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Utility is U(I) = I^b, where I is income. Consumers face a gamble with a ten...

Utility is U(I) = I^b, where I is income. Consumers face a gamble with a ten percent chance they will have $50,000 in the bad state of the world and a 90 percent chance the will have $100,000 in the good state. There are three consumer types represented by b = 0.75, b = 0.5 and b = 0.25. Calculate the risk premium for each consumer type and comment on their (relative) risk preferences

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Answer #1

U(I) = ID 2 states of world 107. Chance (0-1) of 5 904. chauce (0) $ $50,000 $100,000 Expected Imone - Epi. = 0.1 x $ 50,000.U EU E{u} = $5395.44 bele Huore, ulce) - E So, U(CE) = $5395-44 CEP - I = $ 5395.44 CE - I - $ 94,631:52 So, CE = $94631-52lish Premier of consumer 2 $94,224:44 = = $ 95,000 - $ 775.56 0.25 For Consumer 3 . b=0.25 . EU = 0.1% ($ 50, 609) 029 + = 0.We can see, Risk Premium of consumer 1 ($368.48) < Risk Premium of consumer 2 ($775.56) < Risk Premium of consumer 3 ($1318.08)

So, we can say Consumer 3 is relatively most risk averse followed by consumer 2 and then consumer 1 who is relatively least risk averse

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