Fractional Reserves and Demand Deposits

Would banks operating under laissez faire adopt a 100 percent reserve ratio or a fractional-reserve rule that would allow them to affect the money supply? The Chettiar banking system in late-nineteenth-century India functioned without any government regulation, and there is strong evidence that its bankers kept fractional reserves on interest-bearing checking deposits (explicit debt contracts that were redeemable on demand), although their ability to affect the money supply was not very large.