Microeconomics II - 110091-0471
last update: 27/09/2009
1
Optimal Decisions Using Marginal Analysis
Exercise 1.1 A television station is considering the sale of promotional videos. It can have the
videos produced by one of two suppliers. Supplier A will charge the station a setup fee of $1,200
plus $2 for each cassette; supplier B has no setup fee and will charge $4 per cassette. The station
estimates its demand for the cassettes to be given by Q = 1, 600 − 200P , where P is the price in
dollars and Q is the number of cassettes.
• Suppose the station plans to give away the videos. How many cassettes should it order?
From which supplier?
• Suppose instead that the station seeks to maximize its profit from sales of the cassettes.
What price should it charge? How many cassettes should it order from which supplier?
Exercise 1.2 As the exclusive carrier on a local air route, a regional airline must determine the
number of flights it will provide per week and the fare it will charge. Taking into account operating
and fuel costs, airport charges, and so on, the estimated cost per flight is $2,000. It expects to
fly full flights (100 passengers), so its marginal cost on a per passenger basis is $20. Finally, the
airline’s estimated demand curve is P = 120 − .1Q, where P is the fare in dollars and Q is the
number of passengers per week.
• What is the airline’s profit-maximizing fare? How many passengers does it carry per week,
using how many flights? What is weekly profit?
• Suppose the airline is offered $4,000 per week to haul freight along the route for a local firm.
This will mean replacing on of the weekly passenger flights with a freight flight (at same
operating cost). Should the airline carry freight for the local firm? Explain.
Exercise 1.3 Under the terms of the current contractual agreement, Burger Queen (BQ) is entitled
to 20 percent of the revenue earned by each of its franchises. BQ’s best-selling is the Slopper (it
slops out of the bun). BQ supplies the ingredients for the Slopper (bun, mystery meat, etc.) at
cost to the franchise. The franchisee’s average cost per Slopper (including ingredients, labor cost,
and so on) is $.80. At a particular franchise restaurant, weekly demand for Sloppers is given by
P = 3.00 − Q/800.
• If BQ sets the price and weekly sales quantity of Sloppers, what quantity and price should
it set? How much does BQ receive? What is the franchisee’s net profit?
• Suppose the franchise owner sets the price and sales quantity. What price and quantity will
the owner set? How does the total profit earned by the two parties compare to their total
profit in part a?
• Now suppose BQ and an individual franchise owner enter into an agreement in which BQ is
entitled to a share of the franchisee’s profit. Will profit sharing remove the conflict between
BQ and the franchise operator? Under profit sharing, what will be the price and quantity of
Sloppers? (Does the exact split of the profit affect your answer? Explain briefly.) What is
the resulting total profit?
• Profit sharing is not widely practiced in the franchise business. What are the disadvantages
relative to revenue sharing?
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2
Demand Analysis and Optimal Pricing
Exercise 2.1 A private-garage owner has identified two distinct market segments: short-term
parkers and all-day parkers with respective demand curves of PS = 3 − QS /200 and PC = 2 −
QC /200. Here P is the average hourly rate and Q is the number of cars parked at this price. The
garage owner is considering charging different prices (on a per-hour basis) for short-term parking
and all-day parking. The capacity of the garage is 600 cars, and the cost associated with adding
extra cars in the garage (up to this limit) is negligible.
• Given this facts, what is the owner’s appropriate objective? How can he ensure that members
of each market segment effectively pay a different hourly price?
• What price should he charge for each type of parker? How many of each type of parker will
use the garage at these prices? Will the garage be full?
• Answer the questions in part b assuming the garage capacity is 400 cars.
Exercise 2.2 A golf-course operator must decide what greens fees (prices) to set on rounds of golf.
Daily demand during week is: PD = 36 − QD /10 where QD is the number of 18-hole rounds and
PD is the price per round. Daily demand on the weekend is PW = 50 − QW /12. As a practical
matter, the capacity of the course is 240 rounds per day. Wear and tear on the golf course is
negligible.
• Can the operator profit by charging different prices during the week and on the weekend?
