Decision Theory

Student’s Name

Institution Affiliation

Self-Test

A

A

A

A

C

B

C

A

Question 17

What type of decision is Ken facing?*Decision under uncertainty

What decision criterion should he use?*Maximax

What alternative is best*He should choose Sub 100, since it has the best possible outcome.

Question 18

Ken is using maximax criterion and should select sub 100 as it has the maximum payoff of $300000.

As Bob is pessimistic, He should use Maximin criterion. Equipment Favourable Mkt($) Unfavourable Mkt($) Row minimum

Sub 100 $ 300,000.00 $ (200,000.00) $ (200,000.00)

Oiler J $ 250,000.00 $ (100,000.00) $ (100,000.00)

Texan $ 75,000.00 $ (18,000.00) $ (18,000.00)

Maximin $ (18,000.00)

Using Maximin criterion, Bob would select Texan as worst payoff for this alternative

is better than the worst payoffs of other alternatives

Question 20

SOLUTION: (a) What decision would maximize expected profits? To decide the best alternative, we need to calculate EMV for each alternative as shown below.

STATE OF NATURE EMV DECISION ALTERNATIVE GOOD ECONOMY POOR ECONOMY Stock Market 80,000 -20,000 30000 Bonds 30,000 20,000 25000 CDs 23,000 23,000 23000 Probability 0.5 0.5   Maximum EMV 30000 As the EMV is maximum for Stock market, Mickey should invest in the Stock market.

(b) What is the maximum amount that should be paid for perfect forecast of the economy?

Expected Value for Perfect information (EVPI) is the amount that should be paid for perfect forecast of the economy.

EVPI = EV with perfect information – Maximum EMV EV with Perfect information = Best payoff for first state of nature

*Probability of the 1st state of nature +Best payoff for second state of nature

*Probability of the 2nd state of nature

EV with PI 51500 EVPI $ 21,500 Thus, the maximum amount that should be paid is $21,500

Question 24

SOLUTIONS (a) Develop an opportunity loss table.   PROFIT ($)   STRONG FAIR POOR   MARKET MARKET MARKET Large facility 550,000 110,000 -310,000 Medium-sized facility 300,000 129,000 -100,000 Small facility 200,000 100,000 -32,000 No facility 0 0 0   Opportunity loss Table   STRONG MARKET FAIR MARKET POOR MARKET   Large facility 0 19,000 310,000 Medium-sized facility 250,000 0 100,000 Small facility 350,000 29,000 32,000 No facility 550,000 129,000 0 (b) What is the minimax regret decision?   Opportunity loss Table  

  STRONG MARKET FAIR MARKET POOR MARKET MAXIMUM REGRET

  Large facility 0 19,000 310,000 310,000

Medium-sized facility 250,000 0 100,000 250,000

Small facility 350,000 29,000 32,000 350,000

No facility 550,000 129,000 0 550,000

Minimax regret 250,000

Minimax regret decision is to build Medium-sized facility.

Question 29

Payoff

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0.5 $100,000

favourable market Construct Clinic $30,000 Unfavorable market 0.5 ($40,000)

EMV $30,000 $0 Do nothing $0

EMV for node 1(Construct clinic) = 0.5*100000 +0.5*(-40,000) = $30,000 EMV for do nothing=$0 The EMV for tree is maximum of the two, thus $30,000 As, EMV is highest for the alternative of construct a clinic, the medical professionals should construct the clinic.

Reference

Turskis, Z., & Zavadskas, E. K. (2011). Multiple criteria decision making (MCDM) methods in economics: an overview. Technological and economic development of economy, (2), 397-427.