dse 2004 .. duck pls see

[maahi]

Q4 how do we find d competitive eqm ?http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/26_jun_2004_option_a.pdf

won't it be px = py so dd becomes x= m/2px y = m / 2px  so m1= m2 = 1000 so they consume 500 , 500 . whats wrong here ??

[duck]

Hi Maahi.. :)
You've found  just one of the competitive equilibirum allocation.
There are others competitive eqm allocation.

Demand for Agent 1: x1=y1= 1000px/px+py
Demand for Agent2: x2=y2= 1000py/px+py
For market clearing: It should be the case that x1+x2=1000 and y1+y2=1000.
And you can check the market clears for all postive price ratio.
Hence, the corresponding competive equilibirum allocations would be where x1=y1 and x1∈ [0,1000].
(45 degree line constitutes the Set of Competitive equilibirum allocation)

[maahi]

thank you

http://discussion-forum.2150183.n2.nabble.com/dse-2004-td7345502.html;cid=1371563576470-610
for q 10 i did what u told but ans is nt coming can u recheck ?


30 . P (X<-1) = P BECAUSE OF SYMMETRY P (X >1) = p
p (x^2>1 intersectn Y^3 >1) = P(x^2 >1) P (Y^3> 1) =???


20 )  Y(n) = F(n)
d(w) = 1- w = s(w) =w ...>  1/2 = w

now d condition : mpl= w
so f'(n) = w = 1/2
since derivative is 1/2 and f(n) is a fn of n . f (n ) should be 1/2 n . so why is d correct ??


21>  if we are told to min then y is d ans in d max fn


19,24,25

[Sumit]

Hi Duck,
Could you plz tell the right approach to get competitive equilibrium prices in q-6????..Is it can be done by hit and try only???

My approach
Agent-1 Demand for x1=999px/px+py
Agent-2 demand for x2=1000py/px+py

Now,For competitive equilibrium, Total demand for commodity x must equal to total supply.
==>[999px/px+py]+[1000py/px+py]=999.
Now, In this case as I put px=1 & Py=0...above equality satisfy.

At this price competitive equilibrium:  x1=999 and y1 belong [999,1000].

[duck]

Q10) You must have done some calculation error.
Profits = (1-(3-4c/6)-(c/3))(3-4c/6) - c(3-4c/6) - (9c^2-13c/18)
Maximise it wrt c.

Q30) P(X<-1) = P(X>1) = p
Now, P(X^2 > 1) = P( 1<X<-1) = 2p
P(Y^3 > 1) = P(Y>1) = p   [As  X and Y are independent random variables with standard Normal Distribution]

Therefore,
P(X^2>1 & Y^3>1) = P(X^2>1) * P(Y^3>1)  [ As independent]
                                          = 2p*p  
                                          = 2(p^2)

[duck]

Hi Sumit.. :)

No Hit and trial.
Your approach is correct. You must also check whether the market for Good y clears or not.
Another way: Plot the edgeworth and check for competitive equilibrium allocations.

[Sumit]

thanks duck for prompt reply!!

[maahi]

thanks yaar pls tell d odr ques also

[maahi]

Q10) You must have done some calculation error.
Profits = (1-(3-4c/6)-(c/3))(3-4c/6) - c(3-4c/6) - (9c^2-13c/18)
Maximise it wrt c.
 FROM WHERE DOES THIS TERM COMES ?

[duck]

Profit = pq1-Cost-Investment cost.

[maahi]

ohh  and d whole time i was thinking that investment cost is d only cost and that wud determine mc ..urgggh my bad

anyway . thank u .  you are d best

[maahi]

(45 degree line constitutes the Set of Competitive equilibirum allocation)
 always ? if yes , then why ??

[duck]

Hey Maahi.. :)

Thats not the case always.

[maahi]

how do we check for competitive eqm in case of complements ??

[duck]

For Competitive equilibirum, we need to check two conditions:
(i) Given prices, Agents maximize their utility i.e find demand.
(ii) Market clears for all goods.

Now, whether goods are perfect substitutes, perfect complements or whatever, use the above way.

[maahi]

ok suppose there is a min fn and price of one good is zero as its in excess . so how do we check here
similar doubt ::
http://discussion-forum.2150183.n2.nabble.com/DSE-2006-21-General-Equilibrium-Please-help-tp7582678.html;cid=1371992207772-101 
 pls see dis doubt also http://discussion-forum.2150183.n2.nabble.com/DSE-2011-Doubt-td7580645.html;cid=1371992207772-101

[duck]

So just find the demand at zero price and then check whether the market is clearing or not.. :)