How does household heterogeneity affect the transmission of an energy price shock? What are the implications for monetary policy? We develop a small, open-economy TANK model that features labour and an energy import good as complementary production inputs (Gas-TANK). Given such complementarities, higher energy prices reduce the labour share of total income. Due to borrowing constraints, this translates into a drop in aggregate demand. Higher price flexibility insures firm profits from adverse energy price shocks, further depressing labour income and demand. We illustrate how the transmission of shocks in a RANK versus a TANK depends on the degree of complementarity between energy and labour in production and the degree of price rigidities. Optimal monetary policy is less contractionary in a TANK and can even be expansionary when credit constraints are severe. Finally, the contractionary effect of an energy price shock on demand cannot be generalised to alternate supply shocks, as the specific nature of the supply shock affects how resources are redistributed in the economy.