Suppose that there are n college students and n available dorm rooms. For simplicity assume that each room is a single (no roommates). Consider the following procedure for assigning students to dorm rooms: first a lottery is drawn assigning each student a number between 1 and n; each number is drawn only once so that each student has a unique number. The student who drew #1 is given the opportunity to choose any room she likes the most first. Once #1 makes her choice, the student with #2 is asked next to make her selection from the remaining n-1 rooms. Once #2 makes her choice, it is then #3's turn to choose one of the remaining n- 2 rooms, etc. The procedure ends with the last student # n being forced to accept the only available room left. Prove that any allocation of rooms obtained with this algorithm is Pareto Efficient as long as preferences are always strict (ie. if no student is ever indifferent between two dorm rooms).

Suppose that there are n college students and n available dorm rooms. For simplicity assume that each room is a single (no roommates). Consider the following procedure for assigning students to dorm rooms: first a lottery is drawn assigning each student a number between 1 and n; each number is drawn only once so that each student has a unique number. The student who drew #1 is given the opportunity to choose any room she likes the most first. Once #1 makes her choice, the student with #2 is asked next to make her selection from the remaining n-1 rooms. Once #2 makes her choice, it is then #3's turn to choose one of the remaining n- 2 rooms, etc. The procedure ends with the last student # n being forced to accept the only available room left. Prove that any allocation of rooms obtained with this algorithm is Pareto Efficient as long as preferences are always strict (ie. if no student is ever indifferent between two dorm rooms).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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