Explain briefly. What greens fees should the operator set on weekdays and how many rounds
will be played? On the weekend?
• When weekend prices skyrocket, some weekend golfers choose to play during the week instead.
The greater the difference between weekday and weekend prices, the greater are the number of
these defectors. How might this factor affect the operator’s pricing policy? Give a qualitative
answer.
Exercise 2.3 Nearby College Student Recruiting Office has hired a consultant in an effort to boost
enrollment. After detailed surveys are conducted, the consultant reports that elasticities are as
follows: EP = −1.6, EY − .8, EX = .25 (for Competition College tuition). Current tuition at
Nearby is $4,000.
• If tuition at Nearby is set to rise by 7%, income is expected to rise by 1%, and Competition
has announced a tuition increase of 6%, how much will Nearby’s enrollment change?
• The chief financial officer approaches the Recruiting officer, and asks for a copy of the report.
He says that he would like to see a tuition change because the school is facing a budget
crunch. If the marginal cost of a student is $2,750, what should tuition be in order to
maximize profit?
Exercise 2.4 Jonathan Livingstone Yuppie is a prosperous lawyer. Jonathan consumes three
goods, unblended Scotch whiskey ($20 per bottle), designer tennis shoes ($80 per pair), and meals
in French gourmet restaurants ($50 per meal). After he has paid his taxes and alimony, Jonathan
has $400 a week to spend.
• Write down a budget equation.
• Draw a three-dimensional diagram to show his budget set.
• Suppose that he determines that he will buy one pair of designer tennis shoes per week.
What equation must be satisfied by the combinations of the restaurant meals and whiskey
that he could afford?
Exercise 2.5 Nancy Lerner is trying to decide how to allocate her time in studying for her economics course. There are two examinations in this course. Her overall score for the course will be
minimum of her scores on the two examinations. She has decided to devote a total of 1,200 minutes
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to studying for these two exams, and she wants to get as high overall score as possible. She knows
that on the first examination if she doesn’t study at all, she will get a zero score on it. For every
10 minutes that she spends studying for the first examination, she will increase her score by one
point. if she doesn’t study at all for the second examination, she will get a zero score on it. For
every 20 minutes she spends studying for the second examination, she will increase her score by
one point. Determine the optimal allocation of the time spent on studying for the examinations.
Show it on the graph.
Exercise 2.6 The utility maximizing consumer has his preferences over goods x1 and x2 described
by Cobb-Douglas utility function u(x1 , x2 ) = xa1 x1−a
, where a = 1/3.
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• Find the marginal rate of substitution of good x1 with good x2 .
• Suppose that consumer’s disposable income is m = 20, the price of good x1 is p1 = 5, and
the price of good x2 is p2 = 4. What is the amount of good x2 that consumer is willing to
consume? (Both goods are infinitely divisible).
3
Production and Cost Analysis
Exercise 3.1 Suppose that production function of the steelworks is given by Q = 5LK, where
L is the number of workers, and K is the amount of capital used to give Q units of steel daily.
Steelwork can hire labor at $10 per unit, and the cost of capital is $20 per unit. What is the
optimal mix of inputs to produce 40 units of steel?
Exercise 3.2 The owner of the Magic car wash describes the relation between number of cars
washed and labor input as follows: Q = −.8 + 4.5L − .3L2 , where Q is the number of cars washed
per hour, and L is the number of employees. For each car washed the owner gets $5, and he pays
$4.5 per hour to his employees.
• How many persons should the owner employ to maximize profit?
• What is the profit per hour?
• Is the above labor to cars washed relation true for all L? Explain.
Exercise 3.3 Firm Z is developing a new product. An early introduction (beating rivals to market)
would greatly enhance the company’s revenues. However, the intensive development effort needed
to expedite the introduction can be very expensive. Suppose total revenues and costs associated
with the new product’s introduction are given by R = 720 − 8t and C = 600 − 20t + .25t2 , where
t is the introduction date (in months from now). Some executives have argued for an expedited
introduction date 12 months from now (t = 12). Do you agree? How about instant introduction
(t = 0)? What introduction date is most profitable? Explain.
