Example $16\mathrm{.}15$ Decisions with Sample Information

Suppose that a company is developing a new touchscreen

cell phone. Historically, $70\%$ of their new phones

have resulted in high consumer demand, whereas $30\%$ have

resulted in low consumer demand. The company has the

decision of choosing between two alternative models with

different features that require different amounts of investment

and also have different sales potential. Figure $16\mathrm{.}10$

shows a completed decision tree in which all cash flows

are in thousands of dollars. For example,

model $1$ requires

an initial investment for development of $$200,000,$ and

model $2$ requires an investment of $$175,000.$ If demand

is high for model $1,$ the company will gain $$500,000$ in

revenue, with a net profit of $$300,000$; it will receive only

$$160,000$ if demand is low, resulting in a net profit of

$$$$40,000.$ Based on the probabilities of demand, the expected

profit is $$198,000.$ For model $2,$ we see that the

expected profit is only $$188,000.$ Therefore, the best decision

is to select

model $1.$ Clearly there is risk in either

decision, but on an expected value basis, model $1$ is the

best decision.

Now suppose that the firm conducts a market

research

study to obtain sample information and better

understand the nature of consumer demand. Analysis

of past market research studies, conducted prior to introducing

similar products, has found that $90\%$ of all

products that resulted in high consumer demand had

previously received a high survey response, whereas

only $20\%$ of all products with ultimately low consumer

demand had previously received a high survey response.

These probabilities show that the market research is not

always accurate and can lead to a false indication of

the true market

potential. However, we should expect

that a high survey response would increase the historical

probability of high demand, whereas a low survey

response would increase the historical probability of a

low demand. Thus, we need to compute the conditional

probabilities:

P$1$high demand high survey response$2$

P$1$high demand low survey response$2$

P$1$low demand high survey response$2$

P$1$low demand low survey response$2$