Question

Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry 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. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a 5-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable (i.e., predicting a favorable market) or unfavorable (i.e., predicting an unfavorable market).

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 $1 0,000 loss in an unfavorable market. At the present time, he believes that there is a 50–50 chance that the market will be favorable. His old marketing professor will charge him $5,000 for the marketing research. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be favorable given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a favorable market if the marketing research results are not favorable. Jerry is confused.

(a) What should Jerry do?

(b) What would the expected profit be?

Answer 1

Answer a=

EMV for the large shop with no survey =0.5*60000+0.5*(-40000)=10000

EMV for the small shop with no survey == 0.5*30000+0.5*(-10000)=10000

So EMV is same for both the cases

EMV for the large shop with unfavorable survey =0.4 *(0.12*60000+0.88*(-40000)) = -11200

EMV for the small shop with unfavorable survey =0.4 *(0.12*30000+0.88*(-10000)) = -2080

Survey fee is 5000 so

Final EMV for the large shop with unfavorable survey-11200-5000 =-16200

Final EMV for the small shop with unfavorable survey=-2080-5000=-7080

We will select the lower loss which is -7080 related to the small shop with unfavorable survey

EMV for the large shop with favorable survey =0.6 *(0.9*60000+0.1*(-40000)) =30000

EMV for the small shop with favorable survey =0.6 *(.9*30000+0.1*(-10000)) = 15600

Survey fee is 5000 so

Final EMV for the large shop with favorable survey-30000-5000 =25000

Final EMV for the small shop with favorable survey=15600-5000=10600

We will select higher EMV of 25000

So total EMV for the market survey=0.6*25000 +0.4* (-2080) = 14168

As the cost fo having a survey is 5000 which is less than the EMV with a survey so survey must be conducted.

And depending upon the above analysis, EV of a small shop with a survey is more than the large shop with or without a survey so the decision will be to open small shop.

Answer B= EMV =0.6*25000 +0.4* (-2080) = 14168