Slide 1Econ 410: Micro TheoryIntroduction to UncertaintyFriday, September 21st, 2007Slide 2Consumers and Uncertainty Throughout your studies in economics so far, we have assumed that both consumers and producers know all information with certainty Examples Maximizing utility with prices and income known Aggregating market demand from the known demand curves of individuals Is this realistic?Slide 3Risk In many situations, consumers must make choices that involve a certain amount of risk. Risk in Economics Many people refer to a risk as the probability of loss or injury, but we don’t always have to think of it in that way. Risk can refer to the probability of a loss or a gain. Example – Winning the LotterySlide 4Risk and Probability To measure risk we must know: All of the possible outcomes of a situation The probability or likelihood that each outcome will occur Interpreting Probability An objective interpretation of probability is based on the observed frequency of past events A subjective interpretation of probability is based on the perception that an outcome will occur.Slide 5Risk and Probability When probability is interpreted subjectively… Different information or different abilities to process the same information can influence the final probability determined. Based on judgment or experience, people may assign different probabilities to the same event Probabilities help us to find 2 separate measures of risky choices: Expected ValueSlide 6Expected Value Expected value is the weighted average of the payoffs or values resulting from all possible outcomes of an uncertain situation Expected value is a measure of central tendency, which means the payoff or value expected on average Example –If Lauren plays the North Carolina lottery, how much should she expect to win on average?Slide 7Expected Value Formally, the expected value of an event with 2 possible outcomes is given by: E(X) = Pr1X1+ Pr2X2 X1represents the value of outcome #1 if it occurs. Pr1represents the probability of X1occurring. The expected value of an event with npossible outcomes is given by: E(X) = Pr1X1+ Pr2X2+ …+ PrnXn Pr1+ Pr2+ … +Prn= 1Slide 8Expected Value Example According to the website of the North Carolina Lottery: The odds of winning the Powerball jackpot are 1:146,107,962 A normal Powerball ticket has a price of $1.00 Suppose Lauren wants to play Powerball What is the probability of winning?Solution: 1/146,107,962 = .000000006844 What is the probability of losing?Solution: 1 - .000000006844 = .999999993156Slide 9Expected Value Example Is a lottery ticket “a good deal”? Remember that the probability of winning is .000000006844 and tickets cost $1.00 Assume only one person can win the lottery at a time, and that the jackpot is $15,000,000Solution: In order for a ticket to be worth buying, the expected value of winning must be greater than the price of a ticket. E(T) = PRWx $W + PRLx $L E(T) = (.000000006844)$15,000,000 + (.999999993156 ) ($0) = $0.10266, or about 10 cents Slide 10Expected Value Example How high would the jackpot have to be in order to make buying a ticket “a good deal”? Assume again that only one person can win the lottery.Solution: In order for a ticket to be worth buying, the jackpot must be high enough such that the expected value of winning is than the price of a ticket. E(L) = PRWx $W + PRLx $L $1.00 = (.000000006844) $W + (.999999993156 ) ($0)  Solving, W  $146,107,962 This is equal to the original odds of winning? Why?Slide 11Variability Variability measures the extent to which possible outcomes of an uncertain event may differ Or, how much variation exists in the possible choice for the consumer Even though the expected value of two choices may be the same, differences in variability can lead to one choice being preferred to another by the consumerSlide 12For next time… Make sure you have read sections 5.1 and 5.2 in your textbook Quiz Next Wednesday Covering concepts on Chapter 4 that have been discussed in