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Unformatted text preview: 1 Econ 111 Microeconomics Spring 2009 Lecture 3  4 (Chapter 5: Choice Under Uncertainty) Heiwai Tang 2 Today’s Agenda Chapter 5. Choice under Uncertainty 1. How to describe an uncertain outcome 2. How to compare different outcomes – Expected value – Expected utility 3. Preference toward risk 4. Reducing risk: – Diversification – Insurance – Obtaining more information (next lecture) 3 Introduction • If the outcome is certain, the choice is simple: choose the action that gives the highest payoff – Certain action A: payoff $100 – Certain action B: payoff $80 – Choice: A • How do we choose when the outcome is uncertain? – Action A with a certain outcome: net payoff $100 – Action B with an uncertain outcome: $80 (with prob. ½) and $140 (with prob. ½) – Choice? 4 Describing Uncertain Outcomes • To describe an uncertain outcome, we must know: 1) All possible outcomes (events) and the payoff for each for them. 2) The probability of each event happening • Example: flip a coin, o 2 events o Win $100 if Head; o Win $50 if Tail: o Probabilities o 0.5 that the flip turns out to be Head o 0.5 that the flip turns out to be Tail 5 Calculating the Attractiveness of an Uncertain Outcome • Given uncertain outcomes, we want to use a single number to represent the attractiveness of a risky choice. • A natural way is to calculate the “average” value of the outcome s associated with the choice. • For (0.5, 100; 0.5, 50), the average = – 0.5(100) + 0.5(50) = 50 + 25 = $75 . • More generally, we can calculate the expected value associated with the choice. 6 Expected Value • Definition: Probabilityweighted average of the payoffs associated with all possible outcomes . • Notice that Pr 1 + Pr 2 + … + Pr n = 1 • Example: Given (1/4, 40; 1/2, 20; 1/4, 60), EV = (1/4)(40)+(1/2)(20)+(1/4)(60) = 35 n n 2 2 1 1 X Pr ... X Pr X Pr E(X) + + + = 7 Example 1: Uncertain payoffs to a sales job • Which of the two following career options would you choose? • Although both jobs yield the same expected value, but most people would choose job 2, because job 1 involves risks while job B does not. OUTCOME 1 OUTCOME 2 Probability Income ($) Probability Income ($) Expected Income ($) Job 1: Commission Job 2: Fixed Salary 0.5 1 2000 1500 1000 0.5 1500 1500 Income from Sales Jobs 8 How to measure uncertainty? • Uncertainty does matters, but how do we measure it? We use the concept of Variability (or Variance) . • Average deviations are always zero so we must adjust for negative numbers. – (Why? Pr 1 (X 1 E(X)) + Pr 2 (X 2 E(X)) = Pr 1 X 1 + Pr 2 X 2  E(X) = 0 ) • We measure variability with standard deviation – Square root of the average of the squares of the deviations of the payoffs associated with each outcome from the expected value • Standard deviation is a measure of risk – Greater standard deviation means more risk – Individuals generally prefer less variability (i.e., less risk) given the same expected value 9...
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This note was uploaded on 10/11/2009 for the course ACCT 101+ acct 101+ taught by Professor Various during the Fall '09 term at HKUST.
 Fall '09
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