exchange questions urgency

[ritu]

hi amit sir
can u pls discuss on this post the exchange questions involving lexicographic preferences like the one which came in 2010??????
or if anyone else knows how to solve such questions then pls share ur approach....


also i have problem in folllowing questions of dse 2010
55,56,57,60

thanx a lot

[ritu]

if smbdy knos it pls reply...

[anon_econ]

hi ritu. for q31 of 2010 note that the first person wud buy only x. let py=1. then his income is 1 and demand for x is 1/px. the second person wud demand whichever good is cheaper and his income is 2p1. now v can see that p1 can't be less than 1 bcoz then nobody would demand y. for p1>1 demand for x would b 1/p1 but that can't be equal to 2 (the total endowment). now try for p1=1. u can see that the allocations in part d would be demanded by the 2 people..

On Wed, Jun 20, 2012 at 1:49 PM, ritu [via Discussion forum] <[hidden email]> wrote:

if smbdy knos it pls reply...

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[Amit Goyal]

Hi Ritu,

Lets do this problem step by step:

Step 1: Let price of Y, p(y) = 1.
Step 2.1: For p(x) > 0, p(y) = 1, and income of individual 1 as m(1) solve for the demand of agent 1?
Step 2.2: For p(x) > 0, p(y) = 1, and income of individual 2 as m(2) solve for the demand of agent 2?
Do steps 2.1. and 2.2, I will tell you the rest after you are done with these.

[ritu]

sir,
for 2.1 since endowmwnt of agent 1 is (0,1) at (px,1),
m(1)=1
so dd for x is 1/px
for 2.2,agent 2 has endowment (2,0) so at (px,1)
m(2)=2px
his dd depends on actual price ratio ...
*if px/1>1,he chooses (0,m/py)=(0,2px)
*ifpx/1<1 he chooses (2px/px,0)=(2,0)
*if px/1=1 he can choose any point on budget line

[Amit Goyal]

Ok Good. So, this is what you wrote:
Step 2.1: For p(x) > 0, p(y) = 1, and income of individual 1 as m(1) solve for the demand of agent 1?
Demand for X: m(1)/p(x)
Demand for Y: 0

Step 2.2: For p(x) > 0, p(y) = 1, and income of individual 2 as m(2) solve for the demand of agent 2?
Demand for (X, Y):
(m(2)/p(x), 0) for p(x) < 1
Budget line for p(x) = 1
(0, m(2)) for p(x) > 1

Given, endowment of 1 is (0, 1)
and endowment of 2 is (2, 0)
m(1) = 1
m(2) = 2p(x)

Substituting them above, we get:

Demand for (X, Y) by 1:
(1/p(x), 0)

Demand for (X, Y) by 2:
(2, 0) for p(x) < 1
Budget line for p(x) = 1
(0, 2p(x)) for p(x) > 1

Now step 3: Find p(x) such that sum of demands for X is equal to 2.

[ritu]

market wud clear for px/py =1
*if px/py<1 then (say 0.5) 1 demands 2,1 demands 2,,,,but 4 units arent available
*is px/py>1 then (say 2) 1 demands 0.5 units of x nd  2 doesnt dd it at all...mkt 1 doesnt clear...
so px/py=1 for equlibrium.....

[Amit Goyal]

Good.

[deepika]

why is that demand for lexcographical preference x over y
x= m/px
y=0;

the question mentions if x is the same then consumer would prefer the one with more y..
would this not result in change in demand function?
Pls let me know.