Making Decisions with Uncertainty17©2018 Cengage Learnin.docx

Making Decisions
with Uncertainty
17
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CHAPTER
When you’re uncertain about the costs or benefits of a decision,
replace numbers with random variables and compute expected
costs and benefits.
Uncertainty in pricing: When customers have unknown values,
you face a familiar trade-off: Price high and sell only to high-
value customers, or price low and sell to all customers.
If you can identify high-value and low-value customers, you can
price discriminate and avoid the trade-off. To avoid being
discriminated against, high-value customers will try to mimic
the behavior and appearance of low-value customers.
2
Difference-in-difference estimators are a good way to gather
information about the benefits and costs of a decision. The first

difference is before versus after the decision or event. The
second difference is the difference between a control and an
experimental group.
If you are facing a decision in which one of your alternatives
would work well in one state of the world, and you are
uncertain about which state of the world you are in, think about
how to minimize expected error costs.
3
continued
TeleSwitch
A large telecom supplier, TeleSwitch, sold its product only
through distributors.
In 2000, their largest clients wanted to deal directly with
TeleSwitch – and avoid the middle man distributor. TeleSwitch
was unsure what to do.
They might lose large customers if they didn’t switch.
But, they might lose distributors (and their small customers) if
they did.
There is a lower probability of losing dealers (because they
would have to incur costs to change suppliers)
But this would have a much larger impact on profit.
How should we analyze decisions like this??
4

Introduction: Undertainty
This problem illustrates the type of uncertainty that exist in
most business decisions.
This chapter looks at ways to help deal with uncertainty and
arrive at decisions that will best profit your firm.
By modeling uncertainty, you can:
Learn to make better decisions
Identify the source(s) of risk in a decisions
Compute the value of collecting more information.
5
Modeling Uncertainty
To model uncertainty we use random variables to compute the
expected costs and benefits of a decision.
Definition: a random variable is simply a way of representing
numerical outcomes that occur with different probabilities.
To represent values that are uncertain,
list the possible values the variable could take,
assign a probability to each value, and
compute the expected values (average outcomes) by calculating
a weighted average using the probabilities as the weights.
6

Random variables
Definition: a binomial random variable, X, can have two values,
x1 or x2, with probabilities, p and 1-p. The expected value
(mean) for a binomial random variable is:
E[X]=p*x1+(1-p)x2
Definition: a trinomial random variable, X, can have three
values, x1, x2, or x3, with probabilities p1, p2, and 1-p1–p2.
The mean for a trinomial random variable is:
E[X]= p1*x1+ p2*x2+(1- p1-p2) x3
7
How to model uncertainty
“Wheel of Cash” example:
The carnival game wheel is divided like a pie into thirds, with
values of $100, $75, and $5 painted on each of the slices
The cost to play is $50.00
Should you play the game?
Three possible outcomes: $100, $75, and $5 with equal
probability of occurring (assuming the wheel is “fair”)
Expected value of playing the game is
1/3 ($100) + 1/3 ($75) + 1/3 ($5) = $60
But, if the wheel is biased toward the $5 outcome, the
expected value is
1/6 ($100) + 1/6 ($75) + 2/3 ($5) = $32.50
8

TeleSwitch’s Decision Tree
The probability of losing customers is 0.6
The probability of losing distributors is 0.2
9
Entry Decision with Uncertainty
The probability of retaliation (no accommodation) to an entry
decision (as modeled in ch 15) is 0.5
10
Dealing with uncertainty
Discussion: How do you respond to an invitation from a friend
to invest in a real estate venture that depends on uncertain
future demand and interest rates?
Calculate the potential gains and loses based on different
combinations of high and low interest rates and high and low
demand
Whoever proposed the venture probably presented the best case
scenario (low interest rates and high demand) – and that is the
only combination (of four possible outcomes) under which you

will do well.
Either don’t invest or find a way that aligns your friend’s
incentives with your own, i.e., he gets a payoff only if the
venture does well.
11
Uncertainty in Pricing
Uncertainty in pricing arises when the demand for a product is
unknown.
To model this uncertainty, classify the number and type of
potential customers. For example:
High-value consumers willing to pay $8
Low-value consumers willing to pay $5
Suppose there are equal numbers of each consumer group
Discussion: If MC= $3, what is optimal price?
By pricing high, you would earn $5 per sale each time a high-
value costumer shops – or %50 of the time
By pricing low, you would earn $2 per sale but would be able to
sell to both high- and low-value costumers – 100% of the time.
12
Uncertainty in Pricing (cont’d.)
Answer: Price High
13

Price Discrimination Opportunity
If you can identify the two types of customers, set different
prices to each group, and prevent arbitrage between them, then
you can price discriminate.
Price of $8 to the high-value customers
Price of $5 to the low-value customers.
Discussion: When buying a new car, sales people discriminate
between high- and low-value customers. How do they do this?
Discussion: What can you do to defeat this?
14
Natural experiments
To gather information about the benefits and costs of a decision
you can run natural experiments.
Natural experiment example: A national restaurant chain
A regional manager wanted to test the profitability of a special
holiday menu
To do this, the menu was introduced in half the restaurants in
her region.
In comparing sales between the new menu locations and the
regular menu locations (the control group) the manager hoped to
isolate the effect of the holiday menu on profit.

