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Sample paper on Managerial Economics
Sa
Every company is at some point required to conduct
managerial economics, below are some examples of
economics.
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Quantity or Product (Cournot) Duopoly: You are the manager of BlackSpot Computer, which
competes directly with Condensed Computers to sell high-powered computers to businesses. From
the two businesses’ perspectives, the two products are indistinguishable. The large investment
required to build production facilities prohibits other firms from entering this market, and existing
firms operate under the assumption that the rival will hold output constant. The inverse market
demand for computers is P = 5100 – 0.5Q, Q = QBS+ QCC and both firms produce at a marginal cost
of $750 per computer. Currently, BlackSpot earns revenues of $6.38M and profits (net of R&D and
other fixed costs) of $1M. The engineering department at BlackSpot has been steadily working on
developing an assembly method that would dramatically reduce the marginal cost of producing these
high-powered computers and has found a process that allows it to manufacture each computer for a
marginal cost of $500. How will this technological advance impact your production and pricing?
How will it impact BlackSpot’s bottom line? [Hint: Determine the outputs, price and profit for each
firm before the innovation and then determine the outputs, price, and profit for each firm afterwards.
Note only BlackSpot’s costs change in the second scenario.]
Output, price and profit for the two firms before the innovation
P=5100 - 0.5Q But Q=QBS + QCC
P=5100- 0.5(QBS + QCC )
Marginal cost=750
Profit for BlackSpot Computer= (P-C) QBS
Profit BS= (5100-0.5(QBS+ QCC) -750) QBS
Profit BS= (5100- 0.5QBS-0.5QCC-750) QBS
Differentiate the function with respect to QBS
5100-0.5QBS-0.5QCC-750=0
0.5QBS= 4350-0.5QCC
QBS=8700-QCC
Profit CC = (5100-0.5(QBS+QCC)-750) QCC
Profit CC =5100QCC-0.5QBSQCC+0.5QCC2-750QCC
Differentiate the function with respect to QCC
5100-0.5QBS+QCC-750=0
4350-0.5QBS+QCC =0
QCC= -4350+0.5QBS
Solve the two equations simultaneously
QBS=8700-(-4350+0.5QBS)
QBS = 8700+4350 +0.5QBS
0.5BS =13050
QBS=26100
QCC= -4350+0.5*26100
QCC= -4350+13050
QCC=8700
P=5100- 0.5(QBS + QCC )
P=5100-0.5(26100+8700)
P=5100-17400
P=12300
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Profit BS= (5100- 0.5QBS-0.5QCC-750) QBS
(5100-13050-4350-750)26100
13050*26100= 340,605,000
Profit CC = (5100-0.5(QBS+QCC)-750) QCC
(5100-0.5(26100+8700)8700
(5100-13050-4350-750)8700
13050*8700=113,535,000
Output, price and profit for the two firms after innovation
P=5100 - 0.5Q But Q=QBS + QCC
P=5100- 0.5(QBS + QCC )
Marginal cost=500
Profit for BlackSpot Computer= (P-C) QBS
Profit BS= (5100-0.5(QBS+ QCC) -500) QBS
Profit BS= (5100- 0.5QBS-0.5QCC-500) QBS
Profit BS=5100QBS-0.5QBS2-0.5QCCQBS-500QBS
Differentiate the function with respect to QBS
Maximum profit=5100-QBS-0.5QCC-500
4600-QBS-QCC =0
QBS=4600-QCC
Profit CC = (5100-0.5(QBS+QCC)-500) QCC
Profit CC =5100QCC-0.5QBSQCC-0.5QCC2-500QCC
Profit CC=5100QCC-0.5(4600-QCC) QCC-0.5QCC2-500QCC
Profit CC=5100QCC-2300QCC-0.5QCC2+--0.5QCC
2-500QCC
Maximum profit=5100-2300-QCC-QCC-500=0
2QCC=2300
QCC=1150
Therefore, QBS=4600-1150=3450
P=5100- 0.5(QBS + QCC )
5100-(0.5(3450+1150)
5100-2300=2800
Profit BS= (5100- 0.5QBS-0.5QCC-500) QBS
(5100-0.5*3450-0.5*1150-500)3450
(5100-1725-575-500)3450
2275*3450=7,848,750
Profit CC = (5100-0.5(QBS+QCC)-750) QCC
(5100-0.5*(3450+1150)-750)1150
(5100-2300-750)1150
2050*1150=2,357,500
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Summarize your findings in words.
