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Class 19-2010 - C295 Class 19 Uncertainty Assignment 2 due...

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11/18/2010 1 THE UNIVERSITY OF BRITISH COLUMBIA C295: Class 19 – Uncertainty 1 Assignment 2 – due next Tuesday in class. Make sure you do the online portion as well as the hard copy portion. Today: 1. Expected Utility 2. Risk Aversion 3. The Risk Premium 4. Risk Neutrality and Risk Preference 5. The Risk Return Tradeoff 6. Reducing Risk Using Diversification 7. Reducing Risk Using Insurance 8. Summary THE UNIVERSITY OF BRITISH COLUMBIA 1. Expected Utility We can use utility functions to help us understand and interpret decision- making under uncertainty. Consumers get utility from the things they consume. The ability to buy things depends on income. We can therefore think of utility as a function of income: U = U(Y). Expected utility, EU, is the expected value of utility. It is a weighted average of utilities obtained from different possible incomes. Suppose Y is uncertain. It is Y1 with probability Pr1 and Y2 with probability Pr2. Then EU = Pr1U(Y1) + Pr2U(Y2). A higher expected utility makes a consumer better off. We can compare the expected utility that we get from an uncertain prospect (a gamble) with the utility obtained from a certain income to see if the consumer would want to take the gamble. 2
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11/18/2010 2 THE UNIVERSITY OF BRITISH COLUMBIA Clicker Question 1 3 Suppose that Olivia has a utility function defined over income given by U = Y where Y is her hourly wage rate. Olivia has a job that pays $16 per hour with probability 0.6 and otherwise pays $36 per hour. Which of the following statements is true? a. Olivia’s expected utility is less than 4. b. Olivia’s expected utility is more than 6. c. Olivia would be better off if she could earn $25 per hour for certain. d. a. and c. e. None of the above. THE UNIVERSITY OF BRITISH COLUMBIA Risk aversion means that a person would turn down a fair gamble. This definition implies that a risk averse person prefers a sure thing to an uncertain prospect with equal expected value. A concave utility function over income (or wealth) leads to risk aversion.
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