lecture8 - uncertainty - slides

lecture8 - uncertainty - slides - 2/2/2009 Topic 4:...

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2/2/2009 1 Topic 4: Consumer Choice (4) USC Marshal Choice under uncertainty Choice under uncertainty • So far we have analyzed choice over known (certain) alternatives • However, many choices involve uncertainty – Choosing a movie to see – Choosing a restaurant you haven’t tried before USC Marshal – Investing in the stock market –… • How can we model choice under uncertainty? – We use the concept of expected utility • Choose what is in expectation most attractive Choice under uncertainty • Most people are risk-averse: – Prefer a certain outcome over an uncertain one with the same expected payoff • Implications of risk-aversion : – People buy insurance USC Marshal – People require a premium to invest in riskier assets – People pay for information that decreases uncertainty – People diversify their holdings – People are willing to take a lower certain salary than the expected value of an uncertain commission
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2/2/2009 2 Choice under uncertainty Example: Consider a lottery based on a series of coin flips. The rules are as follows: – The coin is tossed four times. If it comes up heads every time, you get $128. Otherwise, you get nothing. It costs $10 to participate. Would you take the bet? USC Marshal – What if the coin was tossed only once but the price was reduced to $20? – What if the coin was tossed twice and you got paid $10 times the number of heads? Choice under uncertainty Buildings blocks: States of nature: each possible outcome –Coin toss: possible states of nature are {H,T} Conditional payoffs: • To each state of nature, we assign a payoff USC Marshal –Coin toss:{$20,$0} (or {$10,-$10}) Probabilities: the likelihood you assign to each possible outcome • Can be objective (Prob(H)=1/2) or subjective Choice under uncertainty • For our example, we can summarize the payoffs as • Single toss: Outcome Payoff probability H $20 1/2 T$ 0 1 / 2 USC Marshal • Double toss • Four tosses Outcome Payoff probability 2H $20 1/4 H $10 1/2 0 1 / 4 Outcome Payoff probability 4H $128 1/16 Not 4H $0 15/16
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2/2/2009 3 Choice under uncertainty Quick statistics review: – Let the possible states be {X 1 ,X 2 ,…,X n }, with associated probabilities {p 1 ,p 2 ,…,p n }, where the probabilities add up to one (something must happen and we’ve specified everything that can happen – even if it is “something else”) Then we can define: USC Marshal something else ). Then we can define: Expected value: EX = p 1 X 1 +p 2 X 2
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lecture8 - uncertainty - slides - 2/2/2009 Topic 4:...

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