15
Natural experiments (cont’d.)
This is a difference-in-difference estimator. The first difference
is before vs. after the introduction of the menu; the second
difference is the experimental vs. control groups
Difference-in-difference controls for unobserved factors that
can influence changes
The manager found that sales jumped during the holiday season
– but the increase was seen both in the control and experimental
groups—both increased by the same amount.
The manager concluded that the holiday menu’s popularity came
at the expense of the regular menu. So the holiday menu only
cannibalized the regular menu’s demand and didn’t attract new
customers to the restaurant.
16
Natural experiments (cont’d.)
Natural experiments can be useful in many different contexts.
When the FTC looked back at a 1998 gasoline merger in
Louisville, they used their own version of a difference-in-
difference estimator.
Three control cities (Chicago, Houston, and Arlington) were
used to control for demand and supply shocks that could affect

price.
The first difference was before vs. after the merger; the second
difference was Louisville prices vs. prices in control cities– this
allowed the FTC to isolate the effects of the merger and
determine its effect
17
1998 LouisGasoline Merger
18
Minimizing expected error costs
Sometimes, when faced with a decision, instead of focusing on
maximizing expected profits (benefits minus costs) it can be
useful to think about minimizing expected “error costs.”
This approach is helpful when one alternative would work well
only under certain conditions, and you are uncertain about
whether the conditions hold.
For example, “should we impose a carbon tax?”
If global warming is caused by human activity then a carbon tax
will help reduce it.
But if global warming is not caused by human activity, then a
carbon tax would only reduce economic activity and would not
cool the Earth.

19
Error costs (cont’d.)
The two global warming alternatives can be modeled by:
20
Type I error is the failure to tax when global warming (GW) is
caused by human activity.
The Type II error is the implementation of a carbon tax when
global warming (GW) is not caused by human activity.
The optimal decision is the one with the smaller expected error
costs, i.e. Tax if (1-p)*Cost(Type I) < p*Cost(Type II)
This type of analysis is especially useful for balancing the risks
associated with pricing errors (over- v. under-), e.g., for
airlines, hotels, cruise ships; as well as production errors (over
v. under)Carbon TaxNo TaxGW is caused by human activity
(p)0(p) x (error cost II)GW is not caused by human activity (1-
p)(1-p) x (error cost I)0
Risk versus uncertainty
Risk is how we characterize uncertainty about values that are
variable.
Risk is modeled using random variables.
Uncertainty is uncertainty about the about the distribution of
the random variables.

E.g., which probabilities should be assigned to the various
values the random variables can take?
This difference is critical in financial markets. Risk can be
predicted, priced and traded – people are comfortable with risk.
Dealing with uncertainty is much more difficult.
Mistaking risk for uncertainty can be a costly mistake
21
IndyMac: Risk vs. Uncertainty
Risk never went away, investors were just ignoring it
Black Swans & fat tails
I have nothing against economists: you should let them entertain
each others with their theories and elegant mathematics,
[But]…do not give any of them risk-management
responsibilities.
—Nassim Nicholas Taleb
22
Dealing with uncertainty
Uncertainty is unavoidable. So to cope with uncertainty in
decision making, gather more or better information.
Best Buy has used dispersed sets of non-experts to predict
future variables, such as a holiday sales rate.

Google uses internal prediction markets to generate demand and
usage forecasting.
The US Marines advise:
Because we can never eliminate uncertainty, we must learn to
fight effectively despite it. We can do this by developing
simple, flexible plans; planning for likely contingencies;
developing standing operating procedures; and fostering
initiative among subordinates.
23
Risk versus uncertainty
Part of the housing crisis can be attributed to an error in
translating uncertainty to risk through a mathematical formula
created by David Li.
The formula was designed to measure the correlation between
returns of various assets that made up collateralized debt
obligations (CDOs).
But there was uncertainty about how one asset’s failure would
related to that of another asset. There was also a lack of
historical data about relationships among the underlying assets.
Li’s solution was to use past credit default swap (CDS) prices
as an indication of correlation returns (clever but imperfect).
CDS data came from a time when housing prices were on the
rise, and the correlation changed during a period of decreasing
prices.
Nearly everyone was using this formula, and… we’ve seen how
it all turned out
24

Telecom Firm
Sell directly to large customers
(.20) × $30 + (.80) × $130 = $110
Sell only through dealers
(.60) × $100 + (.40) × $130 = $112
Distributors leave
(probability = .20)
Firm profit = $30
Distributors stay
(probability = .80)
Firm profit = $130
Large customers leave
(probability = .60)
Firm profit = $100
Large customers stay
(probability = .40)
Firm profit = $130
Entrant
Enter
(.50) × $60 + (.50) × $-40 = $10
Stay Out
(.50) × $0 + (.50) × $0 = $0
Incumbent prices high
(probability = .50)
Entrant profit = $60
Incumbent prices low
(probability = .50)
Entrant profit = $-40
Incumbent prices high
(probability = .50)

Entrant profit = $0
Incumbent prices low
(probability = .50)
Entrant profit = $0
Pricing Decision
Price High
(.50) × $5 + (.50) × $0 = $2.50
Price Low
(.50) × $2 + (.50) × $2 = $2
Get high-value customer
(probability = .50)
Profit = $5
Get low-value customer
(probability = .50)
Profit = $0
Get high-value customer
(probability = .50)
Profit = $2
Get low-value customer
(probability = .50)
Profit = $2
Auctions
18
CHAPTER

