1. (40%) Bubba Wildcat has the opportunity to buy a tract of land under which he believes there is oil with 0.40 probability and natural gas with .60 probability. After buying the land he can choose to make a test drill for $10,000 to gather more information. A "positive" result indicates there is oil. The false positive rate is 20%, and the false negative rate is 10%. The expected cost of full-scale drilling is $100,000 regardless of whether there is oil or gas or whether he made a test drill or not. If oil is discovered, Bubba will receive an expected income of $150,000 above the cost of the land. If natural gas is discovered, then Bubba will receive an expected income of $50,000 above the cost of the land.Assume Bubba is risk neutral.
Draw a decision tree, and solve for an optimal decision plan for Bubba. Show your calculations! 2. (25%) Jason is indifferent between $10 for sure and a lottery that pays $100 with probability 0.09 and $0 with probability 0.91. He is also indifferent between $70 for sure and a lottery that pays $100 with probability 0.80 and $0 with probability 0.20. Jason is given a choice between lottery A or B:
Y = {$100, $70, $10, $0}
pA = (0.10, 0.20, 0.70, 0 )
pB = ( 0, 0.40, 0.50, 0.10)
If Jason's preferences are complete, transitive, continuous and monotone, and satisfy the substitution axiom,
(a) will he prefer lottery A or B? Show your work.
(b) Is Jason risk averse, risk neutral, or risk loving?
3. (15%) Briefly define the following terms:
a) an information set;
b) perfect recall;
c) a lottery (use math)
4. (15%) Irene has committed to meeting a friend at an out of town restaurant tonight. However, she thinks there is a 20% chance her car battery is bad, and if it is bad, she believes she has a 75% chance of being stranded tonight. On the other hand, if the battery is good, then there is no chance she will be stranded tonight. A local service station offers a battery testing service for $10. Their brochure states that 99% of good batteries pass the test, while 90% of bad batteries fail the test.
(a) If Irene has her battery tested, what is the probability it will pass the test?
(b) If Irene has her battery tested and it passes, what is the probability her battery is good?
(c) If Irene has her battery tested and