A new algorithm of equilibrium searching for a linear exchange  model with fixed budgets and financial limits on purchases (spending constraints) is considered. This consideration extends the author’s original polyhedral complementarity approach to the equilibrium problem in a linear exchange model and its variations. The approach has no analogs which made it possible to obtain finite algorithms for such models. This is due to the monotonicity properties inherent in  the models. Especially simple algorithms arise for the models with fixed budgets since the emerging fixed point problems also have the potentiality properties.

exchange model, economic equilibrium, polyhedral complementarity, spending constraints, algorithm.