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Unformatted text preview: Kata Bognar [email protected] Economics 142 Probabilistic Microeconomics UCLA Fall 2009 3 Considering New Information Readings. Chapter 4. Concepts. Payoff relevant events, informational events. Information structure, infor- mation realization, conditional probabilities, Bayes rule, Bayes Theorem. 3.1 Example • Imagine that you are trying to hire someone for your company. There are several applicants however, you do not know much about them. – You know that if you hire a motivated person then you get high profit but if the person you hire is not motivated then you get no profit. Alternatively, you can decide not to hire anyone and try to do all the work yourself but then you are overworked, make mistakes and only realize a small profit. – To simplify things assume that there are only two levels of motivation, i.e. applicants are motivated or not motivated and there are no other/middle levels of motivation. – Unfortunately, you cannot verify if someone is motivated or not. However, you know that usually 1 out of 3 applicants are motivated so you believe that your applicant is motivated with probability 1/3. • Then there is an applicant for the job. How would you decide? Would you hire her or not? We understand that the hiring decision is a decision in the presence of uncertainty. So we want to use our framework to analyze this decision. How can we think about this situation in our states of nature model? What are the elementary events in this example? What are the possible actions? What are the respective acts? – You can find the elementary events by thinking about what is important for you about the candidate, what is that you care about. You care about whether the applicant is motivated or not. So the elementary events (or the small world states) are: the applicant is motivated or is not motivated. – The possible actions are: to hire or not to hire the applicant. – I let you figure out the acts yourself. • Now we can ask again about the optimal decision to make. The answer to this question depends on your preferences over the different profit levels. Later we will specify those preferences but now we rather extend the example to be able to talk about the main topic of this section, how do belief change when new information is revealed. • Assume that you have access to additional information about the candidate. For example, you may read the resume of the applicant and you see if she finished 1 college or not. This is a new piece of information . After seeing either a degree or the lack of the degree, you likely reconsider your decision. Intuitively, a motivated person is more likely to finish college so a BA in the resume signals motivation while the lack of a BA signals no motivation. Depending on what you see in the resume you will change your belief about the candidate, more precisely you will change the probabilities you put on the events that the applicant is motivated / not motivated....
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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