In oral or English auctions, the highest bidder wins by
outbidding the second- highest bidder. This means that the
second-highest bidders’ value determines the price.
A Vickrey or second-price auction is a sealed-bid auction in
which the high bidder wins but pays only the second-highest
bid. These auctions are equivalent to oral auctions and are well
suited for use on the Internet.
In a sealed-bid ﬁrst-price auction, the high bidder wins and pays
his value. Bidders must balance the benefits of bidding higher
(a higher probability of winning) against the costs of bidding
higher (reduced margin if they do win). Optimal bids are less
than bidders’ private values.
2
Bidders can increase their proﬁt by agreeing not to bid against
one another. Such collusion or bid rigging is more likely to
occur in open auctions and in small, frequent auctions. If
collusion is suspected,
do not hold open auctions;
do not hold small and frequent auctions;
do not disclose information to bidders—do not announce who
the winners are, who else may be bidding, or what the winning
bids were.
In a common-value auction, bidders bid below their estimates to
avoid the winner’s curse. Oral auctions return higher prices in
common-value auctions because they release more information
than sealed-bid auctions.
3
continued

Bell Telephone
In 1885, Bell Telephone Company of Canada established
Northern Electric to manufacture its telephone equipment.
By 2000, the company (now Nortel) had a market share of over
$200 Billion
Decade of bad investments, declared bankruptcy in 2011
Nortel approved for sale by bankruptcy court
The court was unsure of the value of some of the company’s
assets, such as the 6000 patents, and decided to sell these assets
with an auction.
The bidding started at $900 million but was pushed up to $4.5
billion after successive rounds of bidding.
4
Introduction: Auctions
Auctions are simply another form of competition, like price
competition or bargaining.
CarBargains is one company that uses auctions to help car
buyers.
In these auctions, though, sellers not buyers are competing.
Local car dealers offer prices to a single consumer in a sealed-
bid auction.
Auctions set a price and identify the high-value buyer or low-

cost seller.
Auctions are often used in combination with bargaining, e.g.,
first an auction is used to identify the high-value buyers and
then there is a negotiation over the final price.
5
Oral Auctions
Definition: In an oral or English auction, bidders submit
increasing bids until only one bidder remains. The item is
awarded to this last remaining bidder.
Example: Suppose there are five bidders with values equal to
{$5, $4, $3, $2, $1}.
The $5 bidder will win the auction, and bids only slightly over
$4 to do so.
The “price” or winning bid is $4, or slightly above.
The winning bidder is willing to pay $5 but doesn’t have to, so
the losing bidders determine the price in oral auctions.
Auctions identify the high-value bidder (“efficiency”) and set a
price for an item, with no negotiating necessary. For these
reasons, economists love auctions.
6
Benefits of auctions
Example: auction vs. posted-price

A retail store is unsure whether they should price high ($8) or
low ($5) for a certain item.
If the store prices high, they sell to only high-value buyers (half
the time). If the store prices low, they sell to all customers at a
lower price.
If MC = $3, then pricing high is preferable
(.5)($8-$3) = $2.50 [versus (1.0)($5-$3) = $2.00]
If the store uses an auction instead, and two bidders show up
with values $8 and $5 – meaning there is again a .5 chance of
selling to a high-value costumer – what will the revenue of the
sale be?
7
Oral Auctions (cont’d)
8
Second-Price Auctions
Definition: A Vickrey or second-price auction is a sealed-bid
auction in which the item is awarded to the highest bidder, but
the winner pays only the second-highest bid.
This at first seems counterintuitive – why leave money on the
table? But second-price auctions encourage bidders to bid more

aggressively.
William Vickrey and James A. Mirrlees shared the 1996 Nobel
Prize in Economics for their work inventing the Vickrey auction
and establishing that there is no difference in outcome between
an oral and second-price auction.
9
Second-price auctions (cont’d)
Because the winning bidder pays the price of the second-highest
bid, bidders are willing to bid up to their values, so the outcome
is the same as an oral auction.
Second-price auctions are easier to run than oral auctions
because the bidders can bid in remotely, and asychronously (at
different places and times).
Discussion: Why are eBay auctions equivalent to second-price
auctions?
Discussion: Why does eBay use second-price auctions?
10
Sealed-Bid Auctions
Definition: In a sealed-bid first-price auction, the highest bidder
gets the item at a price equal to the highest bid.
These auctions present a difficult trade-off for bidders:
A higher bid reduces the profit if you win, but

Also raises probability of winning
Bidders balance these two effects by bidding below their values
(“shading”).
Experience and knowing the competing bidders are the keys to
these auctions, but in general, bid more aggressively – shade
less – if the competition is strong.
11
Bid Rigging or Collusion
Example: an oral auction with bidder values of {$5, $4, $3, $2,
$1}.
Suppose that in this auction the two high-value bidders have
formed a bidding ring (also known as a cartel).
The two decide NOT to bid against each other, so the cartel
wins the item by outbidding the non-cartel members, i.e., price=
$3. The cartel makes a profit of $1 which typically is split
evenly between members.
Bid-rigging is a criminal violation of antitrust laws in the US
and many other countries.
In one type of bid-rigging, cartel members re-auction the items
won in a second-auction to cartel members in a second or
“knockout” auction.
12

