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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!

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I didn't quite understand your objection.

Most theories of market making are derived from a famous paper by Jack Treynor (The Economics of the Dealer Function). In the theory, there are initially no market makers, but there is a backstop seller (in this case someone willing to sell large amounts at 10.10) and a backstop buyer (a Warren Buffet ready to buy lots and lots if it drops to 10.00) and initially there is not much trading at all. By stepping in and trading at 10.04 10.06 the market maker (1) makes trades possible which would not have occurred before, (2) earns a profit for himself as compensation for his short term risk taking. The guy who bought from him at 10.06 is happier than if he had to buy from the big institution at 10.10. The market maker refuses to hold stock long term (in the worst case he may have to dump his inventory at a loss to the backstop buyer) but he facilitates trading among those interested in holding the stock. (In a similar way the existence of supermarkets makes it easier for you to buy food than if you had to deal directly with farmers).

So the point is it is better to have marketmakers in the middle, than to have a market where all trading is directly between long term shareholders (the market with middlemen (market makers) has narrower spreads and less volatility).

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