1. We assume that even if the U.S. develops alternative sources and technologies, it will displace only a limited amount of oil as long as the price of oil stays low so OPEC profit is 100, U.S. costs are 120. But if the price of oil soars, the alternative sources would meet most of our energy needs, and thus relieve our dependence on OPEC, and total energy costs rise only to 170. Since we use so little oil, OPEC profit falls to 40. If no development takes place we save the cost of new technologies. At a low price we only incur costs of 70, but OPEC makes a profit of 120. And if the price gets hight, with no alternatives, the U.S. costs increase to 220, and OPEC makes an astounding 200.
Suppose OPEC wants to maximize its minimum profit. If its sets the price at 20 its minimum profit is 100. At a high price its minimum profit is 40. Thus, its maximin strategy is to keep price low. Notice that it is not a dominant strategy. If the U.S. has no ability to develop energy alternatives, OPEC should raise the price. If, on the other hand, the U.S. wants to minimize its maximum cost of energy - a minimax strategy - it needs an alternative energy development project. Then its largest cost is 170, as opposed to 220 if the price goes high and the U.S. is unprepared. Again, it is not a dominant strategy. If OPEC keeps the price low, we are better off without an alternative energy program.
(THIS LAST PART IS NOT NEEDED FOR A STRONG ANSWER) Assuming the relative values of the payoff matrix are correct, the evidence is that OPEC follows a maximin strategy, but the U.S. is not following a minimax strategy since it has no strong alternative energy or conservation programs. Thus, we are either at the mercy of Saudi Arabia's largess, or the costs of getting hit with expensive oil without any alternatives are much less than predicted.
2. Many people are fooled by the answer, which is that switching gives a better chance for the great prize. The original choice has a 1/3 probability of being correct. Revealing a loser does nothing to that probability. However, since the host has inside information, the fact that he chooses one of the remaining doors over the other door raises the probability that the unchosen door has the great prize. There is a 2/3 chance that the great prize is behind either of the doors you did not choose. Opening a loser does nothing to change either of these odds, so switching moves you from a 1/3 chance of winning the great prize to a 2/3 chance. So you should always switch.
The choice is clearer, perhaps, if the situation is exaggerated. Imagine there are 100 doors, one of which conceals a great prize. After the contestant chooses one, the host proceeds to open 98 others. There are now two closed doors remaining – the contestant’s original choice and the one out of 99 that the host did not open. Which would you choose?
3. An expected 5.25 (probability of an accident per mile x number of trips x the length of a trip = 1/1200,000 x 350000 x 18) truck accidents were expected to occur during the project. Using the 1-mile radius, an individual dwelling along the corridor of transportation had a 5.25/18=0.2917 probability of being affected by a spill sometime during the cleanup. That’s almost a 30 percent chance. Nevertheless, policy makers looked at that figure and decided that truck accidents were too rare to justify investment in the new rail link.
TECHNICAL QUESTIONS
1. Since the game is symmetric, we can look at only one firm. Look at firm A. If B chooses to behave with Cournot conjectures, A's best choice is to be a Stackelberg leader. Then his payoff is increased. If B chooses to be a leader, A's best choice is still to try to be a leader, and get profit of 4556 instead of 0. Symmetry shows B has the same dominant strategy.
2. a. Maximin strategies: The firm determines the worst outcome for each option, then chooses the option that maximizes the worst outcome. If firm A chooses H, the worst payoff would occur if B also chooses H (with a value of 50). If firm chooses L, the worst payoff would be if B chooses L (value of 15). So A will choose H. If B chooses L, the worst payoff would occur if A chooses L (value would be 20). If B chooses H, then the worst payoff is if A chooses H (value of 40) so B chooses H also.
b. To maximize profit, and Firm A chooses first, is will choose H, because it knows that B will then choose L (since it gives L a profit of 45 rather than 40). This gives A a profit of 60. If firm A instead had chosen L first, B would choose H, and A’s profit would be 55. So, A will choose H. If firm B goes first, and it chooses H, then A would choose L, giving B a profit of 55. But if B chooses L, A would choose H, giving B a profit of 45. So B will choose H if it goes early.
c. There is an apparent advantage to the first mover. If A goes first, it gets a profit of 60 and B gets a profit of 45. But if B goes first, A gets a profit of 55 and A gets a profit of 55. So A would spend up to 5 to get to go first. B would spend up to 10 to go early.
3. I'm pushing you on this one, checking to see if you can figure out value over time. If you borrow the $1000 at simple interest, you'll need to pay back $1100 (the $1000 loan plus interest of 10%. 1000x.10=100). You get a return of $1250, so your profit would be $150. Do it!
4. Again I am pushing (checking). the costs are the same, since we had no change. Using the formula given for expected return, we have it equals $1000+$120=$1120, which appears to give a profit of $20 from the investment, at least in expected value. But you might not want to take the risk of losing $500 just for the expected return of $20, even though if you get the good outcome your profit is $150. This is called risk aversion.