Alternative modelling formalisations, such as differential equations and statistical analysis, imposes many restrictions, such as homogeneity, anonymity and perfectly rational. Agent-based modelling and simulations provide a new modelling formalisation approach that relaxes some or all those restrictions. Two agent-based systems are developed to study theories of decentralised, individualistic, boundedly rational, complex behaviour and nonlinear stochastic systems. The first ACE model presents an ACE to study demand- pull and cost-push inflation. Moreover, it studies the effect of different levels of rationality on Macro-Activities for Economic Systems. The second ACE model studies the Lucas-Island model. Specifically, it studies the behaviour of the central bank to stabilise inflation and output. Three different economic models are studied. Simulations show that there is a positive relationship between the equilibrium price and level of rationality while there is a negative relationship with the unemployment rate.