2. Consider three students $1, $2, $3 and three schools c1, C2, C3, that each can take a single student. Preferences (assumed they are truthfully reported ) are P ( s1 ) : B > C > A P(C 1 ) : 51 > $2 > 53 P ( $2 ) : BY A > C P(C2 ) : 53 7 52 7 51 P(s3 ) : C > By A P(C3) : 51 7 53 7 52 (a) Use the DA algorithm to find the student-optimal stable matching. (b) In the student-optimal stable matching the only stable matching? Is it Pareto efficient for the students, or would they like to trade seats ex post? (c) Use the TTC algorithm to find a matching that is Pareto efficient for the students. Is this match stable? (d) Are there other assignments that are Pareto efficient for the students? (e) What would happen if you ran TTC but emphasized the school priorities