Question

Willy Wonka has a chocolate factory. He has the utility function pcf^1/3 + (1 – p)cnf^1/3, where p is the probability of a flood, 1 – p is the probability of no flood, and cf and cnf are his wealth contingent on a flood and on no flood, respectively. The probability of a flood is p =0.4. The value of Willy’s factory is $125,000 if there is no flood and $0 if there is a flood. Charlie wants to buy Willy’s chocolate factory, and he hires you to study Willy’s preference. What price do you suggest Charlie to offer?

Answer 1

Willy Wonka has a chocolate factory

His utility function is the following:

c = $125,000 if there is no flood

c = $0 if there is a flood

Let the probability of flood be p

So her expected utility is given by the following:

Let p be 0.4

Willy wonka's expected utility from the factory is 30.

Charlie wants to buy the willy's factory. Willy will be ready to sell the factory at any amount that gives him a guaranteed utility of at least 30

Mathematically,

Willy will sell the factory if Price is such that

At Price $27000 willy gets the same utility as his expected utility. So, Charlie should offer her $27000 for the factory