Question

Questions 1 – 4 refer to prospects X and Y below, as well as the following information
?? = ($0, 0.50; $40, 0.25; $100, 0.25) ?? = ($0, 0.25; $40, 0.50; $60, 0.25)
Mark has utility of wealth given by ?(?) = ?^0.6
1. What is the expected value of prospect X (?V(?))?
2. What is the standard deviation of prospect X (SD(?))? (Round your answer to the nearest cent,
and don’t worry, I’ll include a healthy margin of error so you won’t get this wrong due to
rounding).
3. What is the value of the expected utility of Y for Mark (EU(Y))?
4. How much is Mark willing to spend to acquire Y (so, what is the value of CE(?))? (Hint, if
?(?) = ?^0.6, ?ℎ?n u^−1(?) = ?^1.67).

Answer 1

1.

Expected value of prospect X = 0.5* $0 + 0.25 * $40 + 0.25 * $100

Expected value of prospect X = $35

2.

X	P(x)	X* P(x)	X^2*P(x)
0	0.5	0	0
40	0.25	10	400
100	0.25	25	2500
	E(x)	35	2900
	Var	1675
	Std dev	40.93

Note that,

Variance = X^2 * P(x) - (E(x))^2 = 2900 - 35^2

Variance = 1675

SD = sqrt ( Variance ) = sqrt( 1675) = 40.93

3.

Similar to the above method,

Y	P(y)	U(y) = y^0.6	U(y)* P(y)
0	0.25	0.00	0
40	0.5	9.15	4.57
60	0.25	11.67	2.92
		E(U(y))	7.49

Hence,

Expected Value = 7.49

4.

Y	P(y)	U(y) = y^0.6	U(y)^1.67	C(y) =(U(y)^1.67)* P(y)
0	0.25	0.00	0	0.00
40	0.5	9.15	40.33	20.16
60	0.25	11.67	60.53	15.13
			E(C(y))	35.29

Hence,

Value of CE(y)= 35.29