Exercise 3.4 In a particular region, there are two lakes rich in fish. The quantity of fish caught
in each lake depends on the number of persons who fish in each, according to Q1 = 10N1 − .1N12
and Q2 = 16N2 − .4N22 , where N1 and N2 denote the number of fishers at each lake. In all, there
are 40 fishers.
• Suppose N1 = 16 and N2 = 24. At which lake is the average catch per fisher greater? In
light of this fact, how would you expect the fishers to redeploy themselves?
• How many fishers will settle at each lake?
• The commissioner of fisheries seeks a division of fisheries that will maximize the total catch
at the two lakes. What division of the 40 fisheries would you recommend?
Exercise 3.5 Let Q = Lα K β . Suppose the firm seeks to produce a given output while minimizing
its total input cost: C = PL L+PK K. Show that the optimal quantities of labor and capital satisfy
L/K = (α/β)(PK /PL ). Provide an intuitive explanation for this result.
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Exercise 3.6 Henry is serving lemonade on the corner of the busy street of Philadelphia. His
1/3 1/3
production function is f (x1, x2) = x1 x2 , where product is measured in liters, x1 is the amount
of lemons in kilograms, and x2 is the number of hours spent on squeezing lemons.
• What are the returns to scale of the above production function?
• If w1 is the price of one kilogram of lemons, and w2 is the hourly wage of lemon-squeezer,
the optimal working method is to work for ............ hours per one kilogram of lemons.
• Given that Henry produced y liters of lemonade, he used ............ kilograms of lemons and
worked for ............ hours.
Exercise 3.7 The production function is f (x1, x2) = min x1, x2.
• Suppose x1 < x2 . The marginal product of x1 is ..........., and with small increase in the
amount of x1 (increases, decreases, remains constant) ........... . The marginal product of x2 is
..........., and with small increase in the amount of x2 (increases, decreases, remains constant)
........... . The technical rate of substitution between x2 and x1 is ............ . This technology
demonstrates (increasing, constant, decreasing) ............ returns to scale.
• Let x1 = x2 . What is the marginal product of x1 with small increase in the amount of x1 ?
What is the marginal product of x1 with small increase in the amount of x2 ? The marginal
product of x1 with small increase in the amount of x2 (increases, decreases, remains constant)
............ .
4
Decision Making under Uncertainty and Value of Information
Exercise 4.1 In 1976, the parents of a 7-year-old boy sued a New York hospital for $3.5 million.
The boy was blinded shortly after he was born two weeks prematurely. His parents claimed that
hospital doctors administered excessive oxygen to the baby and that caused the blindness. The
case went to trial, and just as the jury announced it hat reached the verdict, the lawyers for the
two sides arrived at an out-of-court settlement of $500,000.
• If you were the parents, how would you decide whether to accept the settlement or wait for
the jury’s decision? What probability assessments would you need to make? Would you have
accepted the settlement?
• Answer the questions in part a, taking the hospital’s point of view.
Exercise 4.2 A European consortium has spent a considerable amount of time and money developing a new supersonic aircraft. The aircraft gets high marks on all performance measures
except noise. In fact, because of the noise, the consortium’s management is concerned that the
U.S. government may impose restrictions at some of the American airports where the aircraft can
land. Management judges a 50-50 chance that there will be some restrictions. Without restrictions, management estimates its (present discounted) profit at $125 million; with restrictions, its
profit would be only $25 million. Management must decide now, before knowing the government’s
decision, whether to redesign parts of the aircraft to solve the noise problem. The cost of the
redesign program is $25 million. There is a .6 chance that the redesign program will solve the noise
problem (in which case, full landing rights are a certainty) and a .4 chance it will fail.
• Using decision tree , determine the consortium’s best course of action, assuming management
is risk neutral.
• Find the expected value of perfect information about the redesign program. Calculate separately the expected value of perfect information about the U.S. government’s decision.
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• Suppose the management of the consortium questions its engineers about the success or
failure of the redesign program prior to committing to it. Management recognizes that its
engineers are likely to be biased in favor of the program. It judges that if the program truly
will succeed, the engineers will endorse it 90 percent of the time, but even if the program will
fail, they will endorse it 50 percent of the time. What is the likelihood of success in light of
an endorsement? What if the engineers do not endorse the program?
