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Unformatted text preview: S I D E R E M E N S E A D E M M U T A T O University of Sydney ECOS2201  Lecture 6 1 Uncertainty Let a gamble be a list of probabilities and associated payoffs Let the probability of payoff x i be p i . The expected value of a gamble is EV = i p i x i . The variance of a gamble is 2 = i p i ( x i EV ) 2 2 Let gamble A have probability .5 of payoff 15 and probability .5 of payoff 5. The expected value of gamble A, EV A = . 5 15+ . 5 5 = 10 . The variance of gamble A, 2 A = . 5 25 + . 5 25 = 25 . Let gamble B have probability 1 of payoff 10. EV B = 10 gambles A and B have the same expected value. Are you indifferent between them? I prefer B. So ranking gambles by expected value is not consistent with my preferences 3 Rather than use expected value to rank gambles it is common to use expected utility to rank gambles Let U ( y ) be the utility an individual gets from income of y. Expected Utility is i p i U ( y i ) so that EU A = . 5 U (15) + . 5 U (5) and EU B = U (10) 4 Question: Let U ( y ) be a concave function. See diagram on the board. On this diagram show EU A and EU B . 5 As drawn, EU B > EU A . This person prefers income of 10 for sure to a gamble that has an expected value of 10. We say this individual is risk averse . Risk averse individuals have concave utility functions. Question: On a diagram, show the utility function of a risk preferrer , someone for whom EU B < EU A , and someone who is risk neutral , EU A = EU B 6 The certainty equivalent of a gamble, CE, is the amount of income for sure which is regarded as just as good as the gamble Question: On the diagram on the board, show the certainty equivalent of gamble A, CE A The risk premium is the amount of expected income an individual is prepared to give up rather than face the gamble, RP A = EV A CE A 7 It turns out that the risk premium is approximately given by RP = 1 2 A 2 , where A is the coefficient of absolute risk aversion. The risk premium is greater the greater is A (that is, the greater is the degree of risk aversion) and the greater is the variance. 8 Incentives The second main question of organizational scope is how to motivate individuals to act in the interests of the organization rather than in their own interests 9 Agency Agency theory, or principalagent theory, concerns the design of payment schemes by a principal to provide agents with an incentive to act in the interests of the principal. The principal can be shareholders, an organization, or a division. The agent can be a CEO, a manager, or a worker 10 This becomes an interesting problem when the principal can not observe the actions of the agents, if it could observe agent actions it would just force the agent to act in the interests of the principal. For example, do action a and the principal pays the agent s , if any other action is observed the principal pays the agent nothing....
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