Modern methods of qualitative analysis of dynamic systems go back nearly a century to Poincare (1880, 1892). Since the classic work of Smale (1967), it has become clear that very complicated, or chaotic, trajectories (time path) can easily arise in certain dynamic systems and that such complicates trajectories can persist when small perturbations of the underlying systems occur. Such a phenomenon, referred to as chaos, a case that is emphatically not pathological, is essentially one in which a dynamic mechanism that is very simple, and, above all, deterministic yields a time path so complicated that it will invariably pass all the standard tests of randomness. The seminal contribution of Lorenz (1963), Li and Yorke (1975), May (1976), Stefan (1977), amongst others have greatly facilitated an exploration of the pertinence of such complicated dynamics, arising in simple first order dynamic non-linear systems, to a variety of fields, including physics, biology, ecology and of late economics. In the context of the above literature and the development thereafter we intend to build the model that comprises of four equations. These specific: (1) The demand for real balances, (2) The money- inflation link, (3) the government budget deficit, and (4) the inflation tax revenue. The reduced form of the model is seen to yield a three parameter system whose phase diagram for the inflation rate (expressed in terms of a transcendental equation) produces solutions which are capable of generating stable, cyclic, or chaotic behavior.
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