Question

A market maker faces the following demand and supply for widgets. Eleven buyers are willing to buy at the following prices: $15, $14, $13, $12, $11, $10, $9, $8, $7, $6, $5. Eleven sellers are also willing to sell at the same prices. How many transactions must the market maker make if he wants to maximize his profits?

Answer 1

maximum profit ($30 in total) is obtained by selling 5 units

Step-by-step explanation:

1. if the market maker buys and sells one unit, his/her profit = $15 - $5 = $10
2. if the market maker buys and sells two units, his/her profit = $10 + ($14 - $6) = $18
3. if the market maker buys and sells three units, his/her profit = $18 + ($13 - $7) = $24
4. if the market maker buys and sells four units, his/her profit = $24 + ($12 - $8) = $28
5. if the market maker buys and sells five unit, his/her profit = $28 + ($11 - $9) = $30

the maximum profit per unit is obtained by selling only 1 unit, but the total maximum profit is obtained by selling 5 units.