Economics > QUESTIONS & ANSWERS > Harvard University - ECONOMICS 1051Problem Set 7 Solutions (All)

Harvard University - ECONOMICS 1051Problem Set 7 Solutions

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Problem Set 7 Attila Ambrus, Economics 1051 Spring 2011 Due date: April 5 1. A hold-up problem. [this question introduces you to an important kind of problem in sequential strategic settings] Suppose that Amtrak is choosing whether or not to build a new high-speed railroad on the East coast. Building the railroad will involve an initial up-front sunk cost k. To keep the accounting simple assume that the railway, if built, will run for exactly one year, and that it will generate (new) revenues of 130,000,000. Operating the railroad for that year would cost $10,000,00 in fuel, plus some labor costs. The labor costs depend on the wage. The railroad would need to employ 1000 workers all of whom would be unionized. The current going wage for union rail labor on the East coast is $50,000. That is, without the new railroad, these workers would earn $50,000. a) Very briefly define what is meant by sunk cost, and what is meant by the ‘sunk cost fallacy’. [Go look it up if you do not know] b) Assuming that the labor can be hired at this going wage, for what values of k should Amtrak build the new railroad? (Assume that Amtrak aims to maximize profits without discounting) c) Suppose that, if the railroad is built, after it is built the rail union can make a ‘take it or leave it’ wage demand w to Amtrak to apply just for labor on the new line. The railroad’s only choice is to accept to pay the wage demand w, or close the new line down. What demand will the union make? Given this, if you were Amtrak, for what values of k would you build the new line? Why is your answer different from that in part b? d) What wage demands and wage offers will be presented to the arbitrator after the railroad is built? Given this, if you were Amtrak, for what values of k would you build the new line? Why is your answer different from that in parts b and c? 2. An inspection game. This example combines mixed strategies in two-player, zero-sum games with the use of Zermelo’s algorithm. An environmental protection agency knows that a firm is determined to discharge a pollutant into a river on one of 3 days. The agency will learn immediately when the river is polluted because of the telephone complaints it will receive from local residents. However, to obtain a conviction, the agency has to catch the firm red-handed. This means that it must try and guess in advance the day on which the firm will pollute the river so as to have an inspector on the spot. Unfortunately, the agency’s resources are so overstretched that it can only afford to dispatch an inspector to the side on one of the 3 days, and the firm knows this.

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