Suppose Bob owns and operates a farm, and his utility of wealth function is U(w)

Question

Suppose Bob owns and operates a farm, and his utility of wealth function is U(w) = 15 w. He is concerned that a natural disaster may destroy his crops. If there is no disaster, Bob’s wealth is $360,000, but if a disaster does occur, Bob’s wealth will be $160,000. Further, the probability of a disaster is 1 15 .

17. Calculate Bob’s expected value for the wealth generated from his farm.

18. Calculate Bob’s expected utility.

19. Bob is offered disaster insurance which costs $20,000. If a disaster occurs, the insurance company will pay him $200,000 (in addition to the $160,000 he earns from his farm). If a disaster does not occur, the insurance company pays him nothing. Will he buy the insurance?

20. What is the most Bob is willing to pay for the insurance offered in the previous question? (round to the nearest $100)

21. In describing Bob’s risk preferences, he is:

A. Risk averse

B. Risk neutral

C. Risk loving

D. Cannot determine

E. None of the above

Explanation / Answer

If the probability of disaster is 1/15:

17.Expected value for wealth = 14/15 (360,000) + 1/15(160,000) = $294,000 + $10666 = $304,666

18. Expected utility = 14/15.u(360,000) + 1/15u(160,000) = 8400 + 400 = 8800

19. Expected utility from taking insurance = u(14/15(360,000-20000) + 1/15(360,000 - 20,000)) = u(340,000)

= 15*583 = 8745

It will not be beneficial to take the insurance as his utility is decreasing

21. Risk loving as he is willing to take risk instead of insurance

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