At cournot equilibrium, both BlackSpot Computer and Condensed Computers sets its own
quantity given each forms quantity. This is achieved in such a condition that profit of each firm is
mainly maximized in a situation whereby quantity level gives higher profit. This indicates that both
firms are better off if they both set cournot equilibrium than when any firm sets a different quantity. This
is because at equilibrium, each of the two firms maximizes its profit. On the other hand, in an effort to
maximize profit, the two firms start moving simultaneously in output or quantity competition.
If BlackSpot Computer produces a certain amount of output, Condensed Computers tend to react by
producing a slightly higher quantity. On the other hand, BlackSpot Computer will produce another
output level higher than the earlier produce. This indicates that a firm reacts according to its rival’s
reaction function. This reaction continues until firms converge at cournot equilibrium. Under cournot
equilibrium, none of the two firms have advantages over the other. They, therefore, equal amont of
output. In addition, they also share market demand and thus make equal profits.
Two part pricing consumers with different demands.The University Museum has two types of
visitors. One type is University employees; and the other type is people nonaffiliated with the
University. All University employees have identical annual demands for Museum visits, given
by
(for each University employee)
where is the number of visits demanded if the price is per visit. Nonaffiliated people all
have identical annual demands for Museum visits, butdiffer from University employees:
(for each nonaffiliated person)
where is the number of visits demanded if the price is per visit. TheMuseum can identify
University employees by their University ID card, while a nonaffiliated person does not possess
a University ID.The University’s profit- maximizing Museum is contemplating two different
pricing policies:
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Policy 1
• For University employees: An annual membership fee and an additional price- per- visit.
(Only University employees are eligible for this membership plan.) (Hint: two part price)
• For nonaffiliated visitors: A single price- per- visit, with no membership fee. (This price
per visit is not necessarily the same as the University employee price per visit.) (Hint: one
part price, set MR=MC).
Policy 2
• • This policy would offer a different price- per- visit for each type of visitor,but no
membership fees at all. (Hint: one part prices, set MR=MC).
The museum has a constant marginal cost of 6 per visit, regardless of the visitor’s type. For
simplicity, assume that there is one University employee and one nonaffiliated person in the
target population.
How much more profit does the best policy yield than the other policy?
Solution
Policy 1
Profit for each University employee
University employees demand function=PP=30-QP
Membership fee=30-QP
Total fee= (30-QP+30-QP)
60-2QP
Profit=TR-TC
TR=PQ
TR= (60-2QP)QP
=60QP-2QP2
TC=MC*Q
=6QP
Profit= 60QP-2QP2-6QP
Maximum profit=60-4QP-6=0
4QP=60-6
4QP=54
QP=13.5
PP=30-QP
30-13.5=16.5
Profit=TR-TC
Profit= (60-2*13.5)13.5-(6*13.5)
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= (60-27)13.5-81
445.5-81
=364.5
Profit for each nonaffiliated person
Nonaffiliated person demand function=
Profit=TR-TC
(100-QN)QN
100QN-QN2
TC=MC*Q
6QN
Profit=100QN-QN2-6QN
Maximum profit=100-2QN-6
2QN=100-6
2QN=94
QN=47
PN=100-QN
100-47
53
Profit= (100*47)-472-(6*47)
4700-2209-282
=2209
Total profit=2209+364.5
=2573.5
Policy 2
Profit for each University employee
University employees demand function=PP=30-QP
Profit-TR-TC
TR=PQ
(30-QP)QP
30QP-QP2
TC=MC*QP
6QP
Profit=30QP-QP2-6QP
24QP-QP2
Maximum profit=24-2QP=0
QP=12
PP=30-12
=18
Profit= (30*12)-122-(6*12)
=360-144-72
=144
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Profit for each nonaffiliated person
Nonaffiliated person demand function=
Profit=TR-TC
(100-QN)QN
100QN-QN2
TC=MC*Q
6QN
Profit=100QN-QN2-6QN
Maximum profit=100-2QN-6
2QN=100-6
2QN=94
QN=47
PN=100-QN
100-47
53
Profit= (100*47)-472-(6*47)
4700-2209-282
=2209
Total profit=2209+144
=2353
Policy 1 yield 220.5 more than policy
Two part pricing consumers with different demands. The demand for a strong demander
for a round of golf is
Where is the number of rounds demanded by a weak demander when the price of around of
golf is .
