lecture8 - uncertainty

lecture8 - uncertainty - Topic 4: Consumer Choice (4)...

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opic 4: Consumer Choice (4) Topic 4: Consumer Choice (4) Choice under uncertainty USC Marshall
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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 – 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 USC Marshall
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Choice under uncertainty • Most people are risk-averse: – Prefer a certain outcome over an uncertain one with the same expected payoff USC Marshall
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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 – 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 an the expected value of an uncertain USC Marshall than the expected value of an uncertain commission
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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? hat if the coin was tossed only once but the price – What if the coin was tossed only once but the price was reduced to $20? hat if the coin was tossed twice and you got paid What if the coin was tossed twice and you got paid $10 times the number of heads? USC Marshall
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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 –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 USC Marshall
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Choice under uncertainty • For our example, we can summarize the payoffs as •S i n gle toss: Outcome Payoff probability 20 /2 H $20 1/2 T$ 0 1 / 2 Outcome Payoff probability • Double toss 2H $20 1/4 H $10 1/2 0 /4 our tosses T $0 1/4 Outcome Payoff probability 4H $128 1/16 USC Marshall • Four tosses Not 4H $0 15/16
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Choice under uncertainty Quick statistics review: – Let the possible states be {X ,X ,…,X }, with 1 2 n associated probabilities {p 1 ,p 2 ,…,p n }, where the probabilities add up to one ( something must happen nd we’ve specified everything that can happen ven if it is and we’ve specified everything that can happen – even if it is “something else” ). Then we can define: Expected value: EX = p +p +…+p p 1 1 p 2 2 p n n Variance: E(X-EX) 2 =(p X 2 +p X 2 +…+p X 2 ) -EX 2 USC Marshall 1 1 2 2 n n
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Choice under uncertainty Expected payoffs in our example are then: – Single toss: ½*$20+½*$0=$10 – Double toss: ¼*$20+½*$10+¼*$0=$10
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lecture8 - uncertainty - Topic 4: Consumer Choice (4)...

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