Question

$1M is available to invest in S or B. The percentage yield on each investment depends on whether the econ has a good or bad year.

Econ has a Good year    Econ has a Bad year

Yield on S    22% of 1M 10% of 1M

   (i.e. $220,000)    ($100,000)

Yield on B 16% of 1M 14% of 1M

($160,000) ($140,000)

It is equally likely (50%) that the econ will have a good or bad year.

For $10,000, a firm can be hired to forecast the state of the econ. The firm's forecasts have the following probabilities:

p(Good forecast | Econ is good) = .8

p(GF | EIB) = .2

It is equally likely (50%) for EIG & EIB to occur

a) Calculate the following:

p(EIG | GF) =

p(EIB | GF) =

p(EIG | BF) =

p( EIB | BF) =

b) Draw a decision tree to determine to invest in S or B to maximize expected profits. Should the firm be hired?

c) What are the values of the EVSI and EVPI?

Answer 1

a) We know the accompanying probabilities

Let EIG be the occasion that the economy is great and EIB be the occasion that the economy is awful.

P(EIG) =0.50

P(EIB)=0.50

Let GF be the occasion that the firm conjectures that the economy is great, and BF be the occasion that the firm estimates that the economy is awful.

We know the accompanying restrictive probabilities

The peripheral likelihood of getting a decent conjecture is

The peripheral likelihood of getting a terrible estimate is

P(BF) = 1-P(GF) = 1-0.50=0.50

Presently we get the probabilities that we need

b)

Moving from the directly to one side, we have

Chance hub 6: Hire the firm, disregard the expense to procure for the time being and put resources into S if great figure

The normal esteem is

Chance hub 7: Hire the firm, disregard the expense to procure for the time being and put resources into B if great gauge

The normal esteem is

Chance hub 8: Hire the firm, overlook the expense to contract for the time being and put resources into S if terrible figure

The normal esteem is

Chance hub 9: Hire the firm, disregard the expense to enlist for the time being and put resources into B if terrible gauge

The normal esteem is

Chance hub 10: Do not Hire the firm, and put resources into S

The normal esteem is

Chance hub 11: Do not Hire the firm, put resources into B

The normal esteem is

Choice hub 3: Hire the firm, get a decent conjecture.

We need to choose putting resources into S (expected value=$196,000) versus put resources into B (Expected esteem = $156,000).

the benefit amplifying choice is to put resources into S.

The normal estimation of hub 3 is

EV(3) = $196,000

Choice hub 4: Hire the firm, get an awful figure.

We need to settle on putting resources into S (expected value=$124,000) versus put resources into B (Expected esteem = $144,000).

the benefit boosting choice is to put resources into B.

The normal estimation of hub 4 is

EV(4) = $144,000

Choice hub 5: Do not Hire the firm

We need to choose putting resources into S (expected value=$160,000) versus put resources into B (Expected esteem = $150,000).

the benefit amplifying choice is to put resources into S.

The normal estimation of hub 5 is

EV(5) = $160,000

Chance hub 2: Hire a firm, disregard the expense to procure for the time being

The normal incentive for this hub is

At long last at hub 1, we have 2 alternatives

Contract the firm at a normal estimation of $170,000, however burn through $10,000 employ the firm and consequently the net expected benefit of enlisting the firm is $160,000

Try not to contract and make a normal estimation of $160,000

Since procuring a firm at $10,000 and not employing a firm yield the equivalent anticipate esteem, we ought to be impassive between the 2 choices.

That means it doesn't make a difference, on the off chance that we enlist (at $10,000) or not enlist the firm. It bodes well to enlist the firm in the event that it charges are under $10,000

c) From part b, the normal esteem when the firm is enlisted is $170,000

This is the normal incentive with test data

EVwSI = $170,000

The normal esteem when we don't enlist is the normal incentive without test data

EVwoSI=$160,000

the normal estimation of test data is

EVSI = EVsSI - ECwoSI = $170000-$160000 = $10,000

The result table that we have is

In the event that we know the condition of nature, as Econ has a Good year, at that point we realize that we would put resources into S for a result of $220,000

On the off chance that we know the condition of nature, as Econ has an awful year, at that point we realize that we would put resources into B for a result of $140,000

That means on the off chance that we have the ideal data about the economy, at that point we would put resources into S when the economy is great and put resources into B when the economy is awful.

the normal incentive with impeccable data is

The normal incentive without the ideal data is the normal esteem when we don't contract.

EVwoPI = $160,000

The normal estimation of Perfect Information is

EVPI = EVwPI - EVwoPI = $180,000-$160,000=$20,000