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Ch05_Pindyckfinal - Chapter 5 Uncertainty and Consumer...

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Chapter 5 Uncertainty and Consumer Behavior
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Chapter 5 2 Introduction Choice with certainty is reasonably straightforward How do we make choices when certain variables such as income and prices are uncertain (making choices with risk)?
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Chapter 5 3 Describing Risk To measure risk we must know: 1. All of the possible outcomes 2. The probability or likelihood that each outcome will occur We must determine 2 measures to help describe and compare risky choices 1. Expected value 2. Variability
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Chapter 5 4 Describing Risk Expected Value The weighted average of the payoffs or values resulting from all possible outcomes Expected value measures the central tendency; the payoff or value expected on average
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Chapter 5 5 Expected Value – An Example Offshore drilling exploration: Two outcomes are possible Success – the stock price increases from $30 to $40/share Failure – the stock price falls from $30 to $20/share Probability 100 explorations, 25 successes and 75 failures Probability (Pr) of success = 1/4 and the probability of failure = 3/4
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Chapter 5 6 Expected Value – An Example failure) of )(value Pr(failure success) of )(value Pr(success EV + = ) ($20/share 4 3 ) ($40/share 4 1 EV + = $25/share EV =
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Chapter 5 7 Expected Value In general, for n possible outcomes: Possible outcomes having payoffs X 1 , X 2 , …, X n Probabilities of each outcome is given by Pr 1 , Pr 2 , …, Pr n n n 2 2 1 1 X Pr ... X Pr X Pr E(X) + + + =
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Chapter 5 8 Describing Risk Variability The extent to which possible outcomes of an uncertain event may differ How much variation exists in the possible choice
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Chapter 5 9 Variability – An Example Part-Time Jobs Outcome 1 Outcome 2 Prob. Income Prob. Income Job 1: Commission .5 2000 .5 1000 Job 2: Fixed Salary .99 1510 .01 510
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Chapter 5 10 1500 $ .5($1000) .5($2000) ) E(X 1 = + = Variability – An Example Job 1 Expected Income $1500 .01($510) .99($1510) ) E(X 2 = + = Job 2 Expected Income While the expected values are the same, the variability is not =  Different levels of risk
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Chapter 5 11 Variability – An Example Deviations from Expected Income ($) Outcome 1 Deviation Outcome 2 Deviation Job 1 $2000 $500 $1000 -$500 Job 2 1510 10 510 -900 Variability comes from deviations in payoffs ( expected payoff-actual payoff)
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Chapter 5 12 Variability We can measure variability with standard deviation The square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected value Standard deviation is a measure of risk Measures how variable your payoff will be More variability means more risk Individuals generally prefer less variability – less risk
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Chapter 5 13 Variability The standard deviation is written: [ ] [ ] 2 2 2 2 1 1 ) ( Pr ) ( Pr X E X X E X - + - = σ The standard deviation also can be used when there are many outcomes instead of only two
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Chapter 5 14
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