An Error in the Theory of Seigniorage

The article reveals an error in the theory of seigniorage or government revenue from printing money. Friedman, Cagan, Mankiw, and other economists have repeated the definition of seigniorage as the monetary base multiplied by the rate of inflation (or by the growth in the monetary base). This definition, however, contains a logical error in the formula of seigniorage, confusing the growth rate with the growth rate divided by the growth rate plus one. This often-repeated confusion is consequently common in modern economics textbooks. These many authors have omitted Keynes who – almost one hundred years ago – rightly understood seigniorage to be the monetary base multiplied by the rate of money growth divided by the rate of money growth plus one. This paper presents an unambiguous definition and formula of seigniorage and offers a graphical illustration of seigniorage as a function of monetary growth which corresponds to Keynes’s approach. It is shown that such a graph is an analogy to the Laffer curve in explicit taxation.