Bid-rigging / Collusion (cont’d)
Another type of collusion is known as a bid-rotation scheme.
This scheme uses quid pro quo bidding behavior.
Bidders in these cartels submit weak bids or refrain from
bidding against each other until it is their turn to “win.”
In a bid-rotation scheme each cartel member must wait for his
turn to win – a weakness that leaves these schemes vulnerable
to cheating.
Proposition: Collusion is more likely in oral auctions.
Proposition: Collusion is more likely in small, frequent
auctions.
13
Bid-rigging: Frozen Fish Conspiracy
After this cartel was broken the price of fish dropped 23%
Investigators backcast from the competition period into the
collusive period to determine the cartel’s effect, i.e., what the
price would have been, “but for” the conspiracy.
14
Reacting to bid-rigging
The government is frequently the victim of bid-rigging schemes.
Learning from the government’s experience, some tips to avoid

collusion:
Do not rely on purchasing agents (those running the auction)
who have little interest in buying at a low price. Instead, reward
agents for making good (high-quality and low-price) purchases.
Do not entangle purchasing agents with masses of red tape.
Instead, permit them to negotiate (e.g., to bargain with the
bidders) if they suspect bid rigging.
But beware of patronage
Do not use the procurement process to further a social agenda
(small business set-asides, public lands, national defense, etc.)
that is irrelevant to the goal of purchasing goods at low prices.
15
Avoiding collusion (cont’d)
Keep cartels in the dark, so it is difficult for them to organize
and to punish cheaters.
do not hold open auctions;
do not hold small and frequent auctions;
do not disclose information to bidders—do not announce who
the other bidders are, who the winners are, or what the winning
bids are.
16
Common-Value Auctions

Definition: In a common-value auction, the value is the same
for each bidder, but no one knows what it is. Each bidder has
only an estimate of the value.
Be careful in these auctions lest you suffer the “winner’s curse”
If you win, you learn that you were the one who had the highest
and most optimistic estimate of the unknown value of the item
Bidders should reduce their value estimates to protect against
this.
If you are the auctioneer, release info to mitigate winners’
curse.
Winner’s curse is worse when
More bidders
Other bidders have better information
17
Common-Value Auctions (cont’d)
To avoid the winner’s curse bid less aggressively as the number
of bidders increases.
In common-value settings, oral auctions return higher prices
than sealed-bid auctions because oral bids reveal information.
But oral auctions are more vulnerable to collusion.
Discussion: Why do bidders wait until the last minute of the
auction to submit bids on eBay?
18

Bidder 1 Bidder 2 Probability Winning bid
$5 $5 .25 $5
$5 $8 .25 $5
$8 $5 .25 $5
$8 $8 .25 $8
Bidder 1 Bidder 2 Bidder 3 Probability Winning bid
$5 $5 $5 .125 $5
$5 $5 $8 .125 $5
$5 $8 $5 .125 $5
$8 $5 $5 .125 $5
$5 $8 $8 .125 $8
$8 $5 $8 .125 $8
$8 $8 $5 .125 $8
$8 $8 $8 .125 $8
Bargaining
16
PowerPoint Slides
© Luke M. Froeb,
Vanderbilt 2014
CHAPTER
Strategic view of bargaining: model as either a simultaneous-
move or sequential-move game.
A player can gain bigger share of the “pie” by
changing a simultaneous-move game into a sequential- move
game with a ﬁrst-mover advantage;
or by
committing to a position.
Credible commitments (threats) are difficult to make because

they require players to commit to a course of action against
their self-interest. Thus, the best threat is one you never have to
use.
2
The strategic view of bargaining focuses on how the outcome of
bargaining games depends on who moves ﬁrst and who can
commit to a bargaining position, as well as whether the other
player can make a counteroffer.
The non-strategic view of bargaining focuses on the gains and
alternatives to agreement to determine the outcome of
barganing.
Main insight: The gains from agreement relative to the
alternatives to agreement determine the terms of any agreement.
Anything you can do to increase your opponent’s relative gains
from reaching agreement or to decrease your own will improve
your bargaining position.
3
continued
1: NBA
In summer 2011, National Basketball Assc. owners were
negotiating with the players’ union over how to split revenues

Union wanted 57%, owners only offered 50%
Owners locked out the players, cancelling the start of the season
After months of legal threats and lost revenue, players finally
accepted owners’ initial offer
4
2: Texaco
In 1985, Texaco was found guilty by a Texas jury for
interfering with Pennzoil’s attempt to buy Getty Oil.
Texaco was fined $10.5 billion, but appealed the verdict and
began negotiating with Pennzoil.
In 1987, Texaco filed for bankruptcy. Pennzoil was then unable
to seize control of Texaco’s assets.
Texaco was also freed from the responsibility to pay interest
and dividends.
One year later Texaco and Pennzoil settled the case, with
Texaco having to pay only $3 billion. Texaco successfully used
bankruptcy to reduce its liability by over 70%
This chapter examines bargaining, and strategies to improve
your bargaining position, like those used by Bear Stearns and
Texaco .
5
Introduction: Bargaining
There are two complementary ways to look at bargaining:
the strategic view analyzes bargaining using the tools of game
theory (ch 15). Bargaining can be viewed as either a
simultaneous-move game with two equilibria or a sequential-
move game, where one player gains an advantage by committing
to a position.
the non-strategic view acknowledges that real life negotiations
don’t have fixed rules as formal games do. This view postulates
that the alternatives to agreement determine the terms of
agreement, regardless of the rules of the negotiating game.

