Trains run daily in most major cities, and they can earn signicant prots due totrafc congestion and steady demand fortransportation. Suppose that the daily prots from local trains in a majorcity are $65,000. For the trains to operate, however, the union of railworkers has to agree on a contract with the managers of the city train system. The u nion is obligated to maximize its workers' earnings, whi Ie the managers have a duty to reinvest as much as possible into maintaining and upgrading the trains. Suppose that the union operates on a yearly contract that must be renegotiated. The negotiation proceeds as follows: The management makes an offer to the union on how to divide the prots. The union can accept the offer or reject it and make a counteroffer, but doing so takes one day of deliberation; so. if the offer is rejected, the trains do not run for a day and no prots are earned.Assume that the rstoffer is made before the rst day of the year, so if it is accepted, there are 364 days of prots {also assuming the trains run every day except Christmas]. Each day the two sides fail to come to an agreement is a day of lost protfor all. How will the prots be divided? Part 1 (0.4 point) 0 See Hint This game can be solved through the Rubinstein bargaining framework, which suggests that you lookforward to the very end of negotiations and then work back to the beginning. 50, imagine that a hardnosed union leader led a major strike and a stubborn management team refused to give in, resulting in trains not running for 363 days. Now the union can make one nal offer for the last day of the year. Rationally speaking, management should accept any amount greater than zero, so the offer from the union can provide just under $ for the union and the rest for management from the last day's prot. Part 2 (0.7 point) 0 See Hint Working backward, now consider management's offer for day 363. Management can predict what the union will offer for the last day, so on day 363 management can offer $ to the union, which isjust a bit higher than what itwould get on the last day, leaving $ for management. (Remember that there are now 2 days worth of prots in play.) Part 3 (1.5 points) 0 See Hint Continuing to work backward, now consider the third-to-last day. It is the union's turn to make an offer, and it can rationally expect that an offer ofalmost $ for itself and just over $ for managementwould be accepted. Similarly, on the fourth-to-last day, we should expect management to offer exactly $ for themselves and $ for the union. Part 4 (0.7 point) 0 See Hint Now, let's skip quite a few days and assume that the same pattern holds all the way back to the beginning ofthe year. What should management offer on the very rst day? (Remember that there are 364 days of prots available.) $ for management and $ for the union Part 5 (0.4 point) 0 See Hint Now consider what would happen ifthe union has an outside option: suppose that rail workers in the union can do temporary work if the trains are not running and earn a total of $19,500 per day. Following the same logic as before and assumingthat both parties are completely rational, what share of prots will the union now get? % Part 6 (0.4 point) 0 See Hint Lastly, suppose that managementnds replacement workers who will run the trains (although much less efciently} ifthe union is not under contract. When the trains are run by replacement workers, management earns a daily prot of $26,000. Assuming that the union still has its outside work option, what will be the union's share of prots after negotiations? %