  We consider the problem of fair allocation of $m$ indivisible items to a
group of $n$ agents with subsidy (money). Our work mainly focuses on the
allocation of chores but most of our results extend to the allocation of goods
as well. We consider the case when agents have (general) additive cost
functions. Assuming that the maximum cost of an item to an agent can be
compensated by one dollar, we show that a total of $n/4$ dollars of subsidy
suffices to ensure a proportional allocation. Moreover, we show that $n/4$ is
tight in the sense that there exists an instance with $n$ agents for which
every proportional allocation requires a total subsidy of at least $n/4$. We
also consider the weighted case and show that a total subsidy of $(n-1)/2$
suffices to ensure a weighted proportional allocation.
