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.At the optimal bid,ask spread,what is the total profit that the market maker makes?

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.At the optimal bid,ask spread,what is the total profit that the market maker makes?

Quizplus · Accepted Answer

The optimal bid and ask prices will be at the highest buying price and the lowest selling price respectively, which are $14 and $4. The market maker will earn a profit equal to half the spread for each transaction (as they are buying from the seller at a lower price and selling to the buyer at a higher price).

So, the total profit for the market maker can be calculated as:

Total profit = (Number of transactions) x (half the spread)
Number of transactions = 11 (as there are 11 buyers and 11 sellers)

Spread = $14 - $4 = $10
Half the spread = $5

Total profit = 11 x $5 = $55
But the market maker only earns half of this profit as they only buy from the seller or sell to the buyer in each transaction. Hence, the total profit for the market maker will be:

Total profit = $55/2 = $27.5

Rounded to the nearest dollar, the total profit for the market maker is $28 - $10 (initial cost) = $18, which is option C.

​Suppose There Are 11 Buyers and 11 Sellers,each Willing to Buy

Suppose There Are 11 Buyers and 11 Sellers,each Willing to Buy