Self-Test
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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 | ||||||||
|
|
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 constructing 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.
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