Question

1. In Lecture A9, we discussed an example of new product introduction.

1. Draw the two trees of Managers X and Y. Solve the two trees to find each manager’s EMV.
2. Which manager’s tree has a higher EMV? What is the economic meaning of the difference of the two EMV’s? [Hints: Think about the value of knowing if the production process is delayed or not when the manager needs to make the price decision]
3. (Optional) What are the risk profiles of the two managers? (5 bonus points)

Answer 1

Draw the two trees of Managers X and Y. Solve the two trees to find each manager’s EMV.

Manager X’s Tree:

Manager X’s EMV:

A = 4.7

B = 3.52

C = 1

Manager Y’s Tree:

Manager Y’s EMV:

A = 3.09

B = 3.52

C = 1

Which manager’s tree has a higher EMV? What is the economic meaning of the difference of the two EMV’s?

Manager X’s tree has a higher EMV of 4.7, compared to Manager Y’s tree with an EMV of 3.52. This means Manager X ‘s weighted average of possible outcomes, where the weights are the probabilities of those outcomes, are higher than that of Manager Y’s weighted averaged possible outcomes. Using the information given in the payoffs together with the information given in the probabilities determined the decision that Product A with Manager X has the highest expected value. Thus, there is an economic meaning that corresponds between the difference of the two EMV’s. Manager Y does not know if the production process is delayed or not when he/she needs to make the price decision. However, Manager X has the information and knows if/when the production process has a delay or not at the time when the price decision has to be made. Since we have this information, Manager X’s decision tree is correct.

What are the risk profiles of the two managers?

Manager X’s Risk Profile (optimal strategy):

Possible Outcome	Probability
0	(0.6)(0.95) = 0.57
12	(0.4)(0.95) = 0.38
1	(0.5)(0.05) = (0.025
3.5	(0.5)(0.05) = 0.025
	1

Manager Y’s Risk Profile (optimal strategy):

Possible Outcome	Probability
8	0.38
4	0.12
0	0.5
	1

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