The demand for a weak demander for a round of golf is
Where is the number of rounds demanded by a weak demander when the price of around of
golf is .
The cost of providing an additional round of golf to either type of golfer is a constant 2. There is
one golfer of each type.
The club has decided that the best pricing policy is a two part tariff. It’s your job to tell the club
the optimal entry fee and the optimal use fee to maximize the clubs profit. The club cannot price
discriminate on either the entry or use fees. The club fixed cost is $1.
What are the club’s optimal entry fee and use fee?
Solution
Demand for a strong demander for a round of golf=PS=8-QS
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Profit=TR-TC
(8-QS)QS
8QS-QS2
TC=$1
Profit=8QS-QS2-1
Maximum profit=8-2QS =0
2QS=8
QS=4
PS=8-4=4
Profit=(8*4)-42-1
32-16-1
15
The demand for a weak demander for a round of golf =
Profit=TR-TC
TR= (5-QW) QW
5QW-QW2
TC=$1
Profit=5QW-QW2-1
Maximum profit=5-2QW=0
2QW=5
QW=5/2=2.5
PW=5-5/2
=2.5
Profit=(5*2.5)-2.52-1
12.5-6.25-1
=5.25
Maximum entry fee=4+2.5
=6.5
Usage fee=6.5-2
=4.5
)Bundled Pricing: The University of Pennsylvania basketball team will play both the University
of Kansas and Nowhere University this year on Penn’s campus. Kansas is a nationally ranked
team while Nowhere is just plain terrible. The athletic director traditionally prices each game
separately. You approach him and point out that two other pricing options exist. One possibility
is to offer a pure bundle, i.e., a ticket package containing one Kansas ticket and one Nowhere
ticket. The second possibility is a mixed bundle. In this situation, a pure bundle is offered, but
admissions to the games can also be sold separately. It costs Penn a constant 5 per spectator to
produce a game. It would cost Penn 10 to produce a bundle of a Kansas game and a Nowhere
game. Three types of potential spectators exist (A, B, and C). There are an equal number of types
(for simplicity, assume one of each type). Their reservation prices for each game are shown
below:
Reservation Prices
Spectator Kansas Nowhere Bundle price
A 40 13 40K+43N
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B 49 3 49K+3N
C 3 30 3K+30N
Penn’s policy is not to price discriminate. A spectator’s reservation price for a bundle of the two
games is the sum of their reservation prices for each game. A spectator wants (at most) one
admission to each game.
?
Best Separate Price Strategy
Customer Price per
Unit
Cost per
unit
Profit per
unit
Number of
units
Profit
A 40 5 35
B 49 5 44
C 3 5 -2
A 40 10 30
B 49 10 39
C 3 10 -7
Best Pure Bundling Strategy
Customer Price per
Bundle
Cost per
Bundle
Profit per
Bundle
Number of
units
Profit
A
B
C
Best Mixed Bundling Strategy
Customer Price per
Bundle
Cost per
Bundle
Profit per
Bundle
Number of
units
Profit
Customer Price per
Unit
Cost per
unit
Profit per
unit
Number of
units
Profit
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a. What’s your pricing advice to the athletic director (so that the director maximizes Penn’s
profit)?
b. Given the current pricing policy of Penn, what’s your advice worth to the athletic director?
Bundled Pricing: Food For Life makes health foods for active, outdoor people. Their three basic
products are whey powder, a high protein strength bar, and a mealadditive that has the taste and
consistency of sawdust. Research shows that consumers fall into two types (A and B), and these
are described in the table below by their reservation prices for the products. Each consumer will
demand no more than one unit of any product at their reservation price. The consumers will
value a bundle of the products at the sum of the constituent reservation prices. Each product
costs 3 to produce. A bundle of all three products costs 9 to produce. Food For Life does not
price discriminate.
