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Social ScienceBrandon is considering expansion of a store. If he expands, the interest rate at which he borrows the money is the important factor. He is not sure what kind of interest rate will be obtained. If he does not expand, the only factor influencing the outcome is future economy. The following table summarizes the situation: Probabilities Payoff Expand Large Favorable interest .3 $60k Neutral interest .5 $30k Unfavorable interest .2 ‑$70k Expand Small Favorable interest .3 $50k Neutral interest .5 $30k Unfavorable interest .2 ‑$30k Do not expand Economy up .3 $30k Economy same .5 $20k Economy down .2 $0Draw the decision tree showing all nodes and expected values. Use square for decision node, and circle for chance node. What should he do?
- Brandon is considering expansion of a store. If he expands, the interest rate at which he borrows the money is the important factor. He is not sure what kind of interest rate will be obtained. If he does not expand, the only factor influencing the outcome is future economy. The following table summarizes the situation:
Probabilities Payoff
Expand Large Favorable interest .3 $60k
Neutral interest .5 $30k
Unfavorable interest .2 ‑$70k
Expand Small Favorable interest .3 $50k
Neutral interest .5 $30k
Unfavorable interest .2 ‑$30k
Do not expand Economy up .3 $30k
Economy same .5 $20k
Economy down .2 $0
Draw the decision tree showing all nodes and expected values. Use square for decision node, and circle for chance node. What should he do?
Expert Answer
The decision tree has been represented as shown in the diagram.
The expected values are given as below:
Expand large
Expected value = 0.3x60 + 0.5x 30 – 0.2 x 70 = $47
Expand small
Expected value = 0....
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