2. A Hold-Up Problem. (35 points) [This question introduces you to an important kind of problem in sequential strategic settings.] Suppose that the High Speed Rail consortium (HSR) is deciding whether or not to build a high-speed railway between Melbourne and Sydney. Building the railway 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 revenues of $130, 000, 000. Operating the railroad for that year would cost $10, 000, 000 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 is $50, 000. That is, without the new railway, these workers would earn $50, 000. (a) (5 points) Very briefly define what is meant by a sunk cost, and what is meant by the 'sunk-cost fallacy'. [Go look it up if you do not know.] (b) (10 points) Assuming that the labor can be hired at this going wage, for what values of k should HSR build the new railroad? (Assume that HSR aims to maximize profits without discounting). (c) (10 points) Suppose that, if the railway is built, after it is built the rail union can make a 'take-it-or-leave-it' wage demand w to HSR to apply just for labor on the new line. The railway'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 HSR, for what values of & would you build the new line? Why is your answer different from that in part (b)? Now suppose that the wage demand made after the railway is built is not a 'take-it-or-leave-it' demand but rather part of negotiation. Suppose that, fearing strikes in the transport sector, the government has instituted compul- sory arbitration in wage disputes. The arbitrator always follows a two-step approach. First, she disqualifies any wage offers lower than the current go- ing wage (that is, such that employees would rather walk away than accept the offer), and also any wage demand that would cause the employer to shut 2 down (that is, such that the employee would rather walk away than accept the demand). Provided the offers and demands survive this test, she then "splits the difference". (d) (10 points) What wage demands and wage offers will be presented to the arbitrator after the railway is built. Given this, if you were HSR, for what values of k would you build the new line? Why is your answer different from that in parts (b) and (c)