I am familiar with how currency exchange booths at airports make some of their money: from the bid-ask spread. For example, they will say: "you can sell us 1 USD for 1.32 CAD, and you can buy 1 USD from us for 1.33 CAD". From the perspective of the customer, the ask price fixed by the currency exchange booth (1.32 CAD) is lower than the bid price (1.33 CAD).
However, on the stock market, the bid price is almost invariably lower than the ask price. How does the market maker make any money out of this? Suppose the highest bid is $100, and the lowest ask is $101. The market maker will make a loss by buying at $101, and selling at $100. In fact, the bid price must be higher than the ask price for the market maker to profit from the bid-ask spread in this manner. But from my observations, the bids in the market are always lower than the asks.
I suspect that I have a fundamental misunderstanding of market-making. So my question is: how do market makers actually profit from the bid-ask spread?