Exercise 4.3 Firm A is facing a possible lawsuit by legal firm B. Firm B represents the family
of Mr. Smith, who was killed in a motel fire (allegedly caused by faulty wiring). Firm A was the
builder of the motel. Firm A has asked its legal team to estimate the likely jury award it will be
ordered to pay in court. Expert legal counsel anticipates three possible court outcomes: awards
of $1,000,000, $600,000, or $0, with probabilities .2, .5, and .3, respectively. In addition to any
awards, firm A’s legal expenses associated with fighting the court case are estimated to be $100,000.
Firm A also has considered the alternative of entering out-of-court settlement negotiations with
firm B. Based on the assessments of its lawyers, firm A envisions the other side holding out for one
of two settlement amounts: $900,000 (a high amount) or $400,000 (a more reasonable amount).
Each demand is considered equally likely. If presented with one of these settlement demands, firm
A is free to accept it (in which case firm B agrees to waive any future right to sue) or reject it and
take its chances in court. The legal cost of pursuing a settlement (whether or not one is reached)
is $50,000. Determine the settlement or litigation strategy that minimizes firm A’s expected total
cost (any payment plus legal fees).
Exercise 4.4 Consider the following simplified version of the television game show Let’s Make a
Deal. There is a grand prize behind one of three curtains; the other two curtains are empty. As a
contestant, you get to choose a curtain at random. Let’s say you choose curtain 3. Before revealing
what’s behind the curtain, the game show host always offers to show you what one of the other
curtains contains. She shows you that curtain 2 is empty; in fact, she always shows you an empty
curtain. (You know that’s how the game works; so does the audience and everybody else.) Now
you must decide: Do you stick with your original choice, curtain 3, or switch to curtain 1? Which
action gives you the better chance of finding the grand prize?
Exercise 4.5 Filene’s Basement, a Boston-based department store, has a policy of marking down
the price of sale items each week that they go unsold. You covet an expensive brand of winter coat
that is on sale for $100. In fact, you would be willing to pay as much as $120 for it. Thus, you
can buy it now (for a profit of $120 - $100 = $20) or wait until next week, when the price will be
reduced to $75 if the coat is still available. The chances of its being available next week are 2/3.
If it is available in week 2, you can buy or wait until week 3. There is a 1/2 chance it will be sold
between weeks 2 and 3 and a a 1/2 chance it will be available at a reduced price of $60. Finally,
if it is available in week 3, you can buy or wait until week 4. There is a 1/4 chance it still will be
available, at a price of $50 (and a 3/4 chance it will be sold in the meantime). Week 4 is your last
chance to buy before the coat is withdrawn.
• How long should you wait before buying? Illustrate via a decision tree.
• Filene’s has 120 of these winter coats for sale. What is expected total revenue from the
pricing scheme in part a?
• Alternatively, Filene’s can set a single price for all coats. Its demand curve is P = 180 − Q.
Would it prefer a common-price method or the price-reduction method in part b? Explain.
5
Perfect Competition and Monopoly
Exercise 5.1 In a competitive market, the industry demand and supply curves are P = 200−.2QD
and P = 100 + .3QS , respectively.
• Find the market’s equilibrium price and output.
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• Suppose the government imposes a tax of $20 per unit of output on all firms in the industry.
What effect does this have on the industry supply curve? Find the new competitive price
and output. What portion of the tax has been passed on to consumers via a higher price?
• Suppose a $20-per-unit sales tax is imposed on consumers. What effect does this have on the
industry demand curve? Find the new competitive price and output. Compare this answer
to your findings in part b.
Exercise 5.2 Firm Z, operating in a perfectly competitive market, can sell as much or as little
as it wants of a good at a price of $16 per unit. Its cost function is C = 50 + 4Q + 2Q2 . The
associated marginal cost is M C = 4 + 4Q and the point of minimum average cost is Qmin = 5.
• Determine the firm’s profit-maximizing level of output. Compute its profit.
