Q1. (33 points)
Miles is considering buying a new pickup truck for his lawn service firm.
The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck
The smaller truck would have better fuel economy, but would sacrifice capacity and some durability.
A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices,
and a 50% chance that gas prices will stay roughly unchanged.
The table below indicates the revenue that Miles can make based on which pickup truck he buys in each of the different states of nature.
States of Nature
Lower gas prices Gas prices unchanged Higher gas prices
Probability 0.3 0.5 0.2
Subcompact 16,000 21,000 23,000
Compact 15,000 20,000 22,000
Full size 18,000 19,000 6,000
a. Based on the Maximin principle what decision should Miles make? (7 points)
b. Based on the Maximax principle what decision should Miles make? (7 points)
c. Based on the EMV principle what decision should Miles make? (8 points)
d. What should Miles be willing to pay for perfect information about which state of nature will prevail? (8 points)
Q2. (33 points)
Spencer Industries has to choose among a series of new invesment options.
The net present value of future stream of returns, the capital requirements, and the available capital funds over the next three years are summarized as follows.
Investment 1 2 3 4 5 6 Funds Available
Net Present Value $4,000 $6,000 $10,500 $4,000 $8,000 $3,000
Year 1 $3,000 $2,500 $6,000 $2,000 $5,000 $1,000 $10,500
Year 2 $1,000 $3,500 $4,000 $1,500 $1,000 $500 $7,000
Year 3 $4,000 $35,000 $5,000 $1,800 $4,000 $900 $8,750
b. For a lottery having a payoff of 300,000 with a probability p and $50 with a probability of (1-p), two decision makers expressed the following indifference probabilities.
Find the most preferred decision for each decision maker using the expected utility approach.
Is there a difference in the decision of the two decision makers. If yes, what can you say about the two decision makers.
Indifference Probability (p)
Decision Maker A Decision Maker B
100,000 0.7 0.6
75,000 0.5 0.2
50,000 0.3 0.15