1. Consider the following assignment problem with 6 agents and objects a, b, c, d, e, f, which are all public endowments. Agents' preferences: 2 3 4 5 6 b b a C e b a a a C C C C e a) Is the assignment (e, a, f, b, d, c) Pareto efficient? (Note: assignments are indicated in the order 1, ..., 6 for the agents). b) Determine the assignment obtained by the Serial Dictatorship with agent ordering (1,2,3,4,5,6). Is this assignment Pareto efficient? c) Let house a be called house b, and vice versa for the above problem. How would the Serial Dictatorship assignment change in part b)? d) Consider the Serial Dictatorship with agent ordering (6,5,4,3,2,1). What is the assignment at the above preference profile? Which objects could agent 3 obtain by changing her preferences, if everyone else's preferences are unchanged? If agent 3 is assigned object e at this new preference profile, what would be the Serial Dictatorship assignment at the new profile