• The industry demand curve is Q = 200 − 5P . What is the total market demand at the
current $16 price? If all firms in the industry have cost structures identical to that of firm
Z, how many firms will supply the market?
• The outcomes in part a and b cannot persist in the long run. Explain why. Find the market’s
price, total output per firm in the long run.
• Comparing the short-run and long-run results, explain changes in the price and in the number
of firms.
Exercise 5.3 In a competitive market, the industry demand and supply curves are P = 70 − QD
and P = 40 + 2QS .
• Find the market’s equilibrium price and output.
• Suppose that the government provides a subsidy to producers of $15 per unit of the good.
Since the subsidy reduces each supplier’s marginal cost by 15, the new supply curve is P =
25 + 2QS . Find the market’s new equilibrium price and output. Provide an explanation for
the change in price and quantity.
• A public interest group supports the subsidy, arguing that it helps consumers and producers
alike. Economists oppose the subsidy, declaring that it leads to an inefficient level of output.
In your opinion, which side is correct? Explain carefully.
Exercise 5.4 Until recently, the market for air travel within Europe was highly regulated. Entry
of new airlines was severely restricted, and air fares were set by regulation. Partly as a result,
European air fares were and continue to be higher than U.S. fares for routes of comparable distance.
Suppose that, for a given European air route (say, London to Rome), annual air travel demand
is estimated to be Q = 1, 500 − 3P , where Q is the number of trips in thousands and P is the
one-way fare in dollars. In addition, the long-run average (one-way) cost per passenger along this
route is estimated to be $200.
• Some economists have suggested that during the 1980s and 1990s there was an implicit cartel
among European air carriers whereby the airlines charged monopoly fares under the shield of
regulation. Given the preceding facts, find the profit-maximizing fare and the annual number
of passenger trips.
• In the last five years, deregulation has been the norm in the European market, and this has
spurred new entry and competition from discount air carriers such as Ryanair and easyJet.
Find the price and quantity for the European air rout if perfect competition became the
norm.
Exercise 5.5 Demand for microprocessors is given by P = 35 − 5Q, where Q is the quantity of
microchips (in millions). The typical firm’s total cost of producing a chip is Ci = 5qi , where qi is
the output of firm i.
• Under perfect competition, what are the equilibrium price and quantity?
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• Under perfect competition, find total industry profit and consumer surplus.
• Suppose that one company acquires all the suppliers in the industry and thereby creates a
monopoly. What are the monopolist’s profit-maximizing price and total output?
• Compute the monopolist’s profit and the total consumer surplus of purchasers.
• Discuss changes between your answers in parts b. and d.
Exercise 5.6 Suppose that, over the short run (say, the next five years), demand for OPEC oil is
given by Q = 52.5 − 1.25P . (Here Q is measured in millions of barrels per day.) OPEC’s marginal
cost per barrel is $10.
• What is OPEC’s optimal level of production? What is the prevailing price of oil at this level?
• Many experts contend that maximizing short-run profit is counterproductive for OPEC in the
long run because high prices induce buyers to conserve energy and seek supplies elsewhere.
Suppose the demand curve just described will remain unchanged only if oil prices stabilize at
$20 per barrel or below. If oil price exceeds this threshold, long-run demand (over a second
five-year period) will be curtailed to Q = 60 − 2P . OPEC seeks to maximize its total profit
over the next decade. What is its optimal output and price policy? (Assume all values are
present values.)
Exercise 5.7 Firm 1 is a member of a monopolistically competitive market. Its total cost function
is C = 900 + 60Q1 + 9Q21 . The demand curve for the firm’s differentiated product is given by
P = 660 − 16Q1 .
• Determine the firm’s profit maximizing output, price and profit.
• Attracted by potential profits, new firms enter the market. A typical firm’s demand curve
(say firm’s 1) is given by P = [1, 224 − 16(Q2 + Q3 + ... + QN ) − 16Q1 ], where N is the total
number of firms. (If competitors’ outputs or numbers increase, firm 1’s demand curve shifts
inward.) The long-run equilibrium under monopolistic competition is claimed to consist of
10 firms, each producing 6 units at a price of $264. Is this claim correct?
