The Small-Change Problem and Token Money

Abstract

This chapter analyses the historical and economic logic of small-denomination coin production and circulation from antiquity to the early modern period. The persistent problem of small- change shortages is primarily attributed to the disproportionately high production costs of low-value coins relative to their face value. The ‘standard formula’, as proposed by Cipolla, Sargent, and Velde, emerges as a historical solution: governments should issue small change as token coins, ensure their legal tender status and acceptance for tax payments, and maintain credible—though not necessarily actual—convertibility into full-bodied coins in order to control supply and prevent inflation. This chapter contributes new insights by integrating numismatic evidence with modern economic modelling to reassess long-standing theories about the persistent shortage of small change. The chapter examines supply-side constraints, including minting and melting points, and explores alternative methods to the standard formula, such as debasement, coin division, and advanced minting technologies. Historical case studies from ancient Greece, Rome, the Middle Ages, and early modern Europe illustrate the evolution of these practices. While ancient Greeks and Romans developed early partial versions of this formula, they did not fully solve the problems of quantity control, convertibility, and counterfeiting. Notably, small-change shortages were most acute during the late Middle Ages and early modern period. The use of trade tokens issued by local authorities and private merchants, particularly in England, played a crucial role in mitigating these shortages, leading to the adoption of standardized minting practices and the standard formula by the early nineteenth century. The analysis underscores the complex interplay between production costs, monetary policy, and the availability of small change, highlighting the innovative responses to an enduring monetary problem.