class3+_uncertainty_

class3+_uncertainty_ - Econ 51, Winter 2011 Class #3...

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1 Econ 51, Winter 2011 Class #3 • Welcome back! TA sections begin Friday this week: Still waiting for assignment, will let you know ASAP. • Problem set 1 will be posted on Thursday. • Today: Decision under Uncertainty. Wednesday, January 12, 2011
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2 Uncertainty Wednesday, January 12, 2011
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3 Preferences and utility function Recall from Econ 50 how economists model individual behavior: An individual has a preference relation over commodity bundles (e.g., apples and bananas). Under weak regularity assumptions a preference relation can be represented by a utility function u(.), that is, x is preferred to y if and only if u(x) u(y). (note: u(.) is just a way to write a generic function) Wednesday, January 12, 2011
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4 Uncertainty In the real world most important choices are not whether to consume apples or bananas. People have to choose how much to save, with whom to get married, how much to invest in education, and how much to invest in stocks and bonds. Firms have to choose which new products to produce, which advertising campaigns to use, and where to locate new factories. All these choices involve uncertainty . Wednesday, January 12, 2011
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5 Questions We want to answer the following questions: How can we describe the preferences of a decision maker (e.g., an individual or a firm) over uncertain prospects? • What is a reasonable behavior in the presence of uncertainty? • What happens to overall economic outcomes, e.g., insurance markets? Wednesday, January 12, 2011
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6 States of the world We’ll study a general (and very useful!) model developed by von Neuman and Morgenstern (1944) and then by Savage (1954). Uncertainty is described by a finite set {1,2,. ..,S} . Each element s in {1,2,. ..,S} is called a state of the world. The set {1,2,. ..,S} is a mutually exclusive and exhaustive description of the resolution of any relevant uncertainty, hence the name “states of the world.” That is, one of them must occur, but not more than one. The decision maker does not know which one will occur. Wednesday, January 12, 2011
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7 States of the world - examples Example A (coin) : A coin toss in which you win a dollar if head, and lose a dollar if tail. States are 1 for Head, and 2 for Tail. Example B (firm) : A firm does not know the future price of its input. States are 1 to 10,000 for all possible prices (e.g., in cents). Example C (worker) : A worker does not know whether he would lose his job one week from now. States are 1 if he is fired, and 2 if he is not. Wednesday, January 12, 2011
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8 Commodities and states of the world We could distinguish commodities not only by their physical characteristics but also by the state of the world. If we do this, then we can simply adopt our familiar framework even under uncertainty! Example:
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class3+_uncertainty_ - Econ 51, Winter 2011 Class #3...

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