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Lecture 11 - Utility

# Lecture 11 - Utility - Lecture 11 DADSS Decision Analysis...

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1 Lecture 11 Decision Analysis with Utility Elicitation and Use DADSS

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2 Administrative Details Homework Assignment 5 is due on  Thursday Old Midterms Posted Watch for Review Sessions Midterm 1 March at 6:00 Questions from last class?
3 An Opportunity Toss a fair coin If it comes up heads, you win  \$2 If it comes up tails, you toss  again If it comes up heads on the 2 nd   toss, you win \$4, otherwise  you toss gain Heads on the third toss: \$8 Heads on the fourth toss: \$16 Heads on the  n th  toss: \$2 n What would you be willing to  pay to play this game? Heads on Toss Prize 1 2 \$                          2 4 \$                          3 8 \$                          4 16 \$                        5 32 \$                        6 64 \$                        8 256 \$                      10 1,024 \$                   12 4,096 \$                   15 32,768 \$

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4 The Concept of Utility Expected value is not entirely satisfying Risk preference Non-monetary values Satiation Utility is measure of: happiness, well-being,  satisfaction, welfare… In practical terms: a  subjective  index of  personal  value
5 The St. Petersburg Paradox Daniel Bernoulli, 1738 What is the expected value of the coin  toss gamble? Probability of H: 0.50 Probability of TH: 0.25 Probability of TTH: 0.125 Probability of TTT H: (½) n

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6 The St. Petersburg Paradox The expected value of the game is  infinite, but virtually no one is willing to  pay more than \$10 for it! Risk Aversion = = = = = 1 1 1 2 2 1 n n n n n EV
7 Utility’s Conceptual Origins A quantitative measure of personal value Personal value reflects: Preferences Risk Attitudes/Preferences/Tolerance Heads you win an apple, tails you win an orange – what  is the value to you? Most interesting decisions have consequences that are  either non-monetary or not entirely monetary Additionally, even all-monetary consequences require  considering satiation and risk aversion

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8 Satiation Your net worth is \$100,000 and you inherit  another \$100,000 You’re ecstatic! You’re Bill Gates and you inherit \$100,000 You don’t even notice Satiation: Decreasing marginal utility from  consumption/income/wealth What does the demographic of people who  routinely buy lottery tickets look like?
9 Risk Preference Why do people buy both lottery tickets and  insurance? Risk Seeking: Willing to pay more/accept less

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Lecture 11 - Utility - Lecture 11 DADSS Decision Analysis...

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