Chapter 6 – Page 12 – Example

We are given the utility function and fixed the first two points U(0)=0 and U(4)=1.

We then work out the expectation of the utility function, however I don’t understand the next part of the example where you state that w’=1.8, then we know that U(1.8)=1.5.

How have you determined this?

 

This value of 1.8 has been obtained by asking the individual basically what level of wealth would make them half as happy as they would be if their wealth is 4.

(More precisely, it's the level of wealth that they would need to have to be indifferent between that level of wealth and a gamble that gave them 0 or 4, with equal probability.)

So you can't calculate this value of w from anything - it's just what the individual has answered and could be any value between 0 and 4.

The fact that they are half as happy when wealth is 1.8 as when wealth is 4 means that if U(4)=1, then U(1.8)=0.5.

 

Yes, the w'=1.8 is the answer given by the individual to the question:

"What certain level of wealth would you be indfifferent between having for sure compared to having either 0 and 4, each with a probability of one half?"

w'=1.8 is therefore the certainty equivalent of the gamble with an equal probability of yielding 0 and 4.

However, you cannot therefore work it out in this instance (as you don't have the individual's utility function - which is why you are asking them the question in the first place!)

 

Thanks for the replys, I think I get it now