Questions from ISI MSQE 2014 paper

[Rajat]

Hi,

Can someone please share solution to the following question from ISI 2014.

There are 11 traders and 6 identical (indivisible) chickens. Each
trader wants to consume at most one chicken. There is also a
(divisible) good called \money". Let Di equal to 1 indicate that
trader i consumes a chicken; 0 if he does not. Trader i0s utility
function is given by uiDi + mi, where ui is the value he attaches
to consuming a chicken, mi is the units of money that the trader
has. The valuations for the 11 traders are:
u1 = 10; u2 = 8; u3 = 7; u4 = 4; u5 = 3; u6 = 1; u7 = u8 = 3;
u9 = 5; u10 = 6; u11 = 8:
Initially each trader is endowed with 25 units of money. Traders
6; 7; 8; 9; 10; 11 are endowed with one chicken each.

i. What is a possible equilibirum market price (units of money per chicken) in a competitive market?
ii. Is the equilibrium unique ?
per chicken) in a competitive market? [4 marks]

[Anakin Skywalker]

CONTENTS DELETED

The author has deleted this message.

[L]

It is a very easy question, just the representation is confusing.
Just plot the demand curve (taking Ui as reservation price) and set supply = 6.

[Rajat]

L or annakin, can you please elaborate the entire solution. I am not even able to start.

I got 4<p<5

i am only answering basis common sense. I am looking for an elaborate answer like we would write in the examination


Thanks !

[Anakin Skywalker]

CONTENTS DELETED

The author has deleted this message.

[Anakin Skywalker]

CONTENTS DELETED

The author has deleted this message.

[Rajat]

Annakin, agree with your point that p should be something just shy of the 5 mark, just so that the 6th trader is induced to buy a chicken. Also, in that case p can take a number of values between 4 and 5 which calls into question the possibility of a unique equilibrium. But, lets first define equilibrium. Does the 'uniqueness' depend on the level of p ? or is it the just about the allocation of chickens. Iff it is only about allocation of chickens, then we do have an unique equilibrium.

[Anakin Skywalker]

CONTENTS DELETED

The author has deleted this message.

[L]

What Rajat has said is correct, that, price will be between 5 and 4. Obviously, it can't go below 4 , however, until it is above 5, supply and demand is satisfied.

There is somewhat similar question in Hal Varian's first chapter's Review Questions (Q.2) (for confirmation).
1. Suppose that there were 25 people who had a reservation price of $500,
and the 26th person had a reservation price of $200. What would the
demand curve look like?
2. In the above example, what would the equilibrium price be if there were
24 apartments to rent? What if there were 26 apartments to rent? What
if there were 25 apartments to rent?

For the last part, answer is price between 500 and 200.

[Anakin Skywalker]

CONTENTS DELETED

The author has deleted this message.

[kanv93]

frnds, can any one tell me to which chapter does these types of problems belong to and where to prepare problems of similar kind.


Thanks in advance

Regards,
Kannan

[Jim_Moriarity]

IN maths question no 27.4

I'm getting B as the answer but its given D.
Help me out with it.