In this paper, we examine macroeconomic stability and instability of a dynamic Keynesian Model with a theoretical foundation of Modern Monetary Theory (MMT), often considered as unconventional within mainstream economics. MMT fundamentally emphasizes proactive fiscal policies and passive monetary policies, always striving to maximize employment. A common critique of MMT is the assertion that governments find it challenging to control output and inflation through a fiscal policy. It is also argued that governments should always demonstrate responsibility for the fiscal balance, and without such responsibility, the "credibility" of government bonds is damaged. Opposingly, this study finds that establishing credibility in inflation targets and consistently pursuing proactive fiscal policies in response to deficient output gaps are effective in managing inflation from escalating uncontrollably, which may help stabilize the economy. Although the fundamental tenets of MMT may not heavily emphasize inflation target, which belong to monetary policies, the importance of fiscal policies is reaffirmed by the conclusions drawn from this paper, likely ensuring that crucial aspects of MMT are not disregarded.