Consider the following school choice problem with five students 1, 2, 3, 4, 5 and five schools a, b, c, d, and e with each school having exactly one...

Consider the following school choice problem with five students

1, 2, 3, 4, 5 and five schools a, b, c, d, and e with each school having exactly one seat. The

preferences of the students are as follows from left to right in decreasing order of preference.

1 : e;b;a;c;d

2 : b;a;c;d;e

3 : a;b;c;d;e

4 : a;b;c;d;e

5 : d;b;c;a;e

The priorities of the schools are as follows from left to right in decreasing order of

priority.

a : 2;4;3;5;1

b : 3;2;4;5;1

c : 3;2;4;5;1

d : 5;2;4;3;1

e : 1;2;3;4;5

Find the outcome matching of the student proposing deferred acceptance algorithm and

explain how you found the matching. Prove or disprove that the resultant matching is Pareto

optimal for the students.