Question

Mr. Smith is thinking about opening a bicycle shop in his hometown. He loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all.

Mr. Smith has done some analysis about the profitability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is favorable, but he will lose $40,000 if the market is unfavorable. The small shop will return a $30,000 profit in a favorable market and a $10,000 loss in an unfavorable market. The chance of Favorable market and unfavorable market is 50-50.

His old marketing professor will charge him $5,000 for the marketing study. It is estimated that there is a 50% probability that the survey will be favorable and 50% unfavorable study.

Furthermore, he has given the following probabilities:

Probability that the market will be favorable given a favorable outcome from the study 90%

Probability that the market will be unfavorable given a favorable outcome from the study 10%

Probability that the market will be favorable given an unfavorable outcome from the study 12%

Probability that the market will be unfavorable given an unfavorable outcome from the study 88%

1. Compose the decision tree (25 pts)
2. What is Mr.Smith best option (show all your calculations and interpret the results explain it) (65 pts)
3. What is the Expected Value of Sample of Information (EVSI) ? (10 pts)

Answer 1

Initially there are two paths possible. One of them is is that Mr Smith does the survey and on the other hand he does a marketing study by paying 5000 dollars.

In the first part of Mr Smith doing selurvey himself, he can take two choices of opening a large shop or a small shop. And there are two subsequent possible paths of favouring or unfavouring market each having 50% probability.

For the initial second part where Mr Smith page $5000 to his teacher they are two paths which corresponds weather the marketing study is a favourable study or unfavourable study. Consequently he can opt for large or small shop as two more options after previous step. Here both of the large and small shop will have the probability of 90% for favourable market in case of favourable survey study aur aur will have the probability of of 10% of an unfavourable market in case of favourable study.

On the other hand for an unfavourable study, Mr. Smith can opt for one of both the choices of large or small shop in which favourable market probability is 12% only and for the unfavourable market the probability is 88%, since the study is unfavourable in previous step.