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Why use a viabilistic approach to model economy? Because it is urgent to re-assess the modeling of the business cycle that integrates dynamic money creation and that has at its core the notion of constraints. The purpose of this paper is thus to propose an evolutionary economic model using a mathematical framework derived from set-valued analysis, differential inclusions and viability theory. As this approach is dynamical, the model will not use two concepts on which neo-classical economics are built i.e., (1) the existence of static repeated equilibria, (2) the optimization by an economic agent of a utility function. Furthermore, we will not use any self-organization process or "invisible hand", as in our viabilist framework the economic viability will be maintained by explicit choices of the economic agents and of the lender of last resort over the budgetary and monetary rules to apply. Indeed, even simple constraints on the second-derivative of the means of payments already induce four-phased business cycles. Coupling these constraints over the creation of means of payment with economic evolutions of prices and commodities through a budgetary constraint allows for a single formalism, tackling jointly the question of the viability of economic and monetary evolutions. [ABSTRACT FROM AUTHOR]