ISI 2014- QUESTION 3-part b

[saumya singha]

How do we solve this questions on chickens
where there are 11 traders and 6 identical (indivisible) chickens.
some are saying do it by reservation price model. BUt how can we do it like that.
LOgically what I understand of it is that 6 people endowed with the chickens will be willing to sell only if they get a price higher than the utility received from consuming the chicken and buyers will buy chicken only when they get added utility after paying for the chicken, which should be more than 25 rupees which is there original income.
but now how do I use pareto optimality to find the competitive equilibrium?
Please do help.

[onionknight]

Well, you're essentially saying the same thing. The equilibrium would occur when given their endowment, only 6 people would choose to consume chicken and others would be content with consuming only money. This would happen when the chickens go to the people with the highest 6 uis for a price between 4 and 5. If the price is lower than this, other people could get higher utility by trading their money for a chicken and for a price greater than 5 some of the chicken buyers would be better off trading money for their chicken. Market clearing is essential for equilibrium.