Strategic Behaviour in Business and Economics

Homework 2: The Value of Information
1. I am considering working during the Easter break, but I am not quite sure which is the b est choice. My salary dep ends on the prot of the hotel I chose to work for and this dep ends on the weather conditions. Usually it rains (with probability 0.7), in which case going to the mountains might b e a go o d choice (my salary will b e 100), but if the weather is sunny I will not enjoy the mountains so much (my salary is 30). If contrary to the tradition the weather is sunny and hot (with probability 0.3), the b est choice will b e the b each (salary 120), but sp ending my holiday on the b each when it is raining is horrible (salary 20).
(a) Represent the problem and solve it.
(b) How much am I willing to pay to a witch, if she is able to predict the weather? (c) How much am I willing to pay for a weather forecast, if when it is raining, the prediction is correct in 80% of the cases, but when it is sunny, they predict rain in 10% of the cases?
2. A Spanish company (
Fiesta
) is considering the p ossibility of creating a new chain of sup ermarkets selling organic fo o d. If the sup ermarkets are well accepted by the customers (which might happ ened with probability
0.5) the b enet will b e 10 000 000 Euros, but in the opp osite case this will cause a loss of 2 millions. There exists also another option: renting the shops and receiving a certain prot of 5 000 000Euros.
(a) Draw the decision tree corresp onding to this problem. What is the b est choice for
Fiesta
? Assume that
Fiesta
is risk neutral.
(b) There exist also the option of p erforming a study analyzing the tastes of the customers, which is costly. If customers have p ositive opinion ab out such typ e of shops and they are willing to buy, the study will indicate that this is the case in 80 % of the cases. But if they dislike the idea, the study is not so precise and indicates this negative opinion in only 60% of the cases. What is the highest p ossible amount of money that
Fiesta
is willing to pay for such study?