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Let us say you received a wealth of 'W' pesos from your parents (you don't own anything else yet). With probability 'p', you will find that you also have a sibling with whom you have to share half of the wealth. In this case, you will be left with a wealth of 'W/2'. With probability '1-p', there will be no sibling and your wealth will remain intact at 'W'. A friends of your's is ready to insure you against any such loss if you pay him a premium of 'q' per peso of the insurance you want. Thus, if you buy a coverage for 'X' pesos, you will pay 'qX' as the insurance premium (with this coverage your friend is going to pay you 'X' whenever you find out that you have a sibling and 0 otherwise). Let us say your utility is given as U(W)=log(W). Given that you buy an insurance coverage, how much insurance coverage will you buy? In order to solve this, you need to write the expected utility in terms of p, q, X and W. Then you need to pick X in order to have the highest expected utility. You have to take first order derivative to chose a value of X which maximizes this expected utility. The amount of insurance coverage you buy will therefore be that value of X in terms of p, q and W.

A

W/2

B

Solve this for X: (W-qX)*p*q=(W/2+X-qX)*(1-p)*(1-q)

C

Solve this for X: (W/2-qX)*p*q=(W/2+X-qX)*(1-p)*(1-q)

D

Solve this for X: (W-qX)*p*(1-q)=(W/2+X-qX)*(1-p)*q

E

0

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