2005 dse general equilibrium

[sweata]

sir, in q1 of yr 2005 its given-consider a competitive exchange economy with 2 agents(1,2) and 2 goods(x,y) agent 1s endowment is(100,100) and 2s endowment is (50,0) an allocation for agent i is denoted by (xi,yi) where xi is the allocation of X and yi is the allocation of Y.agent 1s objective is to choose (x1,y1) to max.U=min(x1,y1) agent 2s objective is to choose (x2,y2) to max. u=x2+y2.
an example of competitive equilibrium for this economy is
a. (x1,y1)=(100,50)and (x2,y2)=(50,50)
b. (x1,y1)=(125,100)and (x2,y2)=(25,0)
c. (x1,y1)=(50,50) and (x2,y2)=(100,50)
d. (x1,y1)=(100,100) and (x2,y2)=(50,0)
d ans is option d. but y is it not c??? if u could plz explain sir

[Amit Goyal]

Dear Sweata,

A simple explanation why it cannot be (c) is the following:
We know that endowment is always affordable bacause your income at given prices is the value of your endowment and hence you always have the power to buy back your endowment. Agent 1's endowment is (100, 100), i understand that (50, 50) is affordable for this agent at all prices but we must not forget that (100, 100) is also affordable and a consumer with utility function min{x, y} will not buy (50, 50) when he can buy (100, 100) as he is a utility maximizing consumer. This rules out (c).

[sweata]

Thank you sir.

[manvi ahuja]

In this case though answer is d...bt still ...c and d both are pareto efficient???is it true sir??pls reply..

[duck]

Hi Manvi.. :)

Yes, both are pareto efficient.. :)