If you can increase your opponent’s relative gain, or decrease
your own, you can gain a bigger share of the pie.
By declaring (or threatening) bankruptcy, Bear Stearns and
Texaco were able to improve their bargaining “position”, i.e.,
by changing the alternatives to agreement, they changed the
terms of agreement.
6
Bargaining: a simultaneous-move game
Example: Wage negotiations
Management and labor are bargaining over a fixed sum of $200
million
Two possible strategies are available to each player: “bargain
hard” or “accommodate.”
If both bargain hard, no deal is reached. Neither side gains.
If both accommodate, they split the gains from trade.
If one player bargains hard and the other accommodates, then
the player who bargains hard takes 75% of the “pie”
7
Bargaining: a simultaneous game (cont.)
There are two equilibria for this game
Management prefers the lower-left equilibrium
Labor prefers the upper-right.
This bargaining game has the same structure as a game of
“chicken”
Each party can gain by committing to a position, which turns it
into a sequential game
8
Bargaining: a sequential-move game
In sequential-move bargaining the first “player” makes an offer

that the second “player” can accept or refuse.
Again to analyze a sequential-move game look ahead and reason
back.
The first-mover “looks ahead and reasons back” to determine
the how her rival will react to each possible move. Then the
first-mover can determine the consequences of each possible
move.
In this case, the sequential-move games present a “first-mover
advantage,” i.e., by moving first a player can gain an advantage.
Using the same wage negotiation example, we can look at
sequential-move bargaining and first-mover advantage.
9
Bargaining game: first-mover advantage
Management “wins” by moving first and making a low offer
10
Bargaining game: first-mover advantage
Union can change the outcome by credibly committing to strike
if a low offer is made
11
Sequential-move bargaining (cont.)
Because the management has the first-mover advantage, it is in
their best interest to make a low offer, and it is in the union’s
best interest to accept that offer.
However, if the union can effectively threaten to strike (in such
a way that the management believes them) they can change the
outcome of the game despite management’s first-mover
advantage.
Credible threats are hard to make because they require the union

act against its self interest.
If management doesn’t believe the threat, the union might
actually have to follow through on the threat.
So, again, the best threat is one you never have to use.
12
Non-strategic View of Bargaining
The outcome in strategic bargaining “games” is dependent on
the rules of the game, but in real life, the rules are not always
clear.
John Nash proved that any reasonable outcome to a bargain
would maximize the product of the bargainers’ surplus.
This is known as an “axiomatic” or “non-strategic” view of
bargaining.
In this view, the gains from bargaining relative to the
alternatives to bargaining, determine the terms of any bargain.
This view also teaches that to increase your bargaining power,
you can increase your opponent’s gain from reaching agreement
or decrease your own.
If your rival has more to gain by agreeing, he becomes more
eager to reach agreement, and accepts a smaller share of the
surplus.
13
Non-strategic view (cont.)
Nash’s axiomatic approach:
[ S1(z) – D1 ] x [ (S2(z) – D2 ] , where:
z is the agreement
S1(z) is the value of the agreement to player 1 (sub 2 for player
two)
D1 is “disagreement value,” or pay-off if no agreement is
reached, for player 1 (sub 2 for player two)
So player 1’s gain from agreement is (S1(z) – D1)
14

Non-strategic view (cont.)
For example, two brothers are bargaining over a dollar.
If no agreement is reached, neither participant gains.
If they reach an agreement (z)
Player one, the older brother, has a surplus of z
Player two, the younger brother, has a surplus of 1 – z
Nash’s solution is for them to “split” the gains from trade, i.e.,
{½, ½} is the axiomatic solution.
But, now the older brother receives a $0.50 bonus for “sharing
nicely,” and the total gain rises from $1.00 to $1.50
The Nash bargaining outcome is for the brothers to split to total
gains – each receiving $0.75, meaning the older brother
effectively shares half of his bonus.
By increasing the first player’s gain to reaching agreement, he
becomes more eager to reach agreement, and “shares” his gain
with his brother.
15
Bonuses for agreement
Giving a bonus for reaching agreement is similar to incentive
compensation schemes used by many companies.
When salespeople are offered bonuses it increases their
eagerness to reach agreement and this induces them to accept
“weaker” agreements.
So giving salespeople such a bonus driven incentive will lead to
lower prices when they negotiate with customers.
(This concept will be further addressed in chapter 20)
16
Alternatives to agreement
Nash’s bargaining solution incorporates the effect of
alternatives to agreement on the agreement itself. This creates

some sound bargaining advice:
To improve your own bargaining position, increase your
opponent’s gain from reaching agreement, S2(z) – D2, or reduce
your own gain from reaching agreement, S1(z) – D1.
When you increase your opponent’s gain in agreement, you
make him more willing to agree.
Reducing your own gain makes you less willing to compromise
and helps to improve your position.
17
How Nash’s view differs from strategic
The strategic view of bargaining places a greater emphasis on
timing and commitment in determining the outcome of the
game.
With the labor/management example, the union’s commitment
to strike, or management making the first move, changes the
equilibrium of the game.
But neither action changes the gains of the agreement so neither
would affect the Nash bargaining outcome.
The Nash bargaining outcome incorporates the idea that if you
decrease your own gain to agreement you become a better
bargainer.
EXAMPLE: the best time to ask for a raise is when you have
another attractive offer waiting for you, you have less to gain
by reaching agreement. Your bargaining position improves.
This is similar to the idea of “opportunity cost.” The
opportunity cost of staying at your current job is giving up the
new offer; if the new job pays more, you’re costs (bottom line)
go up.
18
Improving a Bargaining Position
Discussion Question: When is the best time to buy a car?
Hint: Remember, car salesmen are generally paid a commission