Reservation Prices
Consumer
Whey Strength Sawdust Bundle
A 10 16 2 10W+16S+2S
B 3 10 13 3W+10S+13S
There is an equal number of each consumer type (for simplicity, one of each type).
Only bundles of all three products need to be considered.
Best Separate Price Strategy
Customer Price per
Unit
Cost per
unit
Profit per
unit
Number of
units
Profit
Whey
A 10 3 7 3 21
B 3 3 0 3 0
strength
A 16 3 13 3 39
B 10 3 7 3 21
sawdust
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A 2 3 -1 3 -3
B 13 3 10 3 30
Best Pure Bundling Strategy
Customer Price per
Bundle
Cost per
Bundle
Profit per
Bundle
Number of
units
Profit
A
B
Best Mixed Bundling Strategy
Customer Price per
Bundle
Cost per
Bundle
Profit per
Bundle
Number of
units
Profit
Customer Price per
Unit
Cost per
unit
Profit per
unit
Number of
units
Profit
What pricing (profit- maximizing) strategy (among pricing separately, pure bundling, and
mixed bundling) would you recommend to Food For Life?Why?
10w+15s+2s= total revenue
MR (marginal revenue) =change in total revenue
Average revenue=Total revenue/output
ARa wrt whey=10w+15s+2s/w=3
10w+15s+2s=3w
7w+15s+2s=0………………… (i)
ARa wrt strength=10w+15s+2s/s=3
10w+15s+2s=3s
10w+12s+2s=0………………..(ii)
Solve equation (i) and (ii) simultaneously
7w+15s+2s=0…………….. (i)
10w+12s+2s=0……………..(ii)
-3w+3s=0
3w=3s
W=s
Then 10w+15s+2s/w=3
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10s+15s+2s/s=3
27s/s=3
Total cost=9
Mca=change in Tc
=9Q
Average cost=9/Q=3
Q=3 Cournot Duopoly & Monopoly: Steve Win has purchased land from the city of Atlantic City
in the Marina section. There are stories of a new casino building boom in Atlantic City
(MGeeM is also talking about entering, and Gump is opening his fourth casino). Some talk is
circulating that Win will subdivide his new land purchase and perhaps three casinos will be
built on the site. Suppose Win subdivides his land into two parcels. He builds on one site and
sells the other to another gambling entrepreneur. Win estimates that the demand for gambling
in the Marina area of Atlantic City (after accounting for the presence of two existing casinos
in the Marina and adjusting for the rest of the casinos in Atlantic City) is
where P is the price associated with gambling and Q is the quantity of gambling (think of P as
the average amount that a typical patron will net the casino, an amount paid for the entertainment
of gambling, and Q as the number of gamblers).Win, of course, does not sell the other parcel
until his casino is built (or is significantly far along); thus he has a first- mover advantage.
Win’s total cost (TCW) of producing gambling is
where is the number of gamblers in Win’s casino, and the total cost(TCR) of producing
gambling for Win’s rival is
where QR is the number of gamblers in the rival’s casino and
Would Atlantic City have done better to sell the land as two separate parcels rather than as a
single parcel to Win (given that Win was going to subdivide,Win and his rival could not collude,
and Win did not have the ability to produce as a monopolist)? You may assume that Win and his
rival could have been Cournot duopolists. If Atlantic City could do better, show why and by
how much. Carry all calculations to the thousandths decimal point. (Hint: Find Monopoly
solutions and Stackelberg first mover solutions.)
Solution
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But Q=QW+QR
P=750-5(QW+QR)
P=750-5QW-5QR
Leader Profit QW=750-5QW-5QR-(20+40QW+15.5 QW2) QW
(750-5QW-5QR-20-40QW-15.5QW2) QW
Differentiate with respect to QW
710-5QR-40QW =0
710-5QR=40QW
QW=710/40-5/40QR
Follower Profit QR=750-5QW-5QR-(10+5OQR+20QR2) QR
(750-5QW-5QR-10-50QR-20QR2)QR
Differentiate with respect to QR
700-5QW-50QR=0
QR=700/50-5/50QW
Substitute equation one to equation 2
QW=710/40-5/40(700/50-5/50QW)
QW=710/40-7/4-1/80QW
81/80QW=16
QW=15.8024 Units
QR=700/50-5/50(15.8024)
700/50-5/50*1280/81
700/50-128/81
=12.41975 Units
One-shot Technology Adoption Game:Suppose Toyota and Honda must decide whether to
make a new breed of side-impact airbags standard equipment on all models. Side-impact
airbags raise the price of each automobile by $500. If both firms make side-impact airbags
standard equipment, each company will earn profits of $1.5 billion. If neither company
adopts side-impact airbag technology, each company will earn $0.5 billion (due to lost sales
to other automakers). If one company adopts the technology as standard equipment and the
other does not, the adopting company will earn a profit of $2 billion and the other company
will lose $1 billion. If you were a decision maker at Honda, would you make side-impact
airbags standard equipment? Explain. (Make sure to start with a one-shot game matrix.)
