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Sample paper on Managerial 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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(5100-13050-4350-750)26100

13050*26100= 340,605,000


(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=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 =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


(5100-0.5*3450-0.5*1150-500)3450

(5100-1725-575-500)3450

2275*3450=7,848,750


(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

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