This is one question with two scenarios: You are conducting a market. There are

ID: 1252821 • Letter: T

Question

This is one question with two scenarios:

You are conducting a market. There are a number of buyers, and a number of sellers. Each seller has one unit, and each buyer would only want one unit. You asked each group its reservation price for the item. For each of the conditions below, tell us what is the range of possible equilibrium prices in the market, and tell how you would allocate the goods.
a. Sellers’ reservation prices: 150, 110, 87, 72, 64. 50, 40, 22
Buyers’ reservation prices: 106, 92, 73, 54, 32, 18

b. Sellers’ reservation prices: 150, 110, 87, 72, 64. 50, 40, 22
Buyers’ reservation prices: 80, 70, 50, 50, 50, 50, 50, 35, 30

Explanation / Answer

See, this is a little tricky, but I hope I hit it right.
In first scenario, we have
a. Sellers’ reservation prices: 150, 110, 87, 72, 64. 50, 40, 22
Buyers’ reservation prices: 106, 92, 73, 54, 32, 18

If you look at the buyer and selller with least reservation price(R.P) you will notice that buyer is willing to pay only $18 but the least price at which the seller is willing to sell is $22.
So because of this, this buyer ends up buying nothing.
So now buyer with R.P $32 can buy the good at $22, buyer with R.P $54 can buy it in $40, one with R.P $73 can buy it in $50, one with R.P $92 can buy in $64 and the buyer with R.P $106 can buy the good at $72.

So,the range of possible equilibrium prices in this scenario will less than 87 and greater or equal to 72.

If the price is any more larger than this, than the supply of good will exceed the demand and so the price will fall till they are less than or equal to 72.

Similarly in the second case where we have, that the reservation price should be again less than $80 and greater or equal to $72.

Consumer with R.P $30 will buy at $22

One with R.P $50 will buy at $40

One with R.P $50 will buy at $50

One with R.P $70 will buy at $64

One with R.P $80 will buy at $72

The rest will either end up buying nothing or end up selling nothing.

So the quilibrium price should be less than $80 and greater or equal to $72.

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