Spatial non-homogeneous invariant tori in the Multiplier-Accelerator model

In this paper we introduce a boundary value problem based on the well known Multiplier-Accelerator model proposed by Paul Samuelson which is an extension of the works of John Keynes. The suggested boundary value problem is to consider spatial effects when studying processes of macroeconomics. For the boundary value problem given, using the Invariant Manifolds method, the method of Averaging and the Theory of Normal Forms we show the existence of stable spatial non-homogeneous invariant tori.