How do option exchanges make money on profitable long call?

To clear up a few things: Exercising a call does not execute a "buy order" on the exchange. Your option trade is with another counterparty who presumable already has stock to sell you at that price. In other words, your option contract is not with the exchange who must then buy stock (and pay commissions), it's with another counterparty that already has the stock. At worst, they must buy the stock to cover their option, which then creates another fee from the exchange (similarly, they aren't buying the stock from the exchange, but from someone else through the exchange).

So how does the exchange make money?

Various ways, but the bigger ones are:

• Transaction fees (passed through by brokers)
• Membership fees (to allow direct trading)
• Subscriptions to data that they generate (order books, prices, etc.)

Exchanges make money in a myriad of ways but not in the way that you suggest. For details, google for the annual financial report for an exchange such as the CBOE, NASDAQ, NYSE, etc.

An exchange is where securities are listed. A broker is an intermediary that sends your order to an exchange or ECN.

In order for you to buy your long call, there must be a counterparty willing to sell that call to you. Ignoring commissions (if you're still paying them) and fees, option trading is a zero sum game. What one trader makes, the trader on the other side loses.

When you exercise your long call to buy the stock, someone who is short the call is assigned and must sell you the stock at the strike price. If he owns the stock, it is sold to you. If he doesn't own the stock, his broker borrows the stock from a third party to sell and the trader becomes short the stock. If the stock isn't borrowable, the trader is forced to buy the stock in order to deliver it to you.