Question

Maria’s house is worth 1 000 000 SEK. Her utility function is given by U = m^0,5 ,where m represents her wealth (the value of the house). The probability of the house burning down is 0,2. A fire would reduce the house value to 300 000 SEK.

a) Calculate the expected value of Maria’s wealth.

b) Calculate the utility of the expected wealth, given that Maria gets it for sure.

c) Calculate Maria ́s expected utility of Maria’s uncertain situation. Suppose that Maria can buy insurance that yields K SEK in case the house burns down. The insurance will cost her 0,2K SEK.

e) What will Maria’s wealth be in case the house burns down? What will it be in case the house does not burn down?

f) Express Maria’s expected utility of the lottery if she buys insurance.

g) What value of K will Maria choose (that is, what value of K maximizes her expected utility)?

h) Suppose Joseph is in the same situation as Maria, i.e., his house is worth 1 000 000 SEK. His utility function is given by U = m^0,5, where m represents her wealth (the value of the house). The probability of the house burning down is 0,2. A fire would reduce the house value to 300 000 SEK. Fires in the houses are independent in the statistical sense. Is it beneficial for Maria and Joseph to establish a mutual insurance company whereby the share losses? Calculate Maria’s new expected utility given that they have created a mutual insurance company and discuss the result.

Answer step by step and all questions please. 

All the best and thank you!

Answer 1

a. The expected value of the wealth of Maria will be: (probability of house burning down)*(value of house then)+( probability of house not burning down)(the original value of house)

= (0.2)(300,000)+(0.8)(1,000,000)= 60,000+800,000= 860,000 SEK

b. The utility of the expected wealth in case she gets it sure can be calculated by putting the value computed in a in the utility function given. So, it will be U=(860,000)^(0.5)= 927.36

c. In case of uncertain situation, the expected utility will be: (probability of house burning down)*(utility if value of house then)+( probability of house not burning down)(the original utility value of house)= (0.2)((300,000)^(0.5))+(0.8)((1,000,000)^(0.5))= 109.54+ 800= 909.54

e. In case the house burns down, the Maria’s wealth will be equal to the value of house had she not purchased the insurance plus the yield she would receive from the insurance, which will be 300,000+1,000= 301,000 SEK. In other case, if her house would not burn, the utility then will be equal to the value of her house less the premium paid which is 1,000,000-200= 999,800 SEK.

Answer 2