1. A firm is considering the decision of investing in new plants. The following
ID: 1209831 • Letter: 1
Question
1. 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
$20 million
$30 million
$40 million
-$ 3 million
-$ 6 million
-$12 million
$4 million
$6 million
$8 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 _________________________________________________
State of Economy
expands
contracts
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 million
-$ 3 million
-$ 6 million
-$12 million
$4 million
$6 million
$8 million
Explanation / Answer
a. 2 New Plants as maiximizing the maximum gain
b. N0 New Plant as maximizing the minimum gains
c. 1 New Plant as minimizing regret of maximax and maximin
d. 2 New Plant as p = 0.33 for each of three events
No Plant Expected Payoff = 0.33*(20 - 3 + 14) = 0.33*31
1 Plant Expected Payoff = 0.33*(30 - 6 + 6) = 0.33*30
2 Plants Expected Payoff = 0.33*(40 - 12 + 8) = 0.33*36
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