Solutions to ISI PEB2014

[Akash]

Can anyone plz help me with Q3b?


3(b) 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 is 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? [4 marks]
ii. Is the equilibrium unique? [4 marks]

[Dr. Strange]

Traders 6,7,8,9,10,11 are possible suppliers
Traders 1,2,3,4,5 are possible buyers

A buyer  will buy chicken if his u value is greater than or equal to price p
A seller  will sell chicken if his u value is less than or equal to price p

So we can see for P<1, supply = 0,demand=5
1<p<3, supply = 1,demand=5
3<p<4, supply = 3,demand=4
4<=p<=5, supply = 3,demand=3
5<p<6, supply = 4,demand=3
6<p<7, supply = 5,demand=3
7<p<8, supply = 5,demand=2
8<p<10, supply = 6,demand=1
p>10, supply = 6,demand=0
we can see  4<=p<5 is equilibrium with q=3

This eqlm is not unique as p can take values from 4 to 5

[Akash]

Thank you Dr. Strange. Looking forward to your movie in December, it should be awesome!

[Dr. Strange]

I hope so too. :D

[urvashi]

The equilibrium price will be p greater than 4 and less than equal to 5

[Dr. Strange]

p=4 is also an option