Suppose There Are 9 Sellers and 9 Buyers in a Market

Essay

Suppose there are 9 sellers and 9 buyers in a market, each willing to buy or sell one unit of a good. Their values are {$15, $14, $13, $12, $11, $10, $9, $8, $7}. That is, there is one buyer and one seller each valuing the good at $15, one buyer and one seller each valuing the market good at $14, etc.
a) Assuming no transactions costs and a competitive market, what is the equilibrium price and quantity of goods traded in this market?
b) Suppose there is a single market maker in this market and no price controls. Calculate the bid-ask prices that maximize the market maker's profit when the marginal cost of a transaction is $1.
c) If the government imposes a maximum spread of $2 (i.e., controlling the market maker's per transaction profit), what are the bid-ask prices that maximize the market maker's profit when the marginal cost of a transaction is $1? What number of goods will be traded?