Chapter 17: Making Decisions with Uncertainty
1. Introduction
This is Professor Luke Froeb and I am the co author of
Managerial Economics: a problem solving approach.
This video is designed to complement Chapter 17:
Making Decisions with Uncertainty.
In 2000, the largest customers of Teleswitch, a big
telecommunications manufacturer, threatened to go to
a competitor unless Teleswitch began dealing directly
with them. Customers thought that this change would
give them quicker access to the latest technology, which
would allow them to gain a competitive advantage.
This request put Teleswitch in a dilemma: If it dealt
directly with its large customers, it might lose its
distributors , and the small customers they represent.
But if it didn’t sell direct, it might lose its large
customers. Although the probability of losing
distributors was lower (because they would have to
incur costs to switch to a new supplier), losing them
would be catastrophic because the distributors
represented a larger share of TeleSwitch’s sales.
This dilemma illustrates the uncertainty inherent
in most business decisions. In this section, we look at
how to quantify uncertainty, which will help you make
better decisions.
2. Quantifying uncertainty
Here is the big idea of the chapter: Instead of
computing the costs and benefits of a decision (as we
did in Chapter 3) we use random variables to quantify
what we don’t know, and compute the expected benefits
and the expected costs of a decision.
To make this concrete, lets examine the decision
facing TeleSwitch. Total company profit is currently
$130 million, split between large customers ($30
million) and small customers ($100 million).
<<ANIMATE THIS?>>
If the firm sells direct <<DAVID, I KNOW THE
DIFFERENCE BETWEEN AN ADVERB AND AN
ADJECTIVE BUT “SELL DIRECT” IS A TERM OF ART IN
BUSINESS. IN FACT, CAN YOU CHANGE “DIRECTLY” TO
“DIRECT” IN THE FIGURE BELOW>> to large
customers, they keep the large customers, but have a
small probability of losing distributors, and the small
customers they serve.
If they don’t sell direct, they keep their small
customers but face a big probability of losing their large
ones.
We diagram the consequences of the decision in
Figure below, which is a simple decision tree with a
lottery at the end of each branch.
Telecom Firm
Sell directly to large customers
Sell only through dealers
(.20) × $30 + (.80) × $130 = $110
(.60) × $100 + (.40) × $130 = $112
Distributors leave
Distributors stay
Large customers leave
Large customers stay
(probability = .20)
Firm profit = $30
(probability = .80)
Firm profit = $130
(probability = .60)
Firm profit = $100
(probability = .40)
Firm profit = $130
Look first at the left branch of the decision tree.
<<DAVID, DRAW A BETTER DECISION TREE WITH THE
PROBABILITIES ON THE TWIGS>> If TeleSwitch
decides to sell direct, it faces a 20% probability that
distributors will leave, in which case profit drops to $30
million. If distributors stay, profit remains at $130
million. The expected profit of going down the left
branch is a $110 million. <<ANIMATE WEIGHTED
AVERAGE CALCULATION>>
Now check out the right branch of the decision tree.
If TeleSwitch sells only through dealers, it faces a 60%
probability that its large customers will leave, in which
case firm profit drops to $100 million. If they stay
(which has only a 40% probability), profit remains
unchanged at $130 million. Selling only through dealers,
has an expected profit of $112 million. <<ANIMATE?>>
3. making decisions under uncertainty
So what should Teleswitch do?
This is a close call. Just $2 million in expected profit
separates the alternatives. It’s unlikely that the firm has
estimated the probabilities precisely enough to
distinguish between them.
So, a third option presents itself here: TeleSwitch
can gather more information by, for example, about the
surveying large end users and distributors in hopes of
estimating the probabilities more precisely. This would
reduce uncertainty about what the probabilities really
are, and result in a better decision.
Doing the analysis explicitly like this clearly
identifies the two separate risks that TeleSwitch faces.
Another option is to try to find a way to mitigate the
adverse consequences of the risk. For example, perhaps
Teleswitch could find a way to retain its dealers, even if
it does deal directly with large customers—perhaps by
giving them a cut of the profit from large customer
accounts. Or TeleSwitch may be able to prevent large
customers from leaving if it sells only through dealers—
perhaps by providing large customers with in-house
company-trained technicians.
4. BOTTOM LINE:
We have seen that trying to quantify uncertainty has
three advantages: First, by presenting decision makers
analysis that accounts for uncertainty, you alert them to
the riskiness of the decisions and show them how to
compute the do benefit-cost analysis with expected
values.
Second, this kind of analysis identifies the sources of
risk and may suggests ways to mitigate risk.
The final reason for doing this kind of analysis is that it
gives you an excuse if things turn out poorly. You can
correctly say that you foresaw the risk, quantified it,
and reached the best decision using expected benefits
and expected costs. But making good decisions does not
mean that you will always make money.
The final benefit of modeling decisions using random
variables is illustrated with a simple example. Suppose
your colleague invites you to invest in a real estate
venture. He gives you a prospectus that shows how
much money you’ll make if you invest. The prospectus is
based on estimates of future interest rates and future
housing demand in the area. How should you analyze
the prospectus?
If you’re uncertain about the future, you need to
rework the analysis using best- and worst-case
scenarios. You have two sources of risk here—both
future demand and future interest rates, which may be
related—so you should rework the analysis on a
spreadsheet, allowing you to vary the assumptions
about the future.
Your colleague has most likely given you a bestcase scenario (low interest rates/ high demand). Add
other scenarios (low interest rates/low demand, high
interest rates/high demand, high interest rates/low
demand), and assign probabilities to each scenario.
Compute profit under each possible outcome, and
calculate expected profit as the weighted sum of the
possible outcomes.
Here is what you will learn by doing this. Almost
certainly, your colleague will do well under all four
scenarios; you, however, will do well under only under
the favorable scenario.
Don’t invest, or ask him to re-structure the deal so
that his incentives are more closely aligned with your
profitability goals. For example, design the deal so he
gets a share of the profit only after you receive an 8%
return on your investment. If your colleague declines,
then most likely he doesn’t believe his own forecasts.