Please help me solve this problem Thank you! Please in detail! A firm is conside
ID: 374754 • Letter: P
Question
Please help me solve this problem Thank you!
Please in detail!
A firm is considering the decision of investing in new plants. The following is the profit payoff matrix under three conditions: it does not expand, it builds two new plants, or it builds one new plant. Three possible states of nature can exist-no change in the economy, the economy contracts and the economy grows. The firm has no idea of the probability of each state. 2. State of Economy expands $5 million $15 million $40 million unchanged $4 million $6 million $18 million contracts no new plants 1 new plant 2 new plants -$ 3 million -6 million -$18 million Which option would the firm choose under each of the following rules? a. Maximax rule b. Maximin rule Minimax regret rule d. Equal probability ruleExplanation / Answer
a) MaxiMax rule: Find the Maximum payoff for each decision strategy
Max payoff of No new plants = MAX(5, -3, 4) = 5
Max payoff of 1 new plant = MAX(15, -6, 6) = 15
Max payoff of 2 new plants = MAX(40, -18, 18) = 40
Maximum payoff out of the above is 40, associated with decision strategy of 2 new plants.
Chosen option: 2 new plants
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b) MaxiMin rule: Find the Minimum payoff for each decision strategy
Minimum payoff of No new plants = MIN(5, -3, 4) = -3
Minimum payoff of 1 new plant = MIN(15, -6, 6) = -6
Minimum payoff of 2 new plants = MIN(40, -18, 18) = -18
Maximum payoff (least negative) out of the above is -3, associated with decision strategy of No new plants.
Chosen option: No new plants
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c) MiniMax regret rule: Find the Maximum regret for each decision strategy under each state of nature
Maximum regret of No new plants = MAX[ (MAX(5,15,40)-5), (MAX(-3,-6,-18)-(-3)), (MAX(4,6,18)-4)] = MAX[(40-5), (-3-(-3)), (18-4)] = MAX[35, 0, 14] = 35
Maximum regret of 1 new plant = MAX[ (MAX(5,15,40)-15), (MAX(-3,-6,-18)-(-6)), (MAX(4,6,18)-6)] = MAX[(40-15), (-3-(-6)), (18-6)] = MAX[25, 3, 12] = 25
Maximum regret of 1 new plants = MAX[ (MAX(5,15,40)-40), (MAX(-3,-6,-18)-(-18)), (MAX(4,6,18)-18)] = MAX[(40-40), (-3-(-18)), (18-18)] = MAX[0, 15, 0] = 15
Out of the above, Minimum regret is 15, associated with decision strategy of 2 new plants.
Chosen option: 2 new plants
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d) Equal probability rule: In this rule, each state of nature is assigned an equal probability. Find the Average payoff for each decision strategy under each state of nature
Average (equal probability) payoff of No new plants = (5+(-3)+4)/3 = 2
Average (equal probability) payoff of 1 new plant = (15+(-6)+6)/3 = 5
Average (equal probability) payoff of 2 new plants = (40+(-18)+18)/3 = 13.33
Out of the above, Maximum is 13.33, associated with decision strategy of 2 new plants.
Chosen option: 2 new plants