Consider a competitive exchange economy with two agents(1&2)and two goods(X&Y). Agent 1's endowment of (X,Y) is (100,100)& agent 2's endowment of (X,Y) is (50,0).An allocation of agent i is denoted by (xi,yi)where xi is his allocation of X & yi is his allocation of Y.Agent1's objective is to choose(x1,y1) to maximise his utility min{x1,y1}.Agent2's objective is to choose (x2,y2)to maximise his utility x2+y2. An example of a competitive equilibrium allocation is

Question

Consider a competitive exchange economy with two agents(1&2)and two goods(X&Y). Agent 1's endowment of (X,Y) is (100,100)& agent 2's endowment of (X,Y) is (50,0).An allocation of agent i is denoted by (xi,yi)where xi is his allocation of X & yi is his allocation of Y.Agent1's objective is to choose(x1,y1) to maximise his utility min{x1,y1}.Agent2's objective is to choose (x2,y2)to maximise his utility x2+y2.                                An example of a competitive equilibrium allocation is 
a)(x1,y1)= (100,50) and (x2,y2)= (50,50).
 (b)(x1,y1)=(125,100)& (x2,y2)=(25,0).(c)(x1,y1)=(50,50)&(x2,y2)=(100,50). (d)(x1,y1)=(100,100)& (x2,y2)=(50,0). 
An example of Pareto efficient allocation is
(a) (x1,y1)=(50,50)& (x2,y2)=(100,50).
(b) (x1,y1)=(125,100)& (x2,y2)=(25,0).
(c) (x1,y1)=(125,75)& (x2,y2)=(25,25).
(d) (x1,y1)=(50,100)& (x2,y2)=(100,0).
An example of a pair of competitive equilibrium prices (p1,p2) is
(a) (1,0)
(b) (0,1)
(c) (1/3,2/3)
(d) (2/3,1/3).

economyst · Answer

Take a shot, what do you think? Hint: As I understand, the initial endowments of persons 1 and 2 are both utility maximizing. For person 1, he will maximize when x1=y1. For person 2, he is indifferent between getting an extra x2 or a y2. Hint 2: On question 2, I don't believe any of the possible answers are pareto efficient.