for the sales they make.
Discussion Question: How can mergers or acquisitions improve
bargaining power?
19
Merger bargaining example
A Managed Care Organization (MCO) markets its network to an
employer
Network value is $100 if it contains either one of two local
hospitals
But the value rises to $120 if it contains both
And there is no value without at least one of the hospitals
The gain to the MCO from adding either of the hospitals to its
network when it already has the other is $20
Nash bargaining solution predicts this is evenly split
So, each hospital gets $10 for joining the MCO
But if the hospitals merge and bargain together,
The MCO can no longer drop one of the hospitals, so the gain
from striking a bargain with the merged hospital is the full $120
The gain is evenly split in the Nash bargaining solution
The merged hospitals thus receive $60, a post-merger gain of
$40
20
Health care mergers
In Rhode Island in 2003, Blue Cross Blue Shield (BCBS, the
health insurance company covering state employees) hired
PharmaCare to provide pharmaceutical services.
PharmaCare created a network of retail pharmacies willing to
sell drugs to state employees at discounted rates.
The previous contract had allowed employees to buy from any
pharmacy but was considerably more expensive.
In the new PharmaCare contract, 4 retail pharmacies were
excluded from the plan. These 4 firms lobbied RI legislature to

include them in the new plan and offered to provide the same
discounted price but PharmCare declined their request to join.
Pharmacare maintained that allowing the other stores to join
would eliminate the savings generated by having a restricted
network. PharmaCare’s bargaining position would deteriorate.
Many politicians, though, like “freedom-of-choice” bills that
would open any pharmacy willing to meet the negotiated prices.
21
Title?
Under the 2002 CHAOS (Create Havoc Around Our System)
plan, flight attendants threatened to either stage a mass walkout
for several days or to strike individual flights of Midwest
Express, with no advance warning to either customers or
management.
Midwest Express reacted by cancelling all flight attendant
vacation, and threatened to lock out any employee who
participated in the strike
Flight attendant union promised funding from its strike fund to
support any attendant who ended up locked out.
The biggest strength of the union’s threat was that it could be
effective without full implementation.
The threat of random strikes was enough to push passengers to
other airlines.
After 30 days of CHAOS, the union successfully negotiated a
new contract.
22
Management
Union
low offer generous offer
acceptstrike
0 , 0 150 , 50 50 , 150
acceptstrike

0 , 0
Management
Union
low offer generous offer
strike
0 , 0 50 , 150
acceptstrike
0 , 0
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WCN 02-200-203
Australia • Brazil • Mexico • Singapore • United Kingdom •
United States
fifth edition
Managerial
economics

A PRoBLem soLVinG APPRoAch
luke M. Froeb
Vanderbilt University
Mikhael Shor
University of Connecticut
Brian T. McCann
Vanderbilt University
Michael r. Ward
University of Texas, Arlington
06665_fm_ptg01_i-xvi.indd 1 8/9/17 8:56 PM
WCN 02-200-203
© 2018, 2016 Cengage Learning®
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ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced or distributed in any form
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Library of Congress Control Number: 2017947785
ISBN: 978-1-337-10666-5
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Managerial Economics, Fifth Edition
Luke M. Froeb, Brian T. McCann,
Mikhael Shor, Michael R. Ward
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Printed in the United States of America
Print Number: 01 Print Year: 2017
WCN 02-200-203
In loving memory of Lisa, and for our families: Donna,
David, Jake, Halley, Scott, Chris, Leslie, Jacob, Eliana,
Cindy, Alex, and Chris

WCN 02-200-203
WCN 02-200-203
v
Preface: Teaching Students to Solve Problems xiii
SECTION I Problem Solving and Decision Making 1
1 Introduction: What This Book Is About 3
2 The One Lesson of Business 15
3 Benefits, Costs, and Decisions 25
4 Extent (How Much) Decisions 37
5 Investment Decisions: Look Ahead and Reason Back 49

SECTION II Pricing, Costs, and Profits 65
6 Simple Pricing 67
7 Economies of Scale and Scope 83
8 Understanding Markets and Industry Changes 95
9 Market Structure and Long-Run Equilibrium 113
10 Strategy: The Quest to Keep Profit from Eroding 125
11 Foreign Exchange, Trade, and Bubbles 137
SECTION III Pricing for Greater Profit 151
12 More Realistic and Complex Pricing 153
13 Direct Price Discrimination 163
14 Indirect Price Discrimination 171
SECTION IV Strategic Decision Making 183
15 Strategic Games 185
16 Bargaining 205
SECTION V Uncertainty 215
17 Making Decisions with Uncertainty 217
18 Auctions 233
19 The Problem of Adverse Selection 243
20 The Problem of Moral Hazard 255
BrieF COnTenTS

WCN 02-200-203
vi BRIEF CONTENTS
SECTION VI Organizational Design 267
21 Getting Employees to Work in the Firm’s Best Interests 269
22 Getting Divisions to Work in the Firm’s Best Interests 283
23 Managing Vertical Relationships 295
SECTION VII Wrapping Up 307
24 Test Yourself 309
Epilogue: Can Those Who Teach, Do? 315
Glossary 317
Index 325

