Greg Mankiw on how fiat money evolves naturally from commodity money, from his widely popular MACROECONOMICS (5th ed., pp. 78-79): “The government might first get involved in the monetary system to help people reduce transaction costs. Using raw gold as money is costly because it takes time to verify the purity of gold and to measure the correct quantity. To reduce these costs, the government can mint gold coins of known purity and weight. The coins are easier to use than gold bullion because their values are widely recognized.
“The next step is for the government to accept gold from the public in exchange for gold certificates--pieces of paper that can be redeemed for a certain quantity of gold. If people believe the government’s promise to redeem the paper bills for gold, the bills are just as valuable as the gold itself. In addition, because the bills are lighter than gold (and gold coins), they are easier in transactions. Eventually, no one carries gold around at all, and these gold-backed government bills become the monetary standard. “Finally, the gold backing becomes irrelevant. If no one ever bothers to redeem the bills for gold, no one cares if the option is abandoned. As long as everyone continues to accept the paper bills in exchange, they will have value and serve as money. Thus, the system of commodity money evolves into a system of fiat money. Notice that in the end, the use of money in exchange is a social convention: everyone values fiat money because they expect everyone else to value it.