Dse 2006 Micro quest

[SoniaKapoor]

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[Arushi :))]

For ques - 23.

[Arushi :))]

incomes of both the agents are: m1=5xp2 ( bcoz he has only 5 units of y)
m2= 10xp1 ( he has only 10 units for x)
since both of them have min preference we know that they are going to consume equal amounts of x & y.
agent 1 will consume . x1=y1= 5p2/p1+p2
agent 2 will want to consume. x2=y2 = 10p1/p1+P2
Now ourtask is to normalize the prices,
If we let p1=1
then considering the total demand for x gives us:
(5p2/1+p2)+(10p1/1+p2)= 10
this gives 5p2+10=10+10p2
but this is possible only at p2=0
now taking the price vector (1,0) we get taotal demands as
agent1 (0,0) and agent 2 (10,10)
but the demand for y exceeds its supply !! so this cant be an eqm...
now if we let p2=1
then demand for x takes the form
(5/1+p1)+(10p1/1+p1)= 10
we get 5+10p1=10+10p1
no value of p1 can satisfy this..
but taking the market for y ..
(5/1+p1)+(10p1/1+p1)=5
5+10p1=5+5p1
and this is true when p1=0
hence {0,1} is the competitive eqm....because price of good 1 is zero consumer 1 now consumes (5,5) & agent 2 consumes (0,0)

[Arushi :))]

for ques 21
we know now that 0,1 is the competitive eqm,
for agent 1 the budget constraint is
0x1+x2=5
this implies that , the agent 1 must consume only 5 units of y at the C.E
hence this allocation cant be C.E for sure...
so option a and d are ruled out..
for pareto efficiency...
e can compare it with some other points...
at this point
1 gets utility of 3 n 2 gets utility of 2
if we consider some other point that are not on the x=y line
such as 4,1 and 6,4
then agent 1 gets 1 n 2 gets 4
so 2 is made better off and 1 has become worse off..
similiarly taking some othr points . example on the axis.
such as 1,0 and 9,5
agent 1 gets 0 utility and 2 gets utility of 5
so we see that on moving here n there on the edgeworth box ... to any other point.... one person is  made better off n the other id made worse off.. n that is what is pareto efficiency
therefore the allocation is pareto efficient.... ans is b