  Online markets are a part of everyday life, and their rules are governed by
algorithms. Assuming participants are inherently self-interested, well designed
rules can help to increase social welfare. Many algorithms for online markets
are based on prices: the seller is responsible for posting prices while buyers
make purchases which are most profitable given the posted prices. To make
adjustments to the market the seller is allowed to update prices at certain
timepoints.
  Posted prices are an intuitive way to design a market. Despite the fact that
each buyer acts selfishly, the seller's goal is often assumed to be that of
social welfare maximization. Berger, Eden and Feldman recently considered the
case of a market with only three buyers where each buyer has a fixed number of
goods to buy and the profit of a bought bundle of items is the sum of profits
of the items in the bundle. For such markets, Berger et. al. showed that the
seller can maximize social welfare by dynamically updating posted prices before
arrival of each buyer. B\'{e}rczi, B\'{e}rczi-Kov\'{a}cs and Sz\"{o}gi showed
that the social welfare can be maximized also when each buyer is ready to buy
at most two items.
  We study the power of posted prices with dynamical updates in more general
cases. First, we show that the result of Berger et. al. can be generalized from
three to four buyers. Then we show that the result of B\'{e}rczi,
B\'{e}rczi-Kov\'{a}cs and Sz\"{o}gi can be generalized to the case when each
buyer is ready to buy up to three items. We also show that a dynamic pricing is
possible whenever there are at most two allocations maximizing social welfare.
