  We study a class of quasi-variational inequality problems defined over
infinite dimensional Banach space and deduce sufficient conditions for ensuring
solutions to such problems under the upper semi-continuity and
pseudomonotonicity assumptions on the map defining the inequalities. The
special structure of the quasi-variational inequality enables us to show the
occurrence of solutions for such inequalities based on the classical existence
theorem for variational inequalities. This special type of quasi-variational
inequalities is motivated by the pure exchange economic problems and Radner
equilibrium problems for sequential trading game. Further, we study the
solvability of the specific class of quasi-variational inequalities on Banach
spaces in which the constraint map may admit unbounded values. Finally, we
demonstrate the occurrence of dynamic competitive equilibrium for a
time-dependent pure exchange economy as an application.
