The authors consider three one-period models of money lending. The first model represents a two-perishable-good economy before gold demonetization: it has gold as money, no central bank, but has individuals who act as money lenders. The second model considers the effects of demonetization of gold by replacing the transaction use of gold with paper money. All holders of gold are given paper money on a one-to-one basis; but in addition, they are allowed to keep their gold. In the third model, gold is demonetized as in the second model; but the paper money is issued to a central bank instead of the individuals, hence the individuals own the central bank. All models have moneylenders and two types of traders as agents. The traders trade in two perishable goods using -- depending on the model -- gold or paper money as money, and aim to maximize the utility \(u(x,y,z)=2\sqrt{xy} + z + \Pi \hat z\) common for all agents, where \(x\) and \(y\) are the amounts consumed of goods 1 and 2, \(z\) is the amount of gold services consumed, and \(\Pi\hat z\) is the salvage value of the gold remaining at the end of the game. In Model 1, the initial endowments of the traders are \((a,0,m)\) and \((0,a,m)\) for type 1 and type 2 from good 1, good 2, and gold; and the moneylenders start with an initial supply \(B\) of golds and no goods. All trade is to be intermediated with gold as money, and the moneylenders do not take deposits. In Model 2 paper money (gold certificate) is issued for each gold owner which is \(100\%\) backed by gold: hence the initial endowments of the traders are extended by paper money of amount \(m\), and the initial endowments of moneylenders are extended by paper money of amount \(B\). All trade is to be intermediated by paper money; gold becomes a tradeable commodity; and the salvage ratio of paper money may differ from \(\Pi\). In addition, traders are not allowed to lend, and moneylenders cannot borrow. Model 3 differs from Model 2 in that the paper money backed by gold is deposited into a central bank, owned by the gold owners, which is the only lender in the economy. The moneylenders are gold merchants in this model. These models are solved by optimizing trading, consumption, and the common interest rate to the maximize utility for the agents. By comparing the efficiency of the optimal trading/consumption/lending strategies in the three models, the authors show that a gain in efficiency can occur when a switch is made from a durable commodity money to a fiat money, provided there is ``enough money'' in the system, i.e. if \(B\) is large enough relative to \(a\). In addition, if there is not ``enough money'' present, the central bank can also help to increase efficiency.