2. A firm is considering the decision of investing in new plants. The following
ID: 1116884 • Letter: 2
Question
2. 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. State of Economy expands contracts unchanged no new plants 1 new plant 2 new plants $5 million $15 million $40 million $ 3 million $ 6 million $18 million $4 million $6 million $18 million Which option would the firm choose under each of the following rules? a. Maximax rule _________________________________________________ b. Maximin rule __________________________________________________ c. Minimax regret rule _________________________________________________ d. Equal probability rule _________________________________________________
Explanation / Answer
b. The maximin criterion states that the decision maker should make the decision that yields the maximum value in the worst scenario. So the worst scenario here is a contraction and the best alternative is opening no new plants i.e -$3 million.
c. Minimax regret rule is minimizing the maximum regret of choosing one option over the other. We construct a regret table.
$0 Million
The matrix is created by identifying the highest return option in each situation and then subtracting the rest of the options in that category from the highest option giving us the regret. Thus we finally find the minimax regret in the matrix. It is the option which has the least regret other then 0's. Here it is $3 Million.
d. We first identify the expected return of each strategy by calculating the average of all the reurns in each strategy. So, we get expected returns as:
Out of these, the ones with the maximum expected return should be chosen. Here it is two plants i.e $13.34 Million.
STATE OF ECONOMY EXPANSION CONTRACTION UNCHANGED NO NEW PLANTS $35 Million $0 Million $14 Million 1 NEW PLANT $25 Million $3 Million $12 Million 2 NEW PLANTS $0 Million $15 Million$0 Million
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