TOYOTA HONDA
TOYOTA 2, -1 1.5, 1.5
HONDA 0.5, 0.5 2, -1
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As a decision maker at Honda I would make side impact airbags standard equipment.
This is because this is a strategy that gives that highest payoff to the company. In this strategy,
the company is playing its Nash equilibrium. The strategy indicates that no company between
Toyota and Honda has a higher advantage over the other.
One-shot pricing game: While there is a degree of differentiation among general
merchandise retailers like Target and Kmart, weekly newspaper circulars announcing sales
provide evidence that these firms engage in price competition. This suggests that Target and
Kmart simultaneously choose to announce one of two prices for a given product: a regular
price or a sales price. Suppose that when one firm announces the sale price and the other
announces the regular price for a particular product, the firm announcing the sale price
attracts 5 million extra customers and earns a profit of $5 billion, compared to the $3 billion
earned by the firm announcing the regular price. When both firms announce the sale price,
the two firms split the market equally (getting an extra 25 million customers each) for a
profit of $1 billion each. When both firms announce the regular price, each company attracts
only its 50 million loyal customers and the firms each earn $3 billion in profits. If you were
in charge of pricing at one of these firms, would you have a clear-cut pricing strategy? If so,
explain why. If not, explain why not and propose a mechanism that might solve your
dilemma. [Hint: Unlike Wal-Mart, neither of these firms guarantees “Everyday low prices.”]
TARGET KMART
TARGET 5, 3 1, 1
KMART 3, 3 3, 5
If I was in charge of pricing strategy, I would have a clear-cut pricing. This is because
price cut strategy in the market attracts more customers leading to higher profit. In a competitive
market, firms use price cut strategy to increase demand of their products. From the above pricing
game the two firms acquire equal profits after announcing similar prices. This is Nash
equilibrium where none of the two firms have advantage over the other. On the contrary, when
one company announces price cut it attract more customers compared to the other company
leading to higher profits.
American Airlines and Vanguard Airlines (Low Cost Carrier LCC) case Extended Game:
Based on the American Airlines case develop a extended entry game for Vanguard Airlines on
the DFW-MCI (Dallas-Fort Worth to Kansas City) route. What where Vanguard’s options
before entry and what did Vanguard expect American Airlines to do? What were American
Airlines options and what did it do? Did Vanguard perceive a credible threat? Did American
Airlines present a credible threat and did they execute on the threat? What were Vanguards
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options if there was a credible threat after entry and what did it do? Then what did American
do? Draw a multistage extended entry diagram, label it and determine the outcome of the game.
Summarize your findings in words.(Case is on
Webcampus).
1) Two duopoly firms faces a demand of Y=25-O.5P. Assume that the firm has constant
marginal cost of $10 per unit of output. Calculate the cournot Nash equilibrium level of
output and profit for each firm.
Solution
2Y=50-P
P=50=2Y But Y=Y1+Y2
P=50-2(Y1+Y2)
Cost=$10
Firm 1 Profit= (P-C) Y1
= (50-2(Y1+Y2)-10) Y1
Differentiate the equation with respect to Y1
50-2Y1-2Y2-10=0
40-2Y2=2Y1
Y1=20-2Y2
Similarly
Y2= (40-2Y1)/4
Y1= (40-2(40-2Y1)/4)/4
= (40-20-Y1)/4
Y1= (20-Y1)/4
4Y1-Y1=20
3Y1=20
Y1=20/3
Y2= (40-2*20/3)/4
=(40-40/3)/4
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=83.44/4
20.86