Explain step by step A homeowner\'s utility of wealth function is U(w) = Squarer

Question

Explain step by step

A homeowner's utility of wealth function is U(w) = Squareroot 5w. The owner is concerned that a tornado may significantly damage his property. If there is no tornado, the homeowner's wealth is $750,000. The probability of a tornado is 1/30. If a tornado does occur, the homeowner's wealth will fall to $450,000. Round to two decimal places where relevant. Calculate the owner's expected wealth. Show your work. Calculate owner's expected utility. Show your work. Calculate owner's certainty equivalent. Show your work. Calculate the risk premium that the owner is willing to pay for tornado insurance. Show your work.

Explanation / Answer

a)

ans:

i)

EXPEXCTED WEALTH = 750000 X 29/30 + 450000 X 1/30 = 740000

ii)

Expected Utility = (5 X 75)^0.5 X29/30 + (5X45)^0.5 X 1/30 = 19.2194 in “0000” terms

b)

Certainty Equivalent: The amount of payoff that an agent would have to receive to be indifferent between that payoff and a given gamble is called that gamble's 'certainty equivalent'.

Owners certainty equivalent

U(w) = (5w)^0.5

U(450000) = (5 X 450000)^0.5 = 1500

5w=192194^2

W = 192194^2 / 5 = 738000

c)

Premium is = 750000-728000= 32000

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