WCN 02-200-203
vii
Preface: Teaching Students to Solve Problems xiii
SECTION I Problem Solving and Decision Making 1
CHAPTER 1 INTRODUCTION: WHAT THIS BOOk IS ABOUT
3
1.1 Using Economics to Solve Problems 3
1.2 Problem-Solving Principles 4
1.3 Test Yourself 6
1.4 Ethics and Economics 7
1.5 Economics in Job Interviews 9
Summary & Homework Problems 11
End Notes 13
CHAPTER 2 THE ONE LESSON Of BUSINESS 15

2.1 Capitalism and Wealth 16
2.2 Does the Government Create Wealth? 17
2.3 How Economics Is Useful to Business 18
2.4 Wealth Creation in Organizations 21
End Notes 23
CHAPTER 3 BENEfITS, COSTS, AND DECISIONS 25
3.1 Background: Variable, Fixed, and Total Costs 26
3.2 Background: Accounting versus Economic Profit 27
3.3 Costs Are What You Give Up 29
3.4 Sunk-Cost Fallacy 30
3.5 Hidden-Cost Fallacy 32
3.6 A Final Warning 32
End Notes 36
CHAPTER 4 ExTENT (HOW MUCH) DECISIONS 37
4.1 Fixed Costs Are Irrelevant to an Extent Decision 38
4.2 Marginal Analysis 39
4.3 Deciding between Two Alternatives 40
COnTenTS

WCN 02-200-203
CONTENTSviii
4.4 Incentive Pay 43
4.5 Tie Pay to Performance Measures That Reflect Effort 44
4.6 Is Incentive Pay Unfair? 45
End Notes 48
CHAPTER 5 INVESTMENT DECISIONS: LOOk AHEAD AND
REASON BACk 49
5.1 Compounding and Discounting 49
5.2 How to Determine Whether Investments Are Profitable 51
5.3 Break-Even Analysis 53
5.4 Choosing the Right Manufacturing Technology 55
5.5 Shut-Down Decisions and Break-Even Prices 56
5.6 Sunk Costs and Post-Investment Hold-Up 57
End Notes 62

SECTION II Pricing, Costs, and Profits 65
CHAPTER 6 SIMPLE PRICING 67
6.1 Background: Consumer Values and Demand Curves 68
6.2 Marginal Analysis of Pricing 70
6.3 Price Elasticity and Marginal Revenue 72
6.4 What Makes Demand More Elastic? 75
6.5 Forecasting Demand Using Elasticity 76
6.6 Stay-Even Analysis, Pricing, and Elasticity 77
6.7 Cost-Based Pricing 78
End Notes 81
CHAPTER 7 ECONOMIES Of SCALE AND SCOPE 83
7.1 Increasing Marginal Cost 84
7.2 Economies of Scale 86
7.3 Learning Curves 87
7.4 Economies of Scope 89
7.5 Diseconomies of Scope 90
End Notes 94
CHAPTER 8 UNDERSTANDING MARkETS AND INDUSTRy
CHANGES 95

8.1 Which Industry or Market? 95
8.2 Shifts in Demand 96
8.3 Shifts in Supply 98
8.4 Market Equilibrium 99
8.5 Predicting Industry Changes Using Supply and Demand 100
8.6 Explaining Industry Changes Using Supply and Demand
103
8.7 Prices Convey Valuable Information 104
8.8 Market Making 106
WCN 02-200-203
CONTENTS ix
End Notes 111
CHAPTER 9 MARkET STRUCTURE AND LONG-RUN
EqUILIBRIUM 113

9.1 Competitive Industries 114
9.2 The Indifference Principle 116
9.3 Monopoly 120
End Notes 123
CHAPTER 10 STRATEGy: THE qUEST TO kEEP PROfIT
fROM ERODING 125
10.1 A Simple View of Strategy 126
10.2 Sources of Economic Profit 128
10.3 The Three Basic Strategies 132
End Notes 136
CHAPTER 11 fOREIGN ExCHANGE, TRADE, AND BUBBLES
137
11.1 The Market for Foreign Exchange 138
11.2 The Effects of a Currency Devaluation 140
11.3 Bubbles 142
11.4 How Can We Recognize Bubbles? 144
11.5 Purchasing Power Parity 146
End Notes 149
SECTION III Pricing for Greater Profit 151

CHAPTER 12 MORE REALISTIC AND COMPLEx PRICING
153
12.1 Pricing Commonly Owned Products 154
12.2 Revenue or Yield Management 155
12.3 Advertising and Promotional Pricing 157
12.4 Psychological Pricing 158
End Notes 162
CHAPTER 13 DIRECT PRICE DISCRIMINATION 163
13.1 Why (Price) Discriminate? 164
13.2 Direct Price Discrimination 166
13.3 Robinson-Patman Act 167
13.4 Implementing Price Discrimination 168
13.5 Only Schmucks Pay Retail 169
End Notes 170
WCN 02-200-203

CONTENTSx
CHAPTER 14 INDIRECT PRICE DISCRIMINATION 171
14.1 Indirect Price Discrimination 172
14.2 Volume Discounts as Discrimination 176
14.3 Bundling Different Goods Together 177
End Notes 181
SECTION IV Strategic Decision Making 183
CHAPTER 15 STRATEGIC GAMES 185
15.1 Sequential-Move Games 186
15.2 Simultaneous-Move Games 188
15.3 Prisoners’ Dilemma 190
15.4 Other Games 195
End Notes 202
CHAPTER 16 BARGAINING 205
16.1 Strategic View of Bargaining 206
16.2 Nonstrategic View of Bargaining 208
16.3 Conclusion 210

