Question

Suppose there are 11 buyers and 11 sellers, each willing to buy or sell one unit of a good, with values {$14, $13, $12, $11, $10, $9, $8, $7, $6, $5, $4,}. Assume no transaction costs and a competitive market. If there is a market maker in this market. What is the profit maximizing bid-ask spread per unit for a market maker? a. ​$9 bid; $9 ask b. ​$6 bid; $12 ask c. ​$8 bid; $10 ask d. ​$7 bid; $11 ask

Answer 1

Answer:

Explanation:

From the question given; The objective here is to determine the profit maximizing bid-ask spread per unit for a market maker. In order to achieve that; The demand supply schedule of the number of units bought and sold need to be computed which is shown in the table below.

Price       Quantity demanded by buyers        Quantity sold by sellers

$14                 1                                                         11

$13                 2                                                         10

$12                 3                                                         9

$11                  4                                                         8

$10                 5                                                         7

$9                  6                                                         6

$8                  7                                                         5

$7                  8                                                         4

$6                  9                                                         3

$5                 10                                                         2

$4                  11                                                         1

However; As the two transactions are happening simultaneously; There are 11 people participating in buying of a good and selling from one person to the other.

But the maximum even number of people that can be part of this trade is only 10 people.

So; for the individual having an higher value for the good will be able to afford it and which are those that falls into the category of  $14,$13,$12,$11,$10,$9 can place bid for the good.

On the other hand,  the individual having a lower  value for the good will sell it and which are those that falls into the category of  $4,$5,$6,$7,$8,$9 and would want to  sell it for the ask price of the good.

In this trend, we understand that the individual valuing the good for $9 won't be able to participate due to the fact that He appears on both trends because in the demand side , he have the lowest willingness to pay and at the seller's side he has the the highest value for the good and that the equilibrium price in this market is $ 9 because at this price the quantity demanded equals quantity supplied .

Thus; we can conclude that there are 5 transactions in the maximizing bid-ask spread per unit for a market maker.