Quantitative Methods for Business 12e Chapter 5 Problem No 3
Quantitative Methods for Business Chapter 5 Problem No. 3
Homework Solution Problem No. 3
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Problem No. 3
In a certain lottery, a lottery ticket costs $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:
Decision Alternatives
Win s1
Loses s2
Purchase lottery ticket, d1
300,000
-2
Do not purchase lottery ticket, d2 0
0
Payoff Table
a.) A realistic estimate of the chances of winning is 1 in 250,000. approach to recommend a decision.
Use the expected value
Answer:
Given:
Realistic estimate of the probability of winning: 0.000004 (1/250,000)
Realistic estimate of the probability of losing
: 0.999996 (1- 0.000004)
Thus, the expected values for the two decision alternatives are:
EV(d1) = 0.000004(300,000) + 0.999996(-2) = 1.2 + (-1.999992) = -0.799992
EV(d2) = 0.000004(0) + 0.999996(0) = 0.00
Using the expected value approach, the optimal decision is to select decision alternative d2 which is not to purchase a lottery ticket with an expected monetary value of $0.
b.) If a particular decision maker assigns an indifference probability of 0.000001 to the $0 payoff, would this individual purchase a lottery ticket? Use the expected utility to justify your answer.
Answer:
Best payoff is $300,000, we assign a utility value of 10. U($300,000) = 10.00
Worst payoff is -$2.00, we assign a utility value of 0.0. U(-$2.00) = 0.00
We calculate U(M):
U(M) = pU($300,000) + (1 – p)U((-$2.00) = p(10) + (1 – p)0.00 = 10p
Therefore, U($0.00) = 10p = 10 x 0.000001 = 0.00001
Monetary Value
Indifference Value of p
Utility Value
(10p)
$300,000
Does not apply
10.00
$0.0
0.000001
0.00001
-$2.00
Does not apply
0.00
Utility of Monetary Payoffs
State of Nature
Decision
Alternatives
Win s1
Loses s2
Purchase lottery ticket, d1
Homework Solution Problem No. 3
_____________________________________________________________________________________________
Problem No. 3
In a certain lottery, a lottery ticket costs $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:
Decision Alternatives
Win s1
Loses s2
Purchase lottery ticket, d1
300,000
-2
Do not purchase lottery ticket, d2 0
0
Payoff Table
a.) A realistic estimate of the chances of winning is 1 in 250,000. approach to recommend a decision.
Use the expected value
Answer:
Given:
Realistic estimate of the probability of winning: 0.000004 (1/250,000)
Realistic estimate of the probability of losing
: 0.999996 (1- 0.000004)
Thus, the expected values for the two decision alternatives are:
EV(d1) = 0.000004(300,000) + 0.999996(-2) = 1.2 + (-1.999992) = -0.799992
EV(d2) = 0.000004(0) + 0.999996(0) = 0.00
Using the expected value approach, the optimal decision is to select decision alternative d2 which is not to purchase a lottery ticket with an expected monetary value of $0.
b.) If a particular decision maker assigns an indifference probability of 0.000001 to the $0 payoff, would this individual purchase a lottery ticket? Use the expected utility to justify your answer.
Answer:
Best payoff is $300,000, we assign a utility value of 10. U($300,000) = 10.00
Worst payoff is -$2.00, we assign a utility value of 0.0. U(-$2.00) = 0.00
We calculate U(M):
U(M) = pU($300,000) + (1 – p)U((-$2.00) = p(10) + (1 – p)0.00 = 10p
Therefore, U($0.00) = 10p = 10 x 0.000001 = 0.00001
Monetary Value
Indifference Value of p
Utility Value
(10p)
$300,000
Does not apply
10.00
$0.0
0.000001
0.00001
-$2.00
Does not apply
0.00
Utility of Monetary Payoffs
State of Nature
Decision
Alternatives
Win s1
Loses s2
Purchase lottery ticket, d1