Analysis Questions
1. Saudi Arabia is the strongest partner in the OPEC oil cartel. The Saudis have tried to maintain the price to maximize long term profits to the cartel by keeping price low enough that demand is not squelched but high enough to satisfy other members of the cartel. Currently the price of oil is higher than ever before. Analysts believe a that when the price of oil gets too high alternative energy sources may become attractive, and the U.S. economy might wean itself from petroleum.
The problem facing the Saudi's and other members of OPEC is to determine how far the
U.S. can be pushed on oil prices before turning to other sources of energy. The problem
can be modeled as a game where OPEC chooses the price of oil and the U.S. chooses whether
to pursue other sources of power. A hypothetical payoff matrix looks like this:
| OPEC's Price per Barrel is low | OPEC's Price per Barrel is high | |
| U.S. Plans for Alternative Energy | opec profit=100, US energy cost=120 | opec profit=40, US energy cost=170 |
| U.S. Doesn't Plan for Alternative Energy | opec profit=120, US energy cost=70 | opec profit=200, US energy cost=220 |
Question. What should OPEC and the US do?
2. Switching Doors on “Let’s Make a Deal”: In 1990 a puzzle circulated among economists, statisticians and other professionals interested in recreational mathematics. It appeared in the Journal of Economic Perspectives and even in the column "Ask Marilyn" in Parade Magazine (December 2, 1990). The puzzle mimics a proposition offered to contestants on an old TV show "Let's Make a Deal".
Near the end of each show a contestant is given a choice of three doors. Behind one door lies a great prize, but booby prizes are behind the other two. After a door is chosen, but before its contents are revealed, the host opens one of the remaining doors, always revealing a booby prize. (Since there are two booby prizes, at least one of the unchosen doors covers a booby prize.) The contestant can then choose to stick with her original choice, or switch to other (unopened) door.
Question. Does staying or switching give a better chance for the wonderful prize?
3. Transporting Nuclear Waste: The importance of perspective on assessing risk comes through in many environmental problems. One example comes from the cleanup of an old uranium processing plant in Grand Junction, Colorado. Part of the cleanup entailed transporting about 3.8 million cubic yards of radioactive material 18 miles from the old Climax Uranium Company mill site to storage at the Cheney Reservoir.
Two transportation alternatives were considered. The Truck Option was to carry waste by truck on existing roadways in Grand Junction, through and along residential areas, until it reached the railroad at the edge of town. At that point the waste was to be transferred to railcars for the remainder of the distance. The Rail Option was to build a new rail spur linking the main railway to the old Climax site through low population density areas, at an additional cost of about $12 million. The benefit of building the extra rail link was, of course, the avoidance of risk to residential populations.
It was estimated that the truck option would entail about 1 serious accident for every 1.2 million miles of travel. There was so much waste to be moved that over the life of the project it would take about 350,000 truckloads. Analysts not connected with the project estimated that an accident would inflict harm within a ½ mile –1-mile radius.
Question: Using this information, figure out the probability of an accident from a truck accident, and using that estimate, make a policy recommendation. (This is a very hard question -- I don't really expect you to get the answer).
TECHNICAL QUESTIONS
1. Use the first payoff matrix in the web notes to explain why the dominant strategy in a firm's choice is to be a Stackelberg leader.
2. Two computer firms, A and B, are planning to market systems for office information management. Each can develop high-capacity or low-capacity systems. Market research shows that the resulting profit to each firm for each strategy are given by:
| B chooses high capacity | B chooses low capacity | |
| A chooses high capacity | A profit=50, B profit=40 | A profit=60, B profit=45 |
| A chooses low capacity | A profit=55, B profit=55 | A profit=15, B profit=20 |
a. If both firms make their decisions at the same time, and want low-risk strategies (so they maximize their minimum profit), what will the outcome be? Explain.
b. Suppose both firms try to maximize profit, but A has a head start and can commit first. Now what is the outcome? If B has the head start, is the outcome the same? Explain.
c. Getting a head start is costly. Consider a two-stage game in which, first, each firm decides how much money to speed up planning so it can have a head start, and then, second, announces if it will produce a high or low capacity system. Which firm will spend more? How much will it spend? Should the other firm spend anything? Explain.
3. Suppose you are offered an investment which will cost you $1000 today, but gives a definite return of $1250 in one year. You have no cash, but can borrow the $1000 at a simple interest rate of 10%, with only one payment due at the end of the year. Should you make this investment? Explain.
4. Now suppose the investment offers a return of $1250 with a probability of 0.8, and $600 with a probability of 0.2. The expected return is therefore (0.8x$1250) + (0.2x$600). Will your answer to question 3 change? Explain why or why not.