An exchange economy with price rigidities and rationing is considered.
The rationing systems allowed are very general. Several characterizat
ions of the set of constrained equilibria are given, and new equilibri
um existence results are provided. More specifically, well-known prope
rties like the existence of equilibria without rationing of the numera
ire commodity, and the existence of supply and demand constrained equi
libria without rationing on the market of at least one commodity follo
w as special cases from the theorems proved. Finally it is shown that
the equilibrium correspondence is upper semi-continuous, while it is c
ontinuous on a residual set of points. In order to prove these results
a new continuity result for the budget correspondence is given.