Consider an economy in which all consumers have, possibly different, Leontief utilities. Since preferences are not strictly convex, it is not guaranteed that a competitive equilibrium exists. I found some papers that discuss the computational problem of deciding whether a Leontief economy has a competitive equilibrium, but I am interested in general existence results:
A. What conditions on Leontief economies guarantee that a competitive equilibrium exists?
B. In particular, if the initial endowments are equal (each of $m$ agents receives a fraction $1/m$ of each good), is a competitive equilibrium guaranteed to exist?