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Unformatted text preview: TUTORIAL 9– WEEK 10 ECON3107/ECON5106 – Economics of Finance (Suggested solutions) 1. (Expected utility) Suppose you are faced with the following scenario: • Consume $6000 with probability 0.4 • Consume $3000 with probability 0.6. Suppose further that your utility function is of the CRRA (constant relative risk aversion) class: U ( c ) = c 1 γ 1 γ , where coefficient of relative risk aversion γ = 1 / 2 . (a) What is your expected utility? Notice that with γ = 1 / 2 the utility function becomes U ( c ) = c 1 1 / 2 1 1 / 2 = 2 √ c. The expected utility of this gamble is therefore EU = π ( c = 6000) · U (6000) + π ( c = 3000) · U (3000) = 0 . 4 · 2 √ 6000 + 0 . 6 · 2 √ 3000 = 127 . 69 (b) What is your expected level of consumption? E ( c ) = π ( c = 6000) · 6000 + π ( c = 3000) · 3000 = 0 . 4 · 6000 + 0 . 6 · 3000 = 4200 (c) What is your attitude towards risk? See the answer in part (d). (d) Compute the certainty equivalent of the gamble. The certaintyequivalent c ce is defined as U ( c ce ) = π ( c = 6000) · U (6000) + π ( c = 3000) · U (3000) Hence 2 √ c ce = 0 . 4 · 2 √ 6000 + 0 . 6 · 2 √ 3000 , which implies that c ce = 4076 . 4. Notice that the certainty equivalent is lower than the expected consumption. Therefore, the agent in question is riskaverse. (e) Suppose now that the coefficient of relative risk aversion is γ = 2 . Answer to the questions (a)(d) above for with γ = 2 . Are agents more or less tolerant to risk than before? 1 Notice that with γ = 2 the utility function becomes U ( c ) = c 1 2 1 2 = 1 c . The expected utility of this gamble is therefore EU = π ( c = 6000) · U (6000) + π ( c = 3000) · U (3000) = 0 . 4 · 1 6000 + 0 . 6 · 1 3000 = 2 . 6667 × 10 4 To see what happened to the agents attitude to risk, let us compute his/her certainty equivalent...
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This note was uploaded on 07/13/2011 for the course ECON 3107 at University of New South Wales.
 '11
 valentyn
 Economics, Utility

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