In this paper, we study the real effects of different degrees of divisibility of money in a random matching model. When money is very indivisible, as it is seemingly true in most of the world before the 19th century, welfare increases as the divisibility of money increases (non-neutrality). However,
when the degree of divisibility is sufficiently high, as it is seemingly true for the current U.S. coinage system, there would be little or no welfare loss from reducing the degree of divisibility, the elimination of the penny.