The management of a rm, M, and the union representing the employees, U, are bargaining about the terms of a new contract. The crunch has come in the negotiations. The union has made it clear to management that it will go on strike unless management makes a serious and acceptable offer. Management does not want a strike and would offer the minimal amount it had to offer in order to ensure that there would not be a strike ifit knew how much that was. However, management is unsure of the minimal amount the union is willing to accept. Thus, management faces a tradeoff. The more it offers, the less likely a strike but higher the wages it will have to pay if accepted. This problem studies this dilemma. Management acts rst and makes a take-it-orleave-it wage offer of w. The union will accept if the offer if it is above its minimally acceptable level m. If the union accepts, management's payoff is 70w. (You can think of 30 as the maximum wage the rm could pay before starting to lose money.) If the union does not accept the offer and goes on strike, management's payoff is 10. Although the rm is unsure of m, it believes that m is evenly or uniformly distributed over the range from 10 to 60. If, therefore, the rm offered a wage of 30, the probability that this offer would be accepted (i.e., that the offer is at least as large as the union's minimal acceptable amount) is the probability that m is less than or equal to 30, which is (3010)/(6010)=2/5. (a) Write an expression for the rm's expected payoff if it offers w. Your nal answer should not involve m. (b) What is the rm's expected payoff if it offers w=40? (c) Determine the rm's optimal offer, i.e. the offer that maximizes its expected payoff. (You may use calculus or graph the expected payoff as a function of w and graphically determine which offer maximizes the rms payoff.) (d) What is the rm's expected payoff in equilibrium (i.e., when the rm makes its optimal offer)? (e) What is the probability that the union will go on strike in equilibrium