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There may be some duplication. Sorry!1.Two large diversified consumer products firms are about to enter the market for a new pain reliever. The two firms are very similar in terms of their costs, strategic approach, and market outlook. Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price. The market demand curve for the pain reliever is given as:

Q = 2600 - 400P.

Both firms have constant long-run average costs of $2.00 per bottle. Patent protection insures that the two firms will operate as a duopoly for the foreseeable future. Price and quantities are per bottle. If the firms act as Cournot duopolists, solve for the firm and market outputs and equilibrium prices.

2.Lambert-Rogers Company is a manufacturer of petro-chemical products. The firm's research efforts have resulted in the development of a new auto fuel injector cleaner that is considerably more effective than other products on the market. Another firm, G.H. Squires Company, independently developed a very similar product that is as effective as the Lambert-Rogers formula. To avoid a lengthy court battle over conflicting patent claims, the two firms have decided to cross-license each other's patents and proceed with production. It is unlikely that other petrochemical companies will be able to duplicate the product, making the market a duopoly for the foreseeable future. Lambert-Rogers estimates the demand curve given below for the new cleaner. Marginal cost is estimated to be a constant $2 per bottle.

Q = 300,000 - 25,000P.

where P = dollars per bottle and Q = monthly sales in bottles.

a. Lambert-Rogers and G.H. Squires have very similar operating

strategies. Consequently, the management of Lambert-Rogers believes

that the Cournot model is appropriate for analyzing the market,

provided that both firms enter at the same time. Calculate Lambert-

Rogers' profit-maximizing output and price according to this model.

b. Lambert-Rogers' productive capacity and technical expertise could

allow them to enter the market several months before Squires.

Choose an appropriate model and analyze the impact of Lambert

Rogers being first into the market. Should Lambert-Rogers hurry to

enter first?

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3.University Bookstore competes with Campus Bookstore in the textbook market. Since University Bookstore is on campus, they have "first-move" advantage. The bookstores compete by setting price. The demand function for University Bookstore is qU = 12,000 - 80PU + 60PC. The demand function for Campus Bookstore is qC = 12,000 - 80PC + 60PU. Campus Bookstore's marginal revenue function is: MRC(PC,PU) = 12,000 - 160PC + 60PU. Campus Bookstore's marginal cost is: MCC(PC,PU)=-1,600. Determine Campus Bookstore's price reaction function. University Bookstore takes Campus Bookstore's behavior into account in determining it's optimal pricing behavior. University Bookstore's marginal revenue function is: MRU(PU,PC) = 17,100 - 115PU. University Bookstore's marginal cost function is: MCU(PU) = -1,150. Determine University Bookstore's optimal price. What is Campus Bookstore's optimal price? Given that the cost to both bookstores is $20 per book and demand is symmetric, why does University Bookstore charge a different price? Which bookstore makes a larger profit?

4.Buy-Right is a chain of grocery stores operating in small cities throughout the southwestern United States. Buy-Right's major competition comes from another chain, Acme Food Stores. Both firms are currently contemplating their advertising strategy for the region. The possible outcomes are illustrated by the payoff matrix below.

Acme Foods

Increase Don't Increase

Advertising Advertising

Buy-right Increase Advertising 20, 15 35, -5 Don't Increase Advertising 2, 30 25, 25 Entries in the payoff matrix are profits. Buy-Right's profit is before the comma, Acme's is after the comma.

a. Describe what is meant by a dominant strategy.

b. Given the payoff matrix above, does each firm have a dominant

strategy?

c. Under what circumstances would there be no dominant strategy for

one or both firms?

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5.Two firms at the St. Louis airport have franchises to carry passengers to and from hotels in downtown St. Louis. These two firms, Metro Limo and Urban Limo, operate nine passenger vans. These duopolists cannot compete with price, but they can compete through advertising. Their payoff matrix is below:

United Limo

Increase Don't Increase

Advertising Advertising

Metro Limo Increase Advertising 25, 15 30, 0 Don't Increase Advertising 15, 20 40, 5 a. Does each firm have a dominant strategy? If so, explain and what

that strategy is.

b. What is the Nash equilibrium? Explain where the Nash equilibrium

occurs in the payoff matrix.

6.Consider two firms, X and Y, that produce super computers. Each can produce the next generation super computer for the military (M) or for civilian research (C). However, only one can successfully produce for both markets simultaneously. Also, if one produces M, the other might not be able to successfully produce M, because of the limited market. The following payoff matrix illustrates the problem.

Firm Y

M C

Firm X M 2, 1 2, 2 C 1, 1 3, 2 a. Find the Nash equilibrium, and explain why it is a Nash

equilibrium.

b. If Firm X were unsure that the management of Firm Y were

rational, what would Firm X choose to do if it followed a

maximin strategy? What would both firms do if they both followed

a maximin strategy?

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1. Begin by solving for P.

Q = 2600 - 400P

Q - 2600 = -400P

P = 6.5 - 0.0025Q

Denote the two firms A and B and solve for reaction functions.

