Question
Benny is thinking about opening a bike shop. Benny can open a small shop, a large shop, or no shop. The profits depend on the
Benny is thinking about opening a bike shop. Benny can open a small shop, a large shop, or no shop. The profits depend on the size of the shop and whether the market for bikes is favorable or unfavorable. Benny does not want to make the wrong decision. He is thinking about hiring a marketing firm to conduct a research study. If the study is conducted, the study could be favorable or unfavorable.
Benny has done some analysis of the profitability of the bike shop. If Benny builds the large bike shop, he will earn $120,000 if the market is favorable, but he will lose $80,000 if the market is unfavorable. If he decides to build a small shop, he will earn $60,000 profit is the market is profitable and lose $20,000 if the market is unfavorable. These payoffs are based on market study. He predicts that there is a 50-50 chance that the market will be favorable.
If Benny decides to hire the marketing firm to conduct the survey, the survey will cost him $10,000. It is estimated the there is a .7 probability that the survey will be favorable. Furthermore, there is a .8 probability that the market will be favorable given a favorable outcome from the survey. However, the consultant has warned benny that there is only a probability of .15 of a favorable if the research results are not favorable. These are conditional probabilities and they are listed below. You will need to calculate the EV for every node before you can answer the questions
Question:
- What is the EV of the no market survey node?
- Should Benny use the marketing research to make his final decision to open the bike shop (large or small) if research is favorable?
- What if Benny uses the marketing research and the research shows the unfavorable market, should he open a shop (what size), or not open a shop
- What is node #1 EV?
P = (favorable marketfavorable survey) = .8
P = (unfavorable marketfavorable survey) = .2
P = (favorable marketunfavorable survey) = .15
P = (unfavorable marketunfavorable survey) = .85
P = market survey favorable = .7
P = market survey unfavorable = .3
P = (favorable marketno survey) = .5
P = (unfavorable marketno survey = .5
Very Important!!!
Don't forget to subtract the cost of the survey($10,000) from the payoff amounts at the end of the branches for nodes 2, 3, 4, and 5 before you calculate the expected value for each node.
Payoff Table
| Market | ||
| Decisions | Favorable, s1 | Unfavorable, s2 |
| Large Shop, d1 | $120,000 | -$80,000 |
| Small Shop, d2 | $60,000 | -$20,000 |
| No Shop, d3 | $0 | $0 |
Payoff Table
| Market | ||
| Decisions | Favorable, s1 | Unfavorable, s2 |
| Large Shop, d1 | $120,000 | -$80,000 |
| Small Shop, d2 | $60,000 | -$20,000 |
| No Shop, d3 | $0 | $0 |
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School Finance A Policy Perspective
Authors: Allan Odden, Lawrence Picus
5th Edition
0078110289, 978-0078110283
