Willy’s only source of wealth is his chocolate factory. He has
the utility function 
, where p is the probability of
a flood, and cf and cnf are his wealth contingent on a flood and on
no flood, respectively. The probability of a flood is p = 1/6. The
value of Willy’s factory is $500,000 if there is no flood and $0 if
there is a flood. Willy can buy insurance where if he buys $x worth
of insurance, he must pay the insurance company $2x/17 whether
there is a flood or not, but he gets back $x from the company if
there is a flood. What is the value x of insurance that Willy
should buy? If Willy buys this insurance what will his wealth be in
case of a flood and no flood, respectively?
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