TRA = PA QA TRA = (6.5 - 0.0025Q)QA TRA = 6.5QA - 0.0025[(QA + QB)QA]

TRA = 6.5QA - 0.0025QA2 - 0.0025QAQB MRA = 6.5 - 0.005QA - 0.0025QB Set MRA = MC

6.5 - 0.005QA - 0.0025QB = 2

- 0.005QA = 4.5 + 0.0025QB QA = 900 - 0.5QB One can verify that:

QB = 900 - 0.5QA Substitute expression for QB into QA QA = 900 - 0.5(900 - 0.5QA)

QA = 900 - 450 + 0.25QA QA - 0.25QA = 450

QA(1 - 0.25) = 450

450

QA = = 600

0.75

Substitute expression for QA into QB QB = 900 - 0.5(900 - 0.5QB)

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QB = 900 - 450 + 0.25QB QB - 0.25QB = 450

QB(1 - 0.25) = 450

450

QB = = 600

0.75

QT = QA + QB QT = 600 + 600 = 1200

P = 6.5 - 0.0025(1200)

P = $3.5 per bottle

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2. Denote Lambert-Rogers price and quantity as PL, QL and Squires as

PS, QS.

Demand function is given as:

Q = 300,000 - 25,000P

Solve for P:

Q - 300,000 = -25,000P

P = 12 - 0.00004Q

Outcome under Cournot model:

a. TRL = PL QL TRL = (12 - 0.00004Q)QL Q = QL + QS TRL = [12 - 0.00004(QL + QS)]QL 2 TRL = 12QL - 0.00004QL - 0.00004QLQS MRL = 12 - 0.00008QL - 0.00004QS Set MRL = MC

12 - 0.00008QL - 0.00004QS = 2

-0.00008QL - 0.00004QS = -10

QL = 125,000 - 0.5QS So, QS = 125,000 - 0.5QL Substitute for QS:

QL = 62,500 + 0.25QL 62,500

Q = Q = = 83,333

0.75

Q = QL + QS Q = 83,333 + 83,333 = 166,666

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P = 12 - .00004(166,666)

P = 12 - 6.67 = $5.33

P = $5.33 per bottle

166,666 bottles sold per month

b. The Stackelberg model is appropriate when one firm enters first.

Lambert-Rogers determines their output, which Squires then takes

as given. Lambert's total revenue function is given as:

2 TRL = 12QL - 0.00004QL - 0.00004QLQS Squires reaction function QS = 125,000 - 0.5QL can be substituted

into TRL, since Squires will take Lambert's output as given.

2 TRL = 12QL - 0.00004QL - 0.00004QL(125,000 - .5QL)

2 2 TRL = 12QL - 0.00004QL - 5QL + 0.00002QL 2 TRL = 7QL - 0.00002QL MRL = 7 - 0.00004QL Set MRL = MC

7 - 0.00004QL = 2

-0.00004QL = -5

QL = 125,000

To find QS substitute QL into S reaction function

QS = 125,000 - 0.5QL QS = 125,000 - 0.5(125,000)

QS = 62,500

Q = QL + QS Q = 125,000 + 62,500

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Q = 187,500

P = 12 - 0.0004(187,500)

P = 12 - 7.5 = $4.50

Lambert-Rogers gets a much larger share of the market by entering

first. They should advance their schedule in order to enter first.

8.68 - 7.34

L = = 0.15

8.68

3. Campus Bookstore's price reaction function is determined by setting

MRC(PC,PU) = MCC(PC,PU) and solving for the firm's own price as a

function of University Bookstore's price. This implies 12,000 - 160PC 3

+ 60PU = -1,600 PC = 85 + PU. University Bookstore's optimal price

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is determined by setting MRR(PR) = MCR(PR) and solving for the firm's

own price. This implies 17,000 - 115PU = -1,150 PU = 158.69. We can

plug University Bookstore's price into Campus Bookstore's reaction

function to determine Campus Bookstore's profit maximizing price

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choice. This is PC = 85 + (158.69) = 144.50. University Bookstore

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sells 7,974.8 books while Campus Bookstore sells 9,961.4 books.

University Bookstore's profits are $1,106,025 and Campus Bookstore's

profits are $1,240,194.3. Campus Bookstore makes a larger profit even

though University Bookstore has "first-move" advantage. Without

"first-move" advantage, both bookstores would charge $136 per book

and earn profits of $1,076,480. The "first-move" ability allows

University Bookstore to increase profits by over 2.7%. In doing so,

Campus Bookstore's profits rise by over 15.2%.

4.a. A dominant strategy is one that is optimal regardless of the rival

strategy.

b. For both firms, the dominant strategy is to increase advertising.

If Acme increases advertising, Buy-Right earns 20 by increasing, 2

by not increasing.

Profit is higher for Buy-Right by increasing, regardless of Acme's

choice.

The same can be shown to be true for Acme.

c. Either or both firms would not have a dominant strategy if their

best choice depended on the choice of their rival.

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5.a. Firm A has no dominant strategy. If B advertises, then A does

best by advertising; but if B does not advertise, then A should

not advertise. Firm B has a dominant strategy, and it should

advertise.

b. The Nash equilibrium is for both firms to advertise. Each does

best, 25 and 15, respectively, by advertising, given what the

other firm does.

6.a. The Nash equilibrium occurs at the bottom right on the C,C

position. In this position, each firm does its best given what

the other firm does.

b. Firm X would find the maximum of the minimum payoffs. If Firm X

chose M, the minimum payoff for X would be 2. If Firm X chose C,

then the minimum payoff for X would be 1. Thus, the maximum

would be 2. Firm X should choose M. If both firms followed a

maximin strategy, then the top right corner 2,2 would by the

outcome.