  We consider the Max-Buying Problem with Limited Supply, in which there are
$n$ items, with $C_i$ copies of each item $i$, and $m$ bidders such that every
bidder $b$ has valuation $v_{ib}$ for item $i$. The goal is to find a pricing
$p$ and an allocation of items to bidders that maximizes the profit, where
every item is allocated to at most $C_i$ bidders, every bidder receives at most
one item and if a bidder $b$ receives item $i$ then $p_i \leq v_{ib}$. Briest
and Krysta presented a 2-approximation for this problem and Aggarwal et al.
presented a 4-approximation for the Price Ladder variant where the pricing must
be non-increasing (that is, $p_1 \geq p_2 \geq \cdots \geq p_n$). We present an
$e/(e-1)$-approximation for the Max-Buying Problem with Limited Supply and, for
every $\varepsilon > 0$, a $(2+\varepsilon)$-approximation for the Price Ladder
variant.
