A local charity has been given a grant to serve free meals to the homeless in its community, but it is worried that its program might be exploited by nearby college students, who are always on the lookout for a free meal. Assume that both a homeless person and a college student receive a payoff of 1 for a free meal. The cost of standing in line for the meal is t 2/625 for a homeless person and t 2/144 for a college student, where t is the amount of time in line measured in minutes. Assume that the staff of the charity cannot observe the true type (i.e. if an individual is a homeless person or a college student) of those coming for free meals. Assume also that the charity can set a minimum waiting time for a free lunch.

(a) Without doing any math, describe, as completely as you can, what would happen-i.e. who would wait in the line for a free lunch and who wouldn't-in a separating equilibrium to this game.

(b) Suppose the charity sets t = 10 as the minimum waiting time in the line. In other words, everyone is required to wait at least 10 minutes in the line. Will this be a good choice if the charity is willing to serve food only to the homeless people? Why, or why not?

(c) Suppose the charity sets t = 20. Will this be a good choice if the charity is willing to serve food only to the homeless people? Why, or why not?

(d) Suppose the charity sets t = 30. Will this be a good choice if the charity is willing to serve food only to the homeless people? Why, or why not?