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Section+Notes+1[1]

# Section+Notes+1[1] - Department of Economics University of...

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Department of Economics University of California, Berkeley GSI: Josh Tasoff Spring 2010 Econ 119 Last Updated: 1/31/10 Section Notes 1 1 Agenda 1. Announcements 2. Questions? 3. Review of Expected Utility 4. Reference-Dependent Utility 5. Reference-Dependent Utility Practice Problems 2 Announcements 1. Read Botond’s Lecture Notes on bspace. 2. GSI Extraordinaire Rosario Marcera has some great handouts on bspace. 3. Problem Set 1 is due Feb 11th. 4. Letters of introduction are due today. If you haven’t turned it in, email me a letter after class (can take less than 10 minutes so just do it). 3 Review of Expected Utility Expected utility theory is the classical model we use throughout economics to analyze people’s decisions under uncertainty. You should be very familiar with expected utility theory. It was a key subject in Econ 100A and probably came up in every non-macro economics elective course. We define a utility function u ( w ) over wealth w . The utility function represents a preference ordering. If u ( w ) > u ( w ) it means that w is preferred to w . Enough of this dilly-dallying, let’s cut to the chase. We assume that the utility function is increasing in wealth. If the utility function is concave that means the person has ................................. risk preferences. If the utility function is convex that means the person has ................................. risk preferences. Generally we assume 1

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Department of Economics University of California, Berkeley GSI: Josh Tasoff Spring 2010 Econ 119 Last Updated: 1/31/10 that people have concave utility functions. The risk preferences are more realistic, and second it captures diminishing marginal utility of wealth. This means that \$5 for a beggar on Telegraph is far more valuable than \$5 for Bill Gates. These two properties of a concave utility function are useful for capturing lots of real world behavior, like demand for insurance, moral-hazard issues, etc. but the model does not capture small-scale risk aversion. The following example illustrates. 1 Problem: EU Risk Preferences Tammy has \$10,000 of wealth and a utility function of u ( w ) = log ( w ) (natural log). a. Draw this utility function. b. Suppose Tammy is offered a 50-50 gamble of lose 500, gain x. What x is required to make Tammy indifferent to the gamble? c. Suppose Tammy is offered a 30-70 gamble of lose 500, gain x. What x is required to make Tammy indifferent to the gamble? d. Now suppose Tammy is offered a 50-50 gamble of lose 1, gain x. What x is required to make Tammy indifferent to the gamble? e. Does Tammy exhibit small-scale risk aversion? Why or why not? 1 For more practice see Rosario’s handout, Section 1, problem 1; available on bspace. 2
Department of Economics University of California, Berkeley GSI: Josh Tasoff Spring 2010 Econ 119 Last Updated: 1/31/10 Answer: EU Risk Preferences a. Figure 1: Utility as a function of money.

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