“In a truly free market economy, the likelihood that banks will practice fractional-reserve banking will tend to be very low. If a particular bank tries to practice fractional-reserve banking it runs the risk of not being able to honour its checks.”
I concur. In the mythical world of free market banking, banks would be incentivize to ensure they have the proper reserves to lend out money based upon those reserves. The implicit moral hazard, from having a centralized bank, would be non existent.
Banks would also have some sort of tangible precious metal or valuable resource to “back” the money. In this quixotic banking model, banks would base their interest rate upon the overall interest rate(inter temporal time preference) of the market place. Banks would stay in(or lose) business based upon their ability run their operations effectively.
Back to reality, or the current state of banking affairs: Banks are de incentivized to run their operations as effectively knowing there exists a series of back stops in the event they err in their aggressive business practices. The Fed can come in and provide a series of tactics, via monetary policy, they will keep them from failing. This typically includes inflationary measures that is beneficial to the banks, but the economic cost is dispersed in the marketplace.