This paper investigate the stabilization bias that arises in a model of non-cooperative monetary and fiscal policy stabilisation of the economy, when monetary authority implements price level targeting but fiscal policy remains benevolent. We demonstrate the gain in welfare improvement depends on the level of steady state debt. If the steady state level of the government debt is low, then the monetary price level targeting unambiguously leads to social welfare gains, even if the fiscal authority acts strategically and faces different objectives and has incentives to pursue its own benefit and therefore offsets some or all of monetary policy actions. Moreover, if the fiscal policymaker is able to conduct itself as an intra-period leader, the social welfare gain of the monetary price level targeting regime can be further improved. However, if the economy has a high steady state debt level, the gain of the price level targeting is outweighed by the loss arising from the conflicts between the policy makers, and leads to a lower social welfare than under cooperative discretionary inflation targeting.