Standard monopoly theory says that instead of producing output at the competitive level at which Price = Marginal Cost, a monopolist will restrict production to the point at which Marginal Revenue = Marginal Cost. Any producer, whether monopolist or competitive, maximizes profit by producing output at the point where MR = MC. For competitive firms P = MR and therefore, profit maximizing means P = MC. For monopolistic firms P > MR and therefore, profit maximizing means MR = MC which implies producing less output than the point at which P = MC.
This theory of monopoly cannot be applied to the production of fiat money because the MR always exceeds the MC for producing more. It costs around $0.25 to print a $1 bill. If the state took profit maximizing as its rule of determining how much fiat money to produce, it would continue to produce more $1 bills until the prices of paper and ink, etc. used to print them rose to $1, then it would print $5 bills and so on into hyperinflation. But the premise of monopoly theory is that the monopolist produces the amount of the good that maximizes profit. In the case of fiat money that rule will not lead to a restriction of production but to producing indefinite amounts.