lecture 9

# lecture 9 - LECTURE 9 UNCERTAINTY AND INFORMATION ECONOMICS...

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1 LECTURE 9 UNCERTAINTY AND INFORMATION ECONOMICS

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2 Uncertainty In reality, uncertainty usually exists. In general, people do not like uncertainty (incomplete information). So they buy insurance to alleviate its negative impact. The question is: How does insurance work to help them? How does an insurance company make money on selling insurance to people?
3 Uncertainty Probability and Expectation When one event is likely to happen with different outcomes under uncertainty, the expected outcome is defined as the sum of all possible outcomes weighted by the probability that each outcome would happen. For example, suppose you have an initial wealth of \$100 and are considering a gamble, which has a 50:50 chance to win. If you win, you’ll earn an extra money of \$100; but if you lose, you must pay \$50. Then expected gain from this gamble is 0.5(100)+0.5(-50)= \$25. Question: will you take the gamble?

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4 Uncertainty Expected Utility Decisions are made based on expected utility rather than expected income. For the above example, whether you’ll take the gamble does not depend on whether the expected gain from the gamble is greater than 0. In stead, it depends on whether the expected utility of gamble is greater than the utility of not gambling, that is, whether EU > U ( W 0 ). Suppose you gain 15 units of utility from owning \$200, 12 units of utility from owning \$100 and 5 units of utility from owning \$50. Then the expected utility go gamble EU =0.5(15)+0.5(5)=10, which is lower than the utility level of non-gambling U ( W 0 =100)=12. Therefore, you won’t gamble even though its expected gain is positive.
5 Uncertainty Risk Attitudes and Utility Function Risk loving : convex utility function of wealth. Risk averse : concave utility function of wealth. Risk neutral : linear utility function of wealth. Wealth 50 100 200 Utility 15 10 5 15 12 50 100 200 Utility 5 Risk loving Risk averse Risk neutral EU=10 EU=10 EU 50 100 200 Utility 15 8 5

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6 Uncertainty Insurance Desire to buy insurance: risk aversion Suppose an agent who is averse to risk and owns a house that has a current value of \$100. Also suppose that there is a 20% chance that a fire accident might
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lecture 9 - LECTURE 9 UNCERTAINTY AND INFORMATION ECONOMICS...

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