In year a, total expected losses are 10,000,000. Individual losses in year a have a Pareto distribution with α = 2 and θ = 2,000. A reinsurer pays the excess of each individual loss over 3,000. For this, the reinsurer is paid a premium equal to 110% of expected covered losses. In year b, losses will experience 5% inflation over year a, but the frequency of losses will not change. Determine the ratio of the premium in year b to the premium in year a.

Suppose general motors demands labor according to the labor demand function 푤푤= 40−0. 5퐸퐸, where 푤푤 is the hourly wage and 퐸퐸 is the number of employees. the united auto workers union has a utility function given by 푈푈=푊푊∗퐸퐸. a. in 1984, the united auto workers union started negotiations with general motors by assuming that they were a monopoly union. find the wage and employment demands that the united auto workers union would have demanded before any bargaining began. b. if general motors and the united auto workers union both had excellent bargaining representatives, would this be the final labor contract? if not, then explain in words and graphically where they would end up after the bargaining process.