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Summary Class 13 Uncertainty-1-and-2 class notes and Presentation
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ECO204Review Uncertainty 1
Preview Uncertainty 2
Ajaz Hussain, Economics, University of Toronto (STG)
,Uncertainty 1 & Uncertainty 2 Chapters
All “annotated” algebra, topics, (additional) examples, exercises
solutions) are in:
Uncertainty 1: Decision Making Under Uncertainty
“Chapter: Uncertainty I”
Uncertainty 2: Risk Avoidance
“Chapter: Uncertainty II”
,Uncertainty 1: “Review” – Part 1
Attitude Towards Risk [for the Uncertain Situation: {$𝒙𝟏 , $𝒙𝟐 , ; 𝒑𝟏 , 𝒑𝟐 }]
Risk Averse Agent Risk Neutral Agent Risk Loving Agen
Strictly Concave Utility Function: Linear Utility Function: Strictly Convex Utility F
i.e. Either 𝑈 ## $𝑋 < 0 for all $𝑋 i.e. Either If 𝑈 ## $𝑋 = 0 for all $𝑋 i.e. Either If 𝑈 ## $𝑋 > 0
Or: Or: Or:
𝑈 𝑝$ 𝑥$ + 𝑝% 𝑥% > 𝑝$ 𝑈 𝑥$ + 𝑝% 𝑈 𝑥% 𝑈 𝑝$ 𝑥$ + 𝑝% 𝑥% = 𝑝$ 𝑈 𝑥$ + 𝑝% 𝑈 𝑥% 𝑈 𝑝$ 𝑥$ + 𝑝% 𝑥% < 𝑝$ 𝑈 𝑥$
𝑈 𝐸𝑉 > 𝐸𝑈 𝑈 𝐸𝑉 = 𝐸𝑈 𝑈 𝐸𝑉 < 𝐸𝑈
Decision criterion: 𝐸𝑈
Decision criterion:
Decision criterion: 𝐸𝑈 Or
Decision criterion: 𝐸𝑉
, Uncertainty 1: “Review” – Part 2
ONLY Risk-Neutral agents can make “Meta-Decisions” of Whether to Make D
Under Uncertainty with or without costly testing
Calculate Optimal Value of the Decision Making under U
“Meta” Decision Tree: i ther based on (this) Decision Tree without prior costly t
E
Risk Neutral Agent chooses one of the
following “trees” to make the decision
under uncertainty Calculate Optimal Value of the Decision Making under U
Or based on (this) Decision Tree with prior costly testing a
knowledge of test results (all pecuniary terms exclude c
Value of Test Information = 𝐸𝑉[Decision with Test] − 𝐸𝑉[Decision without
≥ Cost of Testing ⇒ Decide with testing
If Value of Test Information 5
< Cost of Testing ⇒ Decide without test
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