L27 - Economics 101:Principles of Microeconomics Professor...

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1 Economics 101:Principles of  Microeconomics Professor Jo Hertel I will have additional office hours F 12:30 - 2. Lecture 27: Risk and uncertainty. Uncertainty in economics: expected value and expected utility. The market for insurance. Asymmetric information: moral hazard and adverse selection.
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2 Uncertainty in economics More generally, if there are N possible future outcomes with probabilities p 1 ,...,p N , and the decision maker values these outcomes with utilities U 1 ,...,U N , the expected utility is We sometimes also need an expression for the (objective, utility-free) expected value of some random variable that can be objectively measured, like future income. If there are N possible values S 1 ,...,S N of the random variable, the expected value is EU = p 1 ∙U 1 + p 2 ∙U 2 + . .. + p N ∙U N EV = p 1 ∙S 1 + p 2 ∙S 2 + . .. + p N ∙S N Definition Definition Definition Definition Definition Definition Definition Definition Definition Definition Definition Definition Definition Definition
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3 Decision making under uncertainty  (1) Before: all alternatives involved certain outcomes. We chose alternative A over B if Utility(A) > Utility(B). Now: some alternatives involve uncertain outcomes. We choose alternative A over B if EU(A) > EU(B) . If an alternative C involves a certain outcome, EU(C)=U(C).
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4 Decision making under uncertainty  (2) Today we will talk mainly about monetary gambles (take out insurance, play the lottery, go to college. ..). We assume people have some utility U(y) over income (=consumption), which has diminishing marginal utility as always. income utils Utility function
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5 An investing example Suppose your income is $20,000. You are thinking of investing in some stock costing $1,000. Next week, there is a 25% chance that the stock is worth $1,600, otherwise it will be worth $800 (assume no other income). Note that the expected value of your income is the same whether or not you invest: EV = 0.25∙20,600 + 0.75 ∙19,800 = $20,000. Then you buy the stock if EU(not investing) < EU(investing). Income Utility 19,800 7 20,000 14 20,600 16
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6 Risk aversion In the previous example, the certain outcome (not investing) and the uncertain outcome (investing) had the same expected value , but the uncertain alternative had a strictly lower expected utility. This is no accident, but a property of utility
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L27 - Economics 101:Principles of Microeconomics Professor...

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