5. This problem revisits the notion of individual rationality in public endowment problems with priorities, when not all individuals are acceptable to all objects. Suppose that 5 public houses (objects) must be allocated among a group of 5 families (individuals), and imagine that the following tables describe rankings and priorities, where f denotes a generic family, and h a generic house: Pr, Pr, PL, Pf, Remember that objects not listed on rankings, or individuals not listed on priorities, are considered unacceptable. One way to interpret these tables is to imagine that they capture, implicitly, some heterogeneity among the different houses (e.g., number of rooms) and families (e.g., number of members in a household.) Consider the following alternative definition of individual rationality (IR), termed "IR for all:" Denition 1. An assignment it is IR for all if either l-lar = Q0?" l-err Qfor every f and either I-lh = 25 0?\" phrtthfo'r every h, where n denotes the priority of house 11. In words, "IR for all" requires that no individual and object receives an assignment that is unacceptable. a. Is "IR for all" stronger or weaker than IR? i.e., must an assignment that is IR also be "IR for all" or the other way around? Why? b. Does Serial Dictatorship (SD) satisfy "IR for all"? i.e., does SD produce an assignment that is "IR for all" for every order of individuals? Why