Assume you want to sell some of your shares of EVE at the current "market" price. The lowest ask price from sellers is $16.00. The market maker or specialist buys it from you at that price, hoping to sell it to someone else for at least $16.25. That $0.25 difference between the two prices is the amount the market maker pockets in return for taking the risk of buying the security without knowing with certainty what price she will realistically be able to sell it for.
Fortunately for that market maker or specialist, I offer to buy the stock at the "market price." The market maker looks around and sees that the highest price currently being "bid" by others who are specifying a purchase price is $16.25 so she sells it to me for $16.25.
It seems to say that a market maker buys at the ask price, and sells at the bid price.
But what I have understood before is contrary to the quote: a market maker buys at the bid price, which is the highest price of those prices at which each market maker is willing to buy, and a market maker sells at the ask price, which is the lowest price of those prices at which each market maker is willing to sell.
So I wonder whether a market maker sell (or buy) at a bid or ask price?