g Suppose you have $100 of endowment, and you are offered a chance to buy a lottery which costs $36. The lottery has 18% of chance to win a prize of $G, or you just lose and get nothing. Suppose your utility function on wealth is U(w)=\sqrt{w}. What is the least prize size G that you will be willing to buy the lottery?

$301.23

Step-by-step explanation:

We have that the function of wealth is U (w) = w ^ (1/2)

So, since what you have at the start is 100, we replace:

U (w) = 100 ^ (1/2)

U = 10

Now we have two cases:

the first one we win, then the winnings would be 100 minus the cost of the lottery, that is 36 and to that add G of the prize:

100 - 36 + G = 64 + G

In the second case, where we lose, the subtraction of 100 that we have minus the cost of the lottery would be equal 36

100 - 36 = 64

Therefore, we have to win with an 18% probability, therefore losing would be 82% (100% - 18%)

0.18 * (64 + G) ^ (1/2) + 0.82 * 64 ^ (1/2)

solving:

0.18 * (64 + G) ^ (1/2) + 6.56

Now this is equal to U which is equal to 10:

10 = 0.18 * (64 + G) ^ (1/2) + 6.56

(10 - 6.56) /0.18 = (64 + G) ^ (1/2)

(64 + G) ^ (1/2) = 19.11

(64 + G) = 365.23

G = 365.23 - 64

G = 301.23

Therefore, the smallest G prize size that the lottery will be willing to buy is $ 301.23