• Based on the cost function given, what would be the outcome if the market were perfectly
competitive? (Presume market demand is P = 1, 224 − 16Q, where Q is total output.)
Compare this outcome to the outcome in part b.
Exercise 5.8 A single buyer who wields monopoly power in its purchase of an item is called a
monopsonist. Suppose that a large firm is the sole buyer of parts from 10 small suppliers. The
cost of a typical supplier is given by C = 20 + 4Q + Q2 .
• Suppose that the large firm sets the market price at some level P . Each supplier acts
competitively (i.e., sets output to maximize profit given P ). What is the supply curve of the
typical supplier? Of the industry?
• The monopsonist values the part at $10. This is the firm’s break-even price, but intends to
offer a price much less than this and purchase all parts offered. If it sets price P , its profit is
simply: π = (10 − P )QS , where QS is the industry supply curve found in part a. (Of course,
QS is a function of P .) Write down the profit expression and maximize profit with respect
to P . Find the firm’s optimal price. Give a brief explanation for this price.
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Oligopoly
Exercise 6.1 The OPEC cartel is trying to determine the total amount of oil to sell on the world
market. It estimates world demand for oil to be QW = 60 −.5P , QW denotes the quantity of oil (in
millions of barrels per day) and P is price per barrel. The cartel’s marginal cost is approximately
$20 per barrel.
• Determine OPEC’s profit-maximizing output and price.
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• OPEC’s economists recognize the importance of non-OPEC oil supplies. These can be described by the estimated supply curve QS = 1.5P − 20. Write OPEC’s net demand curve.
Find its optimal output and price. What portion of the world’s total oil supply comes from
OPEC?
Exercise 6.2 Firm A is the dominant firm in a market where industry demand is given by QD =
48 − 4P . There are four follower firms, each with long-run marginal cost given by M C = 6 + QF .
Firm A’s long run marginal cost is 6.
• Write the expression for the total supply curve of the followers (QS ) as this depends on price.
• Find the net demand curve facing firm A. Determine A’s optimal price and output. How
much output do the other firms supply in total?
Exercise 6.3 In the small town there are two confectioneries: one of the Mr Long and one of the
Mr Short. Nobody can tell the cakes from those confectioneries apart. The marginal costs of Mr
Long are constant - $1 per cake. Mr Short has constant marginal costs of $2 per cake. There are
no fixed costs. The inverse demand function is p(q) = 6 − .01q , where q is the sum of the cakes
sold by both confectionery owners.
• Find the reaction functions, quantities and profits in the equilibrium, assuming that confectionery owners competition is of Cournot type.
• Find the quantities and profits in the equilibrium, assuming that confectionery owners competition is of Bertrand type.
• Assume that Mr Long is a leader of Stackelberg type competition (Probably due to fact,
that he starts working an hour earlier than Mr Short.) Find the quantities and profits in the
equilibrium.
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Game Theory
Exercise 7.1 Firms M and N compete for a market and must independently decide how much
to advertise. Each can spend either $10 million or $20 million on advertising. If the firms spend
equal amounts, they split the $120 million market equally. (For instance, if both choose to spend
$20 million, each firm’s net profit is 60 - 20 = $40 million.) If one firm spends $20 million and
other $10 million, the former claims two thirds of the market and the latter one-third.
• If the firms act independently, what advertising level should each choose? Explain. Is a
prisoner’s dilemma present?
• Could the firms profit by entering into an industry-wide agreement concerning the extent of
advertising? Explain.
Exercise 7.2 A firm sells two goods in a market consisting of three types of consumers. The table
shows the values consumers place on the goods. The unit cost of producing each good is $5.
Consumers
A
B
C
Good
X
13
7
15
Y
6
11
2
Find the optimal prices for (1) selling the goods separately, (2) pure bundling, and (3) mixed
bundling. Which pricing strategy is most profitable?
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Exercise 7.3 Find all Nash equilibriums in the game of two banks, whose management considers selling to debtors their liabilities for the discounted price.
