Examples and exercises on Pareto efficiency and competitive equilibrium
An economy contains 4 people, X, Y, A, and B. X and Y each have one unit of an indivisible good, and no money. The values they attach to the units of the good that they hold are $0 for X and $3 for Y. A and B each have $5 in money and no units of the good. The values they attach to one unit of the good are $5 for A
and $2 for B. No person has any value for a second unit of the good. After the units of the good and the money are reallocated through trade, the payoff of a person with one unit of the good and $m in money is her value for the good plus m.
For each of the following sets of trades, find the allocation of the units of the good and money that results and the resulting payoffs to each person, and determine whether or not the allocation is Pareto efficient.
(a) X sells her unit to A for $2 (and Y keeps her unit).
(b) X sells her unit to B for $2, Y sells her unit to A for $3.
Copyright © 1997 by Martin J. Osborne