End Note 214
SECTION V Uncertainty 215
CHAPTER 17 MAkING DECISIONS WITH UNCERTAINTy
217
17.1 Random Variables and Probability 218
17.2 Uncertainty in Pricing 222
17.3 Data-Driven Decision Making 223
17.4 Minimizing Expected Error Costs 226
17.5 Risk versus Uncertainty 227
End Notes 231
CHAPTER 18 AUCTIONS 233
18.1 Oral Auctions 234
18.2 Second-Price Auctions 235
18.3 First-Price Auctions 236
18.4 Bid Rigging 236
18.5 Common-Value Auctions 238
End Notes 242
CHAPTER 19 THE PROBLEM Of ADVERSE SELECTION 243

19.1 Insurance and Risk 243
19.2 Anticipating Adverse Selection 244
WCN 02-200-203
CONTENTS xi
19.3 Screening 246
19.4 Signaling 249
19.5 Adverse Selection and Internet Sales 250
End Notes 253
CHAPTER 20 THE PRoblEm of moRAl HAzARd 255
20.1 Introduction 255
20.2 Insurance 256
20.3 Moral Hazard versus Adverse Selection 257
20.4 Shirking 258
20.5 Moral Hazard in Lending 260

20.6 Moral Hazard and the 2008 Financial Crisis 261
End Notes 265
SECTIoN VI organizational design 267
CHAPTER 21 GETTING EmPloyEES To WoRk IN THE fIRm’S
bEST INTERESTS 269
21.1 Principal–Agent Relationships 270
21.2 Controlling Incentive Conflict 271
21.3 Marketing versus Sales 273
21.4 Franchising 274
21.5 A Framework for Diagnosing and Solving Problems 275
End Notes 281
CHAPTER 22 GETTING dIVISIoNS To WoRk IN THE fIRm’S
bEST INTERESTS 283
22.1 Incentive Conflict between Divisions 283
22.2 Transfer Pricing 285
22.3 Organizational Alternatives 287
22.4 Budget Games: Paying People to Lie 289
End Notes 294

CHAPTER 23 mANAGING VERTICAl RElATIoNSHIPS 295
23.1 How Vertical Relationships Increase Profit 296
23.2 Double Marginalization 297
23.3 Incentive Conflicts between Retailers and Manufacturers
297
23.4 Price Discrimination 299
23.5 Antitrust Risks 300
23.6 Do Buy a Customer or Supplier Simply Because It Is
Profitable 301
End Notes 304
WCN 02-200-203
CONTENTSxii
SECTION VII Wrapping Up 307
CHAPTER 24 TEST yOURSELf 309

24.1 Should You Keep Frequent Flyer Points for Yourself? 309
24.2 Should You Lay Off Employees in Need? 310
24.3 Manufacturer Hiring 310
24.4 American Airlines 311
24.5 Law Firm Pricing 311
24.6 Should You Give Rejected Food to Hungry Servers? 312
24.7 Managing Interest-Rate Risk at Banks 313
24.8 What You Should Have Learned 313
Epilogue: Can Those Who Teach, Do? 315
Glossary 317
Index 325
WCN 02-200-203
xiii

teaching students to solve Problems1
by Luke Froeb
When I started teaching MBA students, I taught economics as I
had learned
it, using models and public policy applications. My students
complained so
much that the dean took me out to the proverbial woodshed and
gave me
an ultimatum, “improve customer satisfaction or else.” With the
help of some
disgruntled students who later became teaching assistants, I was
able to turn
the course around.
The problem I faced can be easily described using the language
of eco-
nomics: the supply of business education (professors are trained
to provide
abstract theory) is not closely matched to demand (students
want practical
knowledge). This mismatch is found throughout academia, but it
is perhaps
most acute in a business school. Business students expect a
return on a fairly

sizable investment and want to learn material with immediate
and obvious
value.
One implication of the mismatch is that teaching economics in
the usual
way—with models and public policy applications—is not likely
to satisfy stu-
dent demand. In this book, we use what we call a “problem-
solving pedagogy”
to teach microeconomic principles to business students. We
begin each chapter
with a business problem, like the fixed-cost fallacy, and then
give students just
enough analytic structure to understand the cause of the
problem and how to
fix it.
Teaching students to solve real business problems, rather than
learn models,
satisfies student demand in an obvious way. Our approach also
allows stu-
dents to absorb the lessons of economics without as much of the
analytical
“overhead” as a model-based pedagogy. This is an advantage,

especially in a
terminal or stand-alone course, like those typically taught in a
business school.
To see this, ask yourself which of the following ideas is more
likely to stay
with a student after the class is over: the fixed-cost fallacy or
that the partial
derivative of profit with respect to price is independent of fixed
costs.
eleMenTS OF a PrOBleM-SOlving PedagOgy
Our problem-solving pedagogy has three elements.
PreFaCe
WCN 02-200-203
xiv PREFaCE

1. Begin with a Business Problem
Beginning with a real-world business problem puts the
particular ahead of the
abstract and motivates the material in a straightforward way.
We use narrow,
focused problems whose solutions require students to use the
analytical tools
of interest.
2. Teach Students to view inefficiency as an Opportunity
The second element of our pedagogy turns the traditional focus
of benefit–
cost analysis on its head. Instead of teaching students to spot
and eliminate
inefficiency, for example, by changing public policy, we teach
them to view
each underemployed asset as a money-making opportunity.
3. Use economics to implement

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