UNIVERSITY OF CALIFORNIA HAAS SCHOOL OF BUSINESS MBA 201A—Economic Analysis for Business Decisions Fall 2009 Professor Catherine Wolfram Problem Set #1 Doing these problems is optional. The solutions to these questions will be posted on Thursday, September 3rd and discussed in section the next day. The educational value of these exercises will be maximized if you attempt to answer these questions before you look at the answers. Sometimes students find a question in these problem sets frustrating. Since these are not graded, you are free to stop working on a problem whenever you feel the gain from further effort is not worth the cost of further frustration and time. What is important is that you have thought seriously about the problems, not that you have necessarily gotten the correct answer to every one of them. Question 1 Imagine that you work for the World Bank, a development bank that provides loans and policy advice to governments around the world. The World Bank is trying to encourage the Russian government to privatize an industry, and you have been asked to help the Bank determine the market price and quantity that would prevail in the Russian market if competitive forces were allowed to equilibrate the market. The best estimates of the market demand and supply for the Russian good (in U.S. dollar equivalent prices) are given by QD = 10- 2P and Qs = 2 + 2P, respectively. Both QD and Qs are measured in billions of units of the good. (a) Determine the competitive equilibrium price and quantity. The competitive equilibrium is determined by the intersection of the market demand and supply curves. Algebraically, this simply means that QD = QS. Equating demand and supply in this case yields: 10 – 2P = 2 + 2P 8 = 4P P* = 2 Plugging this P back into either the supply or the demand curve yields Q* = 6. (b) Based on your analysis, a Russian minister raises the concern that the free market price might be too high for the typical Russian citizen to pay.MBA 201a Fall 2009—Prof. Wolfram Page 2 Accordingly, he asks you to explain what would happen if the Russian government privatized the market, but then set a ceiling price at the Russian equivalent of $1.50. How do you answer? Since the price ceiling is below the equilibrium price of $2, a shortage will result. Specifically, when the price ceiling is set at $1.50, quantity demanded is: QD = 10 – 2(1.50) = 7 and quantity supplied is: QS = 2 + 2(1.50) = 5 Question 2 Rex Maxprof is trying to decide whether to attempt a certain hostile takeover. One of his advisors, Bobby Surefire thinks that Maxprof Industries should attempt the takeover of Minprof Associates. If successful, the takeover would increase the net value of Maxprof Industries by $1 million. If the attempt failed, the net value Maxprof industries would decline by $200,000. Surefire says that the probability of success is 0.5. Maxprof's other advisor, Rick Steady, says that a new defense against takeovers makes the probability of successfully taking over Minprof Associates only 0.1. Surefire disagrees, saying that this defense is not legal. Rex trusts each of his advisors equally and has no other information, so he thinks that they are equally likely to be correct about the legality of this defense (i.e., a .5 probability that each is correct). There is currently a lawsuit underway in another takeover attempt that will determine whether the new takeover defense is legal. Rex could either pursue the takeover now or wait until the lawsuit is decided. If he waits, however, a successful takeover will be worth only $900,000 since Minprof will have squandered more assets in the mean time, while a failed attempt will still cost $200,000. (a) Draw the decision tree that Rex faces. See Figure 1. (b) If Surefire is right and Rex proceeds with the takeover now, what is the expected value of the attempt?MBA 201a Fall 2009—Prof. Wolfram Page 3 If Surefire is right and the takeover defense is illegal, then the probability of success is 0.5, and the expected profits from proceeding with the takeover now are: 0.5x$1,000,000 + 0.5x-$200,000 = $400,000 (c) If Steady is right and Rex proceeds with the takeover now, what is the expected value of the attempt? If Steady is right and the takeover defense is legal, then the probability of success is 0.1, and the expected profits from proceeding with the takeover now are: 0.1x$1,000,000 + 0.9x-$200,000 = -$80,000 (d) If Rex proceeds with the takeover now, what is the expected value of the attempt? Rex believes that the outcomes in (b) and (c) are equally likely, so the expected value of proceeding with the takeover now is 0.5x$400,000 + 0.5x-$80,000= $160,000. If there were no other information that Rex could obtain before making the decision (and if he were not too risk averse), then Rex would want to proceed with the takeover now. However, Rex can get more information by waiting to see how the ongoing lawsuit is decided. (e) If Rex waits and the current lawsuit shows that Surefire is right, what is the expected value of the attempt after the lawsuit is decided? If after the legal decision Rex knows that Surefire is right, then he knows that the probability of success is 0.5. The expected value of attempting the takeover is 0.5x$900,000 + 0.5x-$200,000 = $350,000. (f) If Rex waits and the current lawsuit shows that Steady is right, what is the expected value of the attempt after the lawsuit is decided? If after the legal decision Rex knows that Steady is right, then he knows that the probability of success is 0.1. The expected value of attempting the takeover is 0.1x$900,000 + 0.9x-$200,000 = -$90,000. In that case, Rex would not attempt the takeover at all, which has an expected value of zero. (g) What should Rex do? If Rex waits, there is a 0.5 probability that he will get the outcome in (e) and a 0.5 probability that he will get the outcome in (f). The expectedMBA 201a Fall 2009—Prof. Wolfram Page 4 value is then 0.5x$350,000 + 0.5x0= $175,000. This is greater than the value in (d). Rex should wait to see how the lawsuit is decided. (h) What is the value of the information that Rex would learn by waiting until after the lawsuit to decide on whether to attempt the takeover? The value of the information is $15,000, the difference between Rex’s expected value of making his choice with the information and his expected value without the information.