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. If the market maker is free to choose the number of transactions he can make, what is his maximum profit

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

Explanation:

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