazil to buy the product and bring it
back to sell in America for somewhere between the Brazilian price of $35.83 and the American
price of $52.50. As a result, the importers would realize arbitrage profits and reduce the demand
and profits for the American product.
D. If it cost the company $1,500,000 annually to eliminate the problem of parallel imports, should it
do so? Explain!
Yes, because the total profit in the U.S. at the optimal output of $5.125 million is greater than the
cost of $1.5 million to eliminate the problem of parallel imports. If the company does not take
action to eliminate the problem of parallel imports, it could face significant losses due to parallel
imports causing consumers to switch to the Brazilian product.
Problem 2.
A. Are there economies of scale for these coffee shops? Explain briefly.
Economies of scale exist for these coffee shops because the ATC for each of these shops will
continually decrease due to constant variable costs and fixed costs being spread over a greater
number of units.
B. What is the optimal price for each of the two operators? Show your work.
Starbucks optimal price: set MR = MC
Q = 500,000 – 220,000P
P = 2.27 – 0.0000045Q
TR = P*Q = 2.27Q – 0.0000045Q^2
MR = 2.27 – 0.0000091Q
TC = 50,000 + 0.6Q
MC = 0.6
MC = 0.6 = 2.27 – 0.0000091Q
Q = 184,000
P = $1.44 per cup of Starbucks coffee
Coffee Bean optimal price: set MR = MC
Q = 400,000 – 200,000P
P = 2 – 0.000005Q
TR = P*Q = 2Q – 0.000005Q^2
MR = 2 – 0.00001Q
TC = 60,000 + 0.6Q
MC = 0.6
MR = MC = 0.6 = 2 – 0.00001Q
Q = 140,000
P = $1.30 per cup of Coffee Bean coffee
C. What is the maximum annual amount that the Airport Commission can get for this franchise?
Show your work.
If Starbucks or Coffee Bean were to produce at the profit maximizing level for each franchise, then
the total profitability for each shop would be:
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Total Revenue
Total Cost
Total Profit
Starbucks
264,960
160,400
104,560
Coffee Bean
182,000
144,000
38,000
Assuming that the Airport commission chose Starbucks since they have the highest expected total
profit at the optimal output, the maximum annual amount that the Airport Commission could charge
would be slightly less than the total Starbucks profit of $104,560 because Starbucks would not
operate unless it could generate a profit.
Problem 3.
A. Use supply and demand curves to illustrate the situation in the market for cab rides before the
two simultaneous decisions to expand the number of medallions and to raise the regulated fare.
Price
S
D
Quantity
Given the regulated price, the supply curve is initially horizontal but then it becomes vertical due to
the limit on the quantity of supply.
B. Use supply and demand curves to illustrate the situation in the market for cab rides after the two
simultaneous decisions to expand the number of medallions and to raise the regulated fare. Be
careful to highlight the effects of these decisions in comparison with the answer in part a) above.
Price
S
S'
additional medallions
D
increase in fare
Quantity
The increase in the fare will shift the supply curve up (while it is horizontal) while the additional
medallions will move the supply curve further to the right before it becomes vertical due to the
increase in the quantity of medallions. This shrinks the gap between supply and demand as more
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cab rides are supplied and fewer are demanded by customers.
C. What factors will determine the price of the medallions sold at the 2004 auctions? Explain.
One factor influencing the price of the medallions is the number of medallions that will be sold at
the auctions. If there is a large increase in the number of medallions then the profit associated
with holding a medallion would decrease and therefore decrease the value of the medallion.
Another factor is how many people want to buy the medallions and how these people value the
medallions. If more people want a medallion, then this will cause the price to increase.
D. Discuss how that new price will compare with prices at which the medallions were trading just
prior to the announcement of the two changes? Explain!
The new price will probably be lower than the prices at which they were trading prior because there
was a smaller quantity of medallions available, and thus the trading price was probably very high
because the medallions were highly regarded prized possessions. However, as more medallions
get added into the mix, the novelty and scarcity of the medallion goes down, thus reducing
people’s willingness to pay.
Problem 4.
In a competitive market, the industry demand and supply curves are P=200-0.2×Qd and
P=100+0.3×Qs, respectively.
A. Find the market's equilibrium price and output.
Demand
P = 200-0.2Q
Supply
P = 100+0.3Q
Market Equilibrium is when Demand and Supply curves cross. Therefore:
200-0.2Q = 100+0.3Q
100 = 0.5Q
Q = 200
P = $160
B. If there is a $20 per unit tax imposed on firms, then the supply curve will shift out (vertically) to:
P = 120 + 0.3Q (where the price intercept is now higher by 20).
The new competitive price and output are:
120 + 0.3Q = 200 – 0.2Q
0.5Q = 80
Q = 160
P = $168
This means that because of the $20 tax/unit on firms, the price to consumers has gone from
$160 to $168 and therefore $8 of the tax has been passed on to consumers.
C. If $20/unit sales tax is imposed on consumers, this means that demand will decrease, and the
demand curve will shift parallel down. Therefore the new demand curve is:
P = 180 – 0.2Q
New Competitive price and output:
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180-0.2Q = 100+0.3Q
80 = 0.5Q
Q = 160
P = $148 (before tax). After tax, the price is $148 + $20 = $168.
This means that the competitive price and quantity are the same, showing that it makes no
difference whether the tax is placed on the consumers or on the firms.
D. The tax considered above is a specific (i.e. per unit) tax, can you find an ad-valorem tax that
would generate the same amount of revenues for the government? Using a diagram discuss which
one of these alternative tax schemes generates the highest dead-weight-loss.
Yes, an ad-valorem tax could be determined and would be based on the fact that the new supply
curve (under the tax) will intersect the demand curve at the exact same point as determined in
question B.
Based on Question B
Price
S'
S
dead-weight loss
$20
D
tax revenue for the government
160
Quantity
Based on Question C
Price
tax revenue for the government
S
dead-weight loss
$20
D
D'
160
Quantity
Based on Ad-Valorem Tax
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Price
S' = S * (1+tax rate)
S
dead-weight loss
$20
D
tax revenue for the government
160
Quantity
Under the ad valorem tax, the slope and the y-intercept of the supply curve will change to P=(1+tax
rate)*(100+0.3Qs). In order to generate the same amount of tax revenue under the ad valorem
scheme, the supply curve should intercept the demand curve at the same position as the question
B case. Therefore, the dead weight loss will be exactly the same under all three cases.
Problem 5.
A. If the three major networks bid, what is the expected amount of the winning bid?
Expected Bid Amount = (1/(N+1))*L+(N/(N+1))*U = (1/(3+1))*500+(3/(3+1))*700 =$650
B. Fox Network has expressed an interest in televising the playoffs. If Fox enters the bidding, what
is the new expected amount of the winning bid?
Expected Bid Amount = (1/(N+1))*L+(N/(N+1))*U = (1/(4+1))*500+(4/(4+1))*700
=$660
C. Explain why the addition of a new bidder raises the level of the expected winning bid.
An increase in the number of bidders makes it more likely that some bidders will overestimate the
value of the auctioned item. This can be seen in the formula where the Lower coefficient becomes
smaller as the number of bidders increases while Upper coefficient moves closer to one.
D. How does an increase in the number of bidders affect the likelihood of the winning bidder
suffering the winner's curse?
The likelihood of the winning bidder suffering from the winner's curse increases with the number of
bidders. This is because with more bidders, it is more likely that some of them have overestimated
the auctioned item's value and the winning bid is likely to exceed the true value of the item. The
bidders suffer from the curse because the bidders do not shade their bids enough.
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