Jamal has a utility function u=w12, where w is his wealth in millions of dollars and u is the utility he obtains from that wealth. in the final stage of a game show, the host offers jamal a choice between (a) $4 million for sure, or (b) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4.

Jamal Should choose option B

Explanation:

The question is unclear with regards to the requirements, we will assume the question wants us to find an option that will maximize jamal's wealth.

Utility Function reflects Jamal's satisfaction that he derives from his wealth.

U = w12

a. Wealth (w) = $4million

U = 12w = (4000 000) x 12

U = 48000 000

b. Wealth =  $1 million with probability 0.6 and $9 million with probability 0.4.

We first need to calculate expected wealth before we can calculate how much utility will Jamal derive from this option

Expected Utility = 1 000 000 x 0.4 + 9000 000 x 0.4 = $4200 000

Utility = w12 = (4200 000) x 12 = 50 400 000

Jamal will have a utility of 48000 000 if he chooses option A and Option B provides Jamal with a Utility of 50 400 000. Option B provides a higher utility than option A, therefore the option that will maximize Jamal's Utility is Option B.

The expected value of both offers are:

Offer A's expected price = $4 million

Offer B's expected price = ($1 million x 0.6) + ($9 million x 0.4) = $4.2 million

Jamal's utility function U = W¹/²  or  U = √W

Offer A's expected utility = √$4,000,000 = 2,000 utils

Offer B's expected utility = √$4,200,000 = 2,049 utils

Both the difference in expected value and utility is not that large, but the difference in risk is great, so if I was Jamal I would choose option A.

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