  This study rigorously investigates the Keynesian cross model of a national
economy with a focus on the dynamic relationship between government spending
and economic equilibrium. The model consists of two ordinary differential
equations regarding the rate of change of national income and the rate of
consumer spending. Three dynamic relationships between national income and
government spending are studied. This study aims to classify the stabilities of
equilibrium states for the economy by discussing different cases of government
spending. Furthermore, the implication of government spending on the national
economy is investigated based on phase portraits and bifurcation analysis of
the dynamical system in each scenario.
