CH_12_DECISION_ANALYSIS

Decision Analysis with Additional Information
Utility (2 of 2)

Expected Cost (insurance) = .992($500) + .008(500) = $500
Expected Cost (no insurance) = .992($0) + .008(10,000) = $80

Decision should be do not purchase insurance, but people
almost always do purchase insurance.
■ Utility is a measure of personal satisfaction derived from money.
■ Utiles are units of subjective measures of utility.
■ Risk averters forgo a high expected value to avoid a low-

probability disaster.

■ Risk takers take a chance for a bonanza on a very low-

probability event in lieu of a sure thing.

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Decision Analysis
Example Problem Solution (1 of 9)

States of Nature

Decision Good Foreign Competitive Poor Foreign Competitive

Expand Conditions Conditions
Maintain Status Quo
Sell now $ 800,000 $ 500,000
1,300,000 -150,000
320,000 320,000

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Decision Analysis
Example Problem Solution (2 of 9)

a. Determine the best decision without probabilities using the 5
criteria of the chapter.

b. Determine best decision with probabilities assuming .70
probability of good conditions, .30 of poor conditions. Use
expected value and expected opportunity loss criteria.

c. Compute expected value of perfect information.

d. Develop a decision tree with expected value at the nodes.

e. Given following, P(Pg) = .70, P(Ng) = .30, P(Pp) = 20,
P(Np) = .80, determine posterior probabilities using Bayes’
rule.

f. Perform a decision tree analysis using the posterior probability
obtained in part e.

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Decision Analysis
Example Problem Solution (3 of 9)

Step 1 (part a): Determine decisions without probabilities.

Maximax Decision: Maintain status quo

Decisions Maximum Payoffs

Expand $800,000
Status quo 1,300,000 (maximum)
Sell
320,000

Maximin Decision: Expand

Decisions Minimum Payoffs

Expand $500,000 (maximum)
Status quo -150,000
Sell 320,000

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Decision Analysis
Example Problem Solution (4 of 9)

Minimax Regret Decision: Expand

Decisions Maximum Regrets

Expand $500,000 (minimum)

Status quo 650,000

Sell 980,000

Hurwicz (α = .3) Decision: Expand

Expand $800,000(.3) + 500,000(.7) = $590,000

Status quo $1,300,000(.3) - 150,000(.7) = $285,000

Sell $320,000(.3) + 320,000(.7) = $320,000

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Decision Analysis
Example Problem Solution (5 of 9)

Equal Likelihood Decision: Expand

Expand $800,000(.5) + 500,000(.5) = $650,000

Status quo $1,300,000(.5) - 150,000(.5) = $575,000

Sell $320,000(.5) + 320,000(.5) = $320,000

Step 2 (part b): Determine Decisions with EV and EOL.

Expected value decision: Maintain status quo

Expand $800,000(.7) + 500,000(.3) = $710,000

Status quo $1,300,000(.7) - 150,000(.3) = $865,000

Sell $320,000(.7) + 320,000(.3) = $320,000

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Decision Analysis
Example Problem Solution (6 of 9)

Expected opportunity loss decision: Maintain status quo

Expand $500,000(.7) + 0(.3) = $350,000

Status quo 0(.7) + 650,000(.3) = $195,000

Sell $980,000(.7) + 180,000(.3) = $740,000

Step 3 (part c): Compute EVPI.

EV given perfect information = 1,300,000(.7) + 500,000(.3) =
$1,060,000

EV without perfect information = $1,300,000(.7) - 150,000(.3) =
$865,000

EVPI = $1.060,000 - 865,000 = $195,000

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Decision Analysis
Example Problem Solution (7 of 9)

Step 4 (part d): Develop a decision tree.

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Decision Analysis 12-59
Example Problem Solution (8 of 9)

Step 5 (part e): Determine posterior probabilities.
P(gP) = P(Pg)P(g)/[P(Pg)P(g) + P(Pp)P(p)]
= (.70)(.70)/[(.70)(.70) + (.20)(.30)] = .891

P(pP) = .109

P(gN) = P(Ng)P(g)/[P(Ng)P(g) + P(Np)P(p)]
= (.30)(.70)/[(.30)(.70) + (.80)(.30)] = .467

P(pN) = .533

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Decision Analysis
Example Problem Solution (9 of 9)

Step 6 (part f): Decision tree analysis.

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