Lecture 10 - ECONOMICS 100A Professor Dan Acland 09/28/10...

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ECONOMICS 100A Professor Dan Acland 09/28/10 Lecture 10 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy, or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. TURN IN PROBLEM SET #2 ICLICKER QUIZ ANNOUNCEMENTS A student in the front row just said to me that convexity is equivalent to risk-aversion, not concavity, which is not what was on the iClicker question. So I will look into that, and if I find the question wrong relative to what it says in the book, then I will not include that question. LECTURE Today we will talk about expected utility and insurance contracts. We will talk about risk preferences, but before we get into buying insurance, I want to point something out about expected utility theory and what it does for us and what it says about an individual’s utility function. Slide : Lecture outline: 1. Risk preference and the shape of the utility function. A. Preferences over certain outcomes tell us the horizontal shape of utility. B. Preferences over risky outcomes tell us the vertical shape of utility. 2. How much will people pay for complete insurance: - Certainty equivalent, risk premium, and maximum willingness to pay You’ll notice that up until now, we’ve been talking exclusively about the horizontal curvature of individuals’ utility functions. We’ve been pretending that people actually have utility functions that help them make decisions. So far, all we’ve said is that the only thing we know about is the horizontal curvature of that function. That’s because the vertical dimension is utils, and because we said utils don’t exist, we can’t say anything about the vertical dimension of the curve. BUT , if we allow ourselves to assume the independence axiom with respect to people’s preferences over risky outcomes, the vertical curvature (the utility function that we’ve been looking at all along) suddenly starts to matter. And it matters crucially. I’m going to try to show you that the utility function, u(x), that we have started looking at is actually directly related to the utility function that we’ve been looking at so far that tells us about people’s preferences over certain outcomes. Then I’ll go over a specific insurance application. Slide : A. Preferences over certain outcomes tell us the horizontal shape of utility. - Three sisters, Magda, Zsa-Zsa, and Eva, each have Cobb-Douglas preferences over clothing, x 1 , and all other goods, x 2 , so their utility function is U(x 1 , x 2 ) = x 1 α x 2 β . -
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Lecture 10 - ECONOMICS 100A Professor Dan Acland 09/28/10...

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