Transcript MANAGERIAL ECONOMICS An Analysis of Business Issues

MANAGERIAL ECONOMICS
An Analysis of Business Issues
Howard Davies
and Pun-Lee Lam
Published by FT Prentice Hall
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Chapter 12:
Risk and Uncertainty
Objectives: After studying this topic you should be
able to:
distinguish alternative states of information
distinguish alternative attitudes to risk
use expected values and expected utilities to
take decisions in a situation of risk
construct and use decision trees
use alternative criteria for decision-making
under uncertainty
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Alternative States of Information
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Certainty: we have perfect information
about future outcomes
Risk: we know what future outcomes
are possible and we can attach
probabilities to each outcome
Uncertainty: we do not know the precise
nature of the outcomes or their
probabilities
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Expected Monetary Values
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
In a situation of RISK we could use
Expected Monetary Values (EMV) to
take a decision
EMV = SpiVi Where:
– pi = probability of the i’th outcome
– Vi = value of the i’th outcome
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Expected Monetary Values
Weather
Probability
Takings
Sunny
0.2
$500
Cloudy
0.4
$300
Raining
0.4
$100
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Limitations of EMV
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Will you accept a 50/50 bet for $5?
Probably YES
Will you accept a 50/50 bet for $5m?
Probably NO
BUT BOTH HAVE AN EMV = 0!
In some way you ‘care’ more about
losing $5m than winning $5m
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Limitations of EMV
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Your house is worth $200,000
The probability of destruction by fire is
1/10,000
EMV of the loss = $20
So $20 is the most you will pay for insurance?
NO, YOU CARE MORE ABOUT THE
CHANCE OF LOSING YOUR HOUSE
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How to Take This Into Account
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Decision-makers have different
‘attitudes to risk’
RISK NEUTRAL - values gains and
losses equally
RISK AVERSE - values losses more
highly than gains
RISK LOVER - values gains more than
losses
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How to Model This?

A Risk-Averse Person
Utility
Income
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How to Model This?

A Risk-Neutral Person
Utility
Income
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How to Model This?

A Risk-Lover
Utility
Income
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Decision-makers Are Usually
Assumed to be Risk-averse
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Instead of using EMV, use Expected
Utility (EU)
EU = SpiUi Where:
– pi = probability of the i’th outcome
– Ui = utility of the i’th outcome
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How to Find Utility Values?
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They depend on the individual or corporate decisionmakers ‘degree of risk aversion’
Standard gamble comparisons, e.g.
– $0 = 0 “utils”
– $100,000 = 1 “util”
What is the “util” value of $50,000?
Ask the decision-maker to choose between $50,000
for certain and a bet involving probability P of winning
$100,000. Start with low P and increase it until the
bet is just preferred. Then:(if P = .6)
U($50,000) = .6(U($100,000)) + .4(U($0)) = .6
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Indifference Curves
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The steeper the curves the greater the risk aversion
Return
Preferred
Direction
Risk
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Decision trees
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Market
Conditions?
See p.247
High price
EMV = $0.8m
EU = 0.45
Yes
Pr = 0.7
Is a New
Product
Found?
Yes
Spend $1m
on R&D?
No
Good
Pr=0.6
No
Pr = 0.3
Profit Utility
+$2m +1.41
Poor
Pr= 0.4
Good
High Price
Pr =0.6
or Low
Price?
Market
Conditions?
Low price
Poor
EMV =$0.1m
Pr = 0.4
EU=0.168
-$1m
-1
$1.5m 1.22
-$2m -1.41
-$1m -1
0 0
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Alternative Types of Probability

Objective probability, which may be:
– a priori - calculated through prior
knowledge or theory. The probability of 6
on a dice is 1/6.
– a posteriori - known from a sample of past
events. The Pr (rain on any day in June) =
.6
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Subjective probability - based on
judgment
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The Expected Value of
Information
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EVPI = difference between the
expected value of future actions, given
the information currently available, and
the expected value of future action, if
perfect advance state revelation were
available
See p.250 for a worked example
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Techniques for Coping with
Uncertainty
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If we do not know the possible
outcomes, there is little we can do
If we know the possible outcomes, but
not their probabilities, a number of
techniques are possible
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Minimax Criterion: Select Action 3
Actions
States of Nature
A
B
C
1
20
40
180
2
-40
100
220
3
60
70
90
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Minimax Regret Criterion: Select
Action 1
Actions
States of Nature
A
B
C
1
40
60
40
2
100
0
0
3
0
30
130
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Maximax Criterion
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An ‘optimistic’ criterion
Identify the best outcome for each
action
Select the action where the best
outcome is the best
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Hurwicz ‘alpha’
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Alpha = ali + (1-a)Li Where:
• a = optimism/pessimism index (0<a<1)
• li = lowest pay-off for action ‘i’
• Li = highest pay-off for action ‘i’
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Estimate ‘a’ by using a standard gamble
type exercise (p.253)
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The Broader Implications of Risk
and Uncertainty
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Remember Chapter 3!
Bounded rationality is a key element in
transactions cost theory
If there were no uncertainty there would
be no firms!
Uncertainty is also central to the
concepts of entrepreneurship and
innovation
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