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# ch12lec - ECON 306 Chapter 12: Uncertainty RUST, CHO, DIAZ...

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ECON 306 Chapter 12: Uncertainty RUST, CHO, DIAZ

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Introduction People face risk all the time: a worker can get sick or have an accident, your house could burn down, and you can win the state lottery. Different outcomes (get sick, stay healthy) occur with some probabilities. The probability distribution of outcomes affects consumer decisions. We are going to use the tools of optimal choice to understand behavior under uncertainty. There are financial institutions (insurance markets, stock market) that can mitigate some of this risk. Contingent Consumption What does the consumer chooses? The consumer is concerned with the probability distribution of getting different consumption bundles of goods. A probability distribution consists of a set of different outcomes –consumption bundles- and the probability associated with each outcome. Example 1: A worker earns \$50,000 a year and she faces some probability of getting sick. With probability ¼ she gets sick and must pay medical bills of \$30,000. With probability ¾ she stays healthy and face no medical bills. The set of outcomes is C = {\$50,000, \$20,000} The associated probabilities are P = { ¾ , ¼ }
Example 2: An individual has initially \$35,000 worth of assets and he may loose \$10,000 with probability . With probability 1% she ends having \$25,000. With probability 99% she ends having \$35,000. The set of outcomes is C = {\$35,000, \$25,000} The associated probabilities are P = { 0.99 , 0.01 } When people face uncertain outcomes, we say that they choose a contingent consumption plan . A contingent consumption plan specifies what would be consumed in each different state of nature. If we think about a contingent consumption plan as being just an ordinary consumption bundle we can apply consumer theory. There are some preferences over contingent consumption bundles and the consumer face some budget constraint. Lets apply this to the case where the individual from example 2 is deciding to buy insurance against the risk of losses. She may purchase K dollars of insurance and has to pay a premium , if the bad state happens she will receive K dollars back. So she faces the gamble: With probability her consumption in the bad state is . With probability her consumption in the good state is . The endowment of the individual is \$25,000 in the bad state and \$35,000 in the good state. Insurance offers her a way to move away from her endowment point. If she purchases K dollars of insurance she gives up dollars of consumption possibilities in the good state in exchange for dollars of consumption possibilities in the bad state. The trade rate she gets from insurance is 01 . 0 S K J K K c b ± J ² ² 000 , 10 000 , 35 01 . 0 S b 99 . 0 S g K c g J ² 000 , 35 K J K K J ² J ² J ² J ² J ² ' ' 1 K K K c c b g

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12.01 This graph describe the budget constraint and the endowment point. We just need to add the indifference curves.
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## This note was uploaded on 10/25/2011 for the course ECON 326 taught by Professor Hulten during the Spring '08 term at Maryland.

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ch12lec - ECON 306 Chapter 12: Uncertainty RUST, CHO, DIAZ...

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