This paper characterises the jointly optimal monetary and fiscal stabilisation policy in a new Keynesian model that allows for consumers who lacking access to asset markets consume their disposable income each period. With full asset market participation, the optimal policy relies entirely on the interest rate to stabilise cost-push shocks and government expenditure is not changed. When asset market participation is limited, there is a case for fiscal stabilisation policy. Active use of public spending raises aggregate welfare because it enables a more balanced distribution of the stabilisation burden across asset-holding and non-asset-holding consumers. The optimal response of government expenditure is sensitive to the financing scheme and whether the policymaker has access to a targeted transfer that can directly redistribute resources between consumers.