Consider the following two-player game: each player i has a value vi that the mechanism knows but the other player does not. each player simultaneously and independently tells the mechanism one of two actions, "keep" or "switch." if both players choose "switch," then each player receives a payoff equal to the value of the other player. otherwise, each player i receives vi as payoff. suppose the values are independently chosen at random from a finite set of values v according to some distribution, not necessarily uniform. prove that in any bayesian-nash equilibrium for this game, the highest value for which any player switches is the lowest value that could be drawn with nonzero probability from v.

Upscale hotels in the united states recently cut their prices by 20 percent in an effort to bolster dwindling occupancy rates among business travelers. a survey performed by a major research organization indicated that businesses are wary of current economic conditions and are now resorting to electronic media, such as the internet and the telephone, to transact business. assume a company's budget permits it to spend $5,000 per month on either business travel or electronic media to transact business. graphically illustrate how a 20 percent decline in the price of business travel would impact this company's budget set if the price of business travel was initially $1,000 per trip and the price of electronic media was $500 per hour. suppose that, after the price of business travel drops, the company issues a report indicating that its marginal rate of substitution between electronic media and business travel is 1. is the company allocating resources efficiently? explain.

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.

The smelting department of kiner company has the following production and cost data for november. production: beginning work in process 3,700 units that are 100% complete as to materials and 23% complete as to conversion costs; units transferred out 10,500 units; and ending work in process 8,100 units that are 100% complete as to materials and 41% complete as to conversion costs. compute the equivalent units of production for (a) materials and (b) conversion costs for the month of november. materials conversion costs total equivalent units