Your friend is the owner of Sweetilicious, a local cupcake shop in Geneseo, NY$.$ Recently, Letchworth

Bakery, a local competitor of Sweetilicious, gave your friend an offer to sell the shop for $$80,000.$

Suppose that the probabilities of Sweetilicious$$ expected profits in the future are given as follows:

P$($$$60,000)=0\mathrm{.}5,$ P$($$$80,000)=0\mathrm{.}1,$ P$($$$100,000)=0\mathrm{.}2,$ and P$($$$120,000)=0\mathrm{.}2.$

a$.$ Do you recommend your friend to sell the shop? Apply expected value approach.

Hint: Since there are four different scenarios for the future profitability, you can consider there are four

different states of nature.

b$.$ Now, your friend considers hiring Geneseo Advisor, a local research & consulting firm, to get some

information on future local business conditions. The forecast information may indicate either O $($which

means good condition$)$ or X $($which means bad condition$).$ Suppose that conditional probabilities of the

forecast indicators that are conditional on Sweetilicious$$ expected profitability are given as follows:

P$($O $|$ $$60,000)=0\mathrm{.}1$; P$($O $|$ $$80,000)=0\mathrm{.}2$; P$($O $|$ $$100,000)=0\mathrm{.}3$; P$($O $|$ $$120,000)=0\mathrm{.}4.$

If the consulting service costs $$1,200,$ do you recommend your friend to hire Geneseo Advisor? Why or

why not? Include a decision tree in your answer to visualize this decision$-$making problem.

Hint: Explain your answer by computing EVSI $($expected value of sample information$).$ You may also

need to compute branch probabilities. The use of a tabular approach will help you.

c$.$ As studied in class, using a graph, provide the Risk Profile for the case of O$,$ good local business

condition. Be sure to label probabilities and expected values.

How to solve?

Apply you did in Question #$3$ here. Note that there are four states of nature, which can be denoted as s$1,$

s$2,$ s$3,$ and s$4.$

Then, the payoff table will look like as follows:

s$1$ S$2$ S$3$ S$4$

Sell $$8,000$ $$8,000$ $$8,000$ $$8,000$

Do not sell $$6,000$ $$8,000$ $$100,000$ $$120,000$

If you apply the Bayes$$ Theorem, you will have P$($O$)=0\mathrm{.}21$ and P$($X$)=0\mathrm{.}79.$ Using these probabilties,

you can find P$($s$1|$O$),$ P$($s$2|$O$),$ P$($s$3|$O$),$ P$($s$4|$O$).$ P$($s$1|$X$),$ P$($s$2|$X$),$ P$($s$3|$X$),$ and P$($s$4|$X$).$