Recent versions of pairwise random matching models of money with divisible
and perishable goods are amended to allow individuals to hold more than one
unit of an indivisible asset. The asset resembles a fiat asset, except tha
t nominal holdings of it yield a small amount of utility. There is a genera
l upper bound on the number of units of the asset that individuals can hold
. A steady state with trade is shown to exist. The model is applied to stud
y numerically the effect on welfare of the degree to which the asset is div
isible.