Bank I
S
NS
Bank II
S
6,6
11,6
NS
6,11
6,6
Exercise 7.4
• Identify the equilibrium outcome(s) in each of the three payoff tables.
I.
R1
R2
C1
12,10
4,8
C2
10,4
9,6
II.
R1
R2
C1
12,10
4,4
C2
4,4
9,6
III.
R1
R2
C1
12,10
4,-100
C2
4,4
9,6
• In each table, predict the exact outcome that will occur and explain your reasoning
• In table III, suppose the column player is worried that the row player might choose R2 (perhaps a one-in-ten chance). Given the risk, how should the column player act? Anticipating
the column player’s thinking, how should the row player act?
Exercise 7.5 Two firms dominate the market for surgical sutures and compete aggressively with
respect to research and development. The following payoff table depicts the profit implications of
their different R&D strategies.
• Suppose that no communication is possible between the firms; each must choose its R&D
strategy independently of the other. What actions will the firms take, and what is the
outcome?
• If the firms can communicate before setting their R&D strategies, what outcome will occur?
Explain.
Firm A’s R&D Spending
Low
Medium
High
Firm B’s R&D Spending
Low Medium
High
8,11
6,12
4,14
12,9
8,10
6,8
11,6
10,8
4,6
Exercise 7.6 One way to lower the rate of auto accidents is strict enforcement of motor vehicle laws (speeding, drunk driving, and so on). However, maximum enforcement is very costly. The
following payoff table lists payoffs of a typical motorist and a town government. The motorist can
obey or disobey motor vehicle laws, which the town can enforce or not.
Motorist
Obey
Don’t Obey
Town
Enforce
0,-15
-20,-20
Don’t Enforce
0,0
5,-10
• What is the town’s optimal strategy? What is the typical motorist’s behavior in response?
• What if the town could commit to a strict enforcement policy and motorists believed that
this policy would be used? Would the town wish to do so?
• Now suppose the town could commit to enforcing the law part of the time. (The typical motorist cannot predict exactly when the town’s traffic police will be monitoring the roadways.)
What is the town’s optimal degree (i.e., percentage) of enforcement? Explain.
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Exercise 7.7 In the following game, players A and B alternate moves. At each turn, a player can
terminate the game or pass move to the next player. By passing, the player increases the rival’s
potential payoff by five units and reduces her own by one unit. Thus, as long as both players pass
the move on to one another, their payoffs increase. If the game terminates immediately - the payoff
is (2,2). Player A starts the game.
• Draw a game tree for this extensive form game.
• Suppose you are paired with another student with whom you will play the game. Just based
on your judgment (no analysis), how would you play?
• Now analyze the game tree by working backward. What actions should the players take?
What is the outcome? Briefly explain this result.
• The experiments with the above described game show that many of the players A decides to
pass the move. How could you explain this result?
Exercise 7.8 Over the last decade, the Delta Shuttle and the U.S. Air Shuttle have battled for
market share on the Boston New York and Washington, DC New York routes. In addition to
service quality and dependability (claimed or real), the airlines compete on price via periodic fare
changes. The hypothetical payoff table lists each airline’s estimated profit (expressed on a per-seat
basis) for various combinations of one-way fares.
Delta Shuttle
$139
$119
$99
U.S.
$139
34,38
42,20
35,7
Air Shuttle
$119
$99
15,42 6,32
22,22 10,25
27,9 18,16
• Suppose that the two airlines select their fares independently and once and for all. (The
airlines’ fares cannot be changed.) What fares should the airlines set?
• Suppose, instead, that the airlines will set fares over the next 18 months. In any month, each
airline is free to change its fare if it wishes. What pattern of fares would you predict for the
airlines over the 18 months?
• Pair yourself with another student form the class. The two of you will play the roles of Delta
and U.S. Air and set prices for the next 18 months. You will exchange written prices for
each month. You then can determine your profit (and your partner’s profit) from the payoff
table. The competition continues in this way for 18 months, after which time you should
compute your total profit (the sum of your monthly payoffs). Summarize the results of your
competition. What lessons can you draw from it?
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