Question

1.    John Smith, owner of Happy Acres Farm produced young seedless grapes which can be used for raisins or making wine. The bulk of Smith’s crop is contracted at the beginning of season so John must decide how to allocate his acreage. Weather conditions after the decision is made are crucial and difficult to predict. Raisins are sun-dried in the open an drain during this time can inflict heavy losses. If John decides to product grapes for wine, rain doesn’t do as much damage.

John is considering three courses of action: 1) allocate all of his acreage to raisins; 2) allocate all of the crop to wind; 3) allocate approximately half to raisins and half to wine.

The rainfall possibilities are described as none at all, light rain or heavy rain. John has access to weather reports of the previous 20 years and estimates probabilities as follows: no rain; 0.50; light rain, 0.30; and heavy rain, 0.20.

John has constructed the table below to illustrate his anticipated payoffs per acre.

	No rain	Light rain	Heavy rain
Allocate all to raisins	60	50	-20
Allocate all to wine	15	30	30
Half to raisins, half to wine	50	40	10

a. Calculate the expected value for each alternative.

b. Make a recommendation based on expected values

c. Calculate the EVwith PI and EVofPI

d. Write an interpretation of the EVofPI

Answer 1

(a) Here the given information is

Pr(No rain) = 0.50
Pr(Light Rain) = 0.30

Pr(Heavy rain) = 0.20

(a) Now, we have to find the expected value for each alternative

Alternative 1 : Allocate all to raisins

Expected value =

=60 * 0.50 + 50 * 0.3 + (-20) * 0.2 = 41

Alternative 2 : Allocate all to wine

Expected value =

=15 * 0.50 + 30 * 0.3 + (30) * 0.2 = 22.5

Alternative 3 : Allocate half to raisins and half to wine

Expected value =

=50 * 0.50 + 40 * 0.3 + 10 * 0.2 = 39

(b) Here as we can see that the highest payoff is for the alternative 1 : Allocate all to raisings

so we will go for alternative 1.

(c) Now we have to find EV with PI

so now we can see that if we have perfect information of weather we will do things according to weather and choose suitable alternative. Like if its no rain we will go for  all to raisin, when there is light rain we will go for all raising and when there is heavy rain we will go for all allocated to wine.

so for perfect alternative expected value = 60 * 0.50 + 50 * 0.30 + 30 * 0.20 = 51

EVwith PI = 51

so here as we don't have the perfect information we will go for alternative 1 which will give us expected payoff = 41

so EV of PI = 51 - 41 = 10

(d) Here the interpretation of the EV of PI is as that if we are provided the perfect information we are willing to spend an MAXIMUM amount of 10 to get that perfect information. Here word maximum is important as if we are getting this information in less or equa to 10 than we will persue to get this information.