Australia's resources boom is underpinned by increased demand from industrialising China and a rise in export prices. Current depletion rates will soon exhaust currently known reserves of iron ore and coal. This paper presents a dynamic optimisation model of a growing open economy where a social planner chooses the time path for depletion of a non‐renewable resource during a demand‐led resources boom. We find that for particular functional forms and in the absence of extraction and social costs, the optimal depletion rate equals the difference between the price elasticity of export demand times the world interest rate and growth in export demand. In contrast to the existing literature, we show that the optimal depletion rate is unaffected by a temporary increase in price, but reduced by growth in demand which is in turn sustained by offshore steel production and urbanisation. The main theoretical implication is that growth in export demand from China reduces the depletion rate. Australian iron ore exports, simulated using this theory, move together with actual volumes over the period 1995–2011, and the error between simulated and actual iron ore exports is lower for the model in this paper than it is for the model without growth in export demand.