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Unformatted text preview: Lecture 10: Uncertainty c & 2008 Je/rey A. Miron Outline: 1. Introduction 2. The Issue Raised by Uncertainty 3. Contingent Commodities and the State Space 4. Utility Functions and Probabilities 5. Expected Utility Functions 6. Risk Aversion 7. Mathematical Application of Expected Utility 1 Introduction Our analysis of consumer behavior so far has been carried out under some implicit and explicit assumptions. For example, we restrict the analysis to two goods or two periods. That is easy to &x; it makes things messier but not really di/erent or harder. A di/erent assumption, however, is far more fundamental: the assumption that the consumer faces zero uncertainty in making consumption choices. In the examples we have studied so far, the uncertainty issue is only relevant to the two-period model, since that has a time dimension. If the model is literally one period, there is no room for uncertainty to arise. In the way we have done the two-period model, however, uncertainty is not an issue: the consumer knows exactly what all prices will be for the two (or more) periods, what the interest rate will be, what endowments or income will be in the 1 second period, and so on. 1 Given these assumptions the consumer can be sure that any choices made now can be carried out in future. This is obviously not at accurate description of many real world settings. Future prices, interest rates, endowments and the like are not perfectly forecastable in ad- vance. In particular, it is perfectly possible to make a plan today that you will not be able to carry out next period because of shocks to your income or to the relevant prices or interest rates. So, uncertainty arises in more realistic versions of the two-period problem. In addition, uncertainty arises in many settings besides the two period consumption model: allocating a &nancial portfolio, choosing a profession, deciding whom to marry, whether to buy insurance, and so on. This uncertainty raises two issues, broadly speaking: First, uncertainty means we need to modify our model of decision-making. Second, uncertainty will turn out to imply a demand for institutions lsuch as &nancial markets and insurance policiesthat can help consumers insulate themselves from uncertainty. Our analysis in the next two lectures is mainly about the &rst of these issues, modeling consumer choice under uncertainty. We will discuss some aspects of the second issue along the way 2 The Issue Raised by Uncertainty The key issue we have to confront when uncertainty is present is that it becomes problematic to talk about trading consumption today for consumption tomorrow. The reason is that one does not necessarily know the rate of tradeo/ at the time one has to make initial decisions. This has implications both for the budget constraint and for how we think about utility....
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- Fall '09