econ assessment 2

# econ assessment 2 - = 5.33 iii(8-1.6667(1 3-1.333 = 5.67...

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Amal Radia Econ 395 11. (a): Expected Utility from being an uninsured hair model u(x) = log 2 (x) = (2/3)(log(8) / log(2)) + (1/3)(log(1) / log (2)) = (2/3)(3) + 0 = 2 (b) He is risk averse because the vNM function is concave. This means that the marginal Utility(slope) of the \$ decreases as his income increases. (c) (.667)(8) + (.333)(1) so 5.6667 is his expected value, thus his expected loss is 8-5.6667 = 2.333 If he buys \$7 in coverage: .333(7) = 2.333 But he is risk averse so he is willing to buy more coverage so he will buy \$8 at this price Because he is willing to accept a lower expected wealth to reduce risk. (d) u(8-P) >= 2 so log(8-P) / log(2) = 2 Solving for P, we get P = \$4 mill. is the highest premium he would pay for full insurance. This makes sense because since he is risk averse, he commits to paying more than the

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Expected loss of \$2.333 million (e) i) (8-4)(.6667) + (1+7-4)(.333) = 4 ii) (8-2)(.667) + (1+5-2)(.333)
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Unformatted text preview: = 5.33 iii) (8-1)(.6667) + (1+3-1)(.333) = 5.67 iv) (8)(.667) + (1)(.333) = 5.67 Thus, the highest to lowest expected income go iv ~ iii, ii, i. The least to greatest exposure to risk go: i, ii, iii, iv To say anything about his preferences between the four options, we will need to use his vNM function as we do in part (f). (f) i) (log (8-4) / log (2))(.6667) + (log(1+7-4) / log(2))(.333) = 2 ii) (log (8-2) / log (2))(.667) + (log(1+5-2) / log(2))(.333) = 2.38 iii) (log (8-1) / log(2))(.667) + (log(1+3-1) / log(2))(.333) = 2.40 iv) (log (8) / log (2))(.667) + = 2 He will choose contract ii or iii because his utility for this insurance contract is higher Than if he were uninsured. He will not choose to be fully insured because in part d), the highest premium he would Pay is \$4m, and contract i only offers \$7m in coverage instead of \$8m (full) for \$4m....
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## This note was uploaded on 04/13/2010 for the course ECON 330 taught by Professor Minetti during the Fall '08 term at Michigan State University.

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econ assessment 2 - = 5.33 iii(8-1.6667(1 3-1.333 = 5.67...

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