We study the implications of a ‘dual mandate’ of price and output stability in a heterogeneous agent New Keynesian economy where fiscal policy is set in nominal terms. Specifically, we explore the scenario where the government controls the quantity of nominal debt, enabling price level determination independent of the interest rate trajectory, as highlighted by Hagedorn (2021). Our analysis reveals that when the central bank pursues a dual mandate, local price level determinacy is compromised, and the economy may not converge to a stable equilibrium if the central bank aims to stabilize inflation and economic activity. This instability is attributed to the dynamics of government spending. In contrast, if the central bank stabilizes only inflation, real government spending acts as an automatic stabilizer. We demonstrate that targeting the price level can restore determinacy, positing that central banks with dual mandates may benefit from adopting a Wicksellian-type rule.