The primary objectives and the strategies of a national electricity market are the efficient delivery of network services and the electricity infrastructure to meet the long-term consumer's interests. Therefore, the objective of this study is to explore whether electricity prices across the six Australian States display instability. Such instability is closely associated with the presence of structural breaks in relevance to policy events on Australian carbon policies. The study makes use of weekly Australian wholesale electricity prices spanning the period from June 8th, 2008 to March 30th, 2014 along with linear and non-linear unit root testing methodologies. The results provide supportive evidence that the Australian electricity market can be described as a less stable electricity market, which implies that a high degree of market power is exercised by generators across regional markets. These findings are expected to have substantial consequences for the effectiveness of carbon dioxide mitigating policies, especially, when there is uncertainty as to whether the planned environmental policy is put in place for the lifespan of undertaken investments.