I'm reading about high frequency trading and market making. I'm trying to understand the following example from my book:
Here is an example of how market making helps investors. Suppose that the best buy order from a long-term investor who really wants to own the stock is $\$10.00$ and the best sell order from a long-term shareholder who wants to exit their position is $\$10.10$. In other words, there exists a potential buyer who refuses to pay more than $\$10$, and a seller who would not accept less than $\$10.10$. A market maker who has no position in the stock (and who does not really want one) is willing to quote a bid price at which he or she is willing to buy of $\$10.04$ and an offer price at which he or she is willing to sell for $\$10.06$. When another long-term shareholder comes into sell shares at the market bid price, the market maker buys it at $\$10.04$. Later, another would-be long-term investor arrives who is willing to buy at the current offer price, and the market maker sells at $\$10.06$ for a two cent profit. Note that both the buyer and the seller got better prices than they would otherwise have gotten: Without the marketmaker, the seller would have received only $\$10.00$ and the buyer would have paid $\$10.10$. Furthermore, there has been less volatility in the price as well: Instead of the price bouncing from $\$10$ to $\$10.10$, its range was reduced to $\$10.04$ to $\$10.06$.
(From Angel & McCabe: Fairness in Financial Markets, Page 6)
Question: I'm having trouble understanding this example and especially the statement "Note that both the buyer and the seller got better prices than they would otherwise have gotten: Without the marketmaker, the seller would have received only $\$10.00$ and the buyer would have paid $\$10.10$".
This would mean that in absence of the market maker, the buyer would have bought the stock from a third agent for $\$10.10$ and the seller would have sold the stock to a fourth agent at $\$10.00$. This is equivalent to the original buyer buying the stock from the original seller at either $\$10.00$ or $\$10.10$ right? Which means that there not necessarily both better off.
Thanks in advance!