Question

Carlos has a utlity function U wi, where W is his wealth in millons or dollars and U is the ueity he obtains from that weath. In the final stage of a game show, the host offers Carlos a choice between (A) 59 miltion for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6 Use the blue curve (circle points) to graph Carlos's utlity function at wealth levels of so, $1 million, $4 milion, $9 million, and $16 million. 5.0 4.5 ulity Function 40 3 5 3.0 2.5 20 0.0 2G0 120820 Wealth (Milions of doliars True or False: Carlos is risk averse. True

Answer 1

W	U(W)=W1/2
0	0
1	1
4	2
9	3
16	4

4.5 4 3.5 16,4 E 2.5 1.5 1,1 0.5 0 0 2 46810 12 14 1618 20 Wealth, million $

Choice A

Expected prize=$9 million

U(9)=9^1/2=3

Choice B

Probability of prize being $1=p=0.40

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

Probability of prize being $16=1-p=0.60

U(16)=16^1/2=4

Expected prize=0.4*1+0.6*16=$10 million

Expected Utility=p*U(1)+(1-p)*U(16)=0.40*1+0.60*4=2.80

Utility curve is concave, we can say that person is Risk averse

Carlos is risk averse

True

We can see that in above calculations that

Choice B gives Carlos a higher expected prize

Choice A gives Carlos a higher expected utility

Since Carlos is Risk Averse, he will pick Choice A