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, the government controls the quantity of nominal debt, enabling price level determination independently of the interest rate trajectory (Hagedorn (2021)). Our findings indicate that under an inflation-targeting regime, price level determinacy is often the exception than the norm when the central bank pursues a dual mandate. The dynamics of government spending emerge as a crucial driver of this result. To address this challenge, we show that possible solutions include price level targeting and stabilizing consumption inequality.