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Unformatted text preview: Kata Bognar [email protected] Economics 142 Probabilistic Microeconomics UCLA Fall 2009 2 States of Nature and Expected Utility Readings. Chapter 3. Concepts. State of nature, event, partition. Consequence function, act, elementary events, state dependent and state independent utility. Statewise dominance. 2.1 Examples • We have been talking about uncertain prospects for a while and all along we thought about the probabilities of the different prizes (outcomes/contingencies) as something exogenously given. For example we talked about lotteries such as you win 10 , 000 dollars with probability 1 / 2 and you lose 10 , 000 with probability 1 / 2. 1 • It is reasonable to ask what determines these probabilities. In this section, we talk about a richer model of uncertainty. • EXAMPLE 1: Imagine that you have a house in Malibu which may burn down in October with probability 1 / 2. Then, we can construct two lotteries: – Lottery I: you get 10 , 000 dollars if your house burns down and you pay 10 , 000 if it does not. – Lottery II: you get 10 , 000 dollars if your house does not burn down and you pay 10 , 000 if it does. Not knowing the source of the uncertainty, both lotteries look like the lottery that pays you 10 , 000 dollars with probability 1 / 2 and- 10 , 000 dollars with probability 1 / 2. Therefore, the two lotteries may seem to be the same. Are they really? • EXAMPLE 2: Assume that you have a lottery ticket . Whether you win or not with your ticket is uncertain but really no one tells you the respective probabilities. How can you come up with those probabilities? You can think that somewhere a number is drawn, it can be the number of any tickets and you win if this number happens to be yours. Therefore, the probability that your number is drawn determines your winning probability. • EXAMPLE 3: Suppose that you go for a hike and you want to decide whether to take an umbrella or not. – To make the decision you want to know the benefits of carrying the umbrella with you. It is very good to have an umbrella if it rains but it is useless if it does not rain. You do not know for sure how the weather will turn out, so taking / not taking the umbrella implies an uncertain prospect. 1 Losing 10 , 000 can be represented by a payoff- 10 , 000 which simply means that you are obliged to pay that amount. 1 – What is this uncertain prospect? How likely it is that you actually need the umbrella? You have already realized that the weather matters, more precisely what matter is whether it rains or not. Notice that the weather has many other aspects that are not important for you. For example, the temperature does not really matter for you. – You most likely have a belief about the chance of rain. Therefore, you can say how likely it is that the umbrella is useful for you, i.e. allows you to stay dry in a rain. Then you know that not carrying the umbrella generates the uncertain prospect of x % chance of getting wet and 100- x % chance of staying dry. While carrying the umbrella allows you to stay dry no matterstaying dry....
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This note was uploaded on 01/25/2010 for the course ECON ECON 142 taught by Professor Bognar during the Fall '09 term at UCLA.
- Fall '09