  We study a pricing problem where a seller has $k$ identical copies of a
product, buyers arrive sequentially, and the seller prices the items aiming to
maximize social welfare. When $k=1$, this is the so called "prophet inequality"
problem for which there is a simple pricing scheme achieving a competitive
ratio of $1/2$. On the other end of the spectrum, as $k$ goes to infinity, the
asymptotic performance of both static and adaptive pricing is well understood.
  We provide a static pricing scheme for the small-supply regime: where $k$ is
small but larger than $1$. Prior to our work, the best competitive ratio known
for this setting was the $1/2$ that follows from the single-unit prophet
inequality. Our pricing scheme is easy to describe as well as practical -- it
is anonymous, non-adaptive, and order-oblivious. We pick a single price that
equalizes the expected fraction of items sold and the probability that the
supply does not sell out before all customers are served; this price is then
offered to each customer while supply lasts. This extends an approach
introduced by Samuel-Cahn for the case of $k=1$. This pricing scheme achieves a
competitive ratio that increases gradually with the supply. Subsequent work by
Jiang, Ma, and Zhang shows that our pricing scheme is the optimal static
pricing for every value of $k$.
