Optimal divisibility of money when money is costly to produce

There is wide agreement that currency was not available in conveniently small denominations prior to the 19th century. Here, estimates of the costs of providing and maintaining money (coins) in 15th century Europe and parameterized versions of a matching model of money are used to find the optimal degree of divisibility. Although the optima are sensitive to the specification of the matching model, the optimal sizes we find agree in order of magnitude with the sizes of the most common coins in 15th century Europe.