Australian Aborigines faced a resource management problem, which they addressed though burning regimes, referred to as fire‐stick farming. While dynamic economic analysis is clearly applicable, to date there have been no attempts to use it to model burning regimes. This paper develops a delayed‐response optimal‐control model to describe Aboriginal fire‐stick farming. The model explains a collective welfare maximizing burning regime that successfully controlled wildfires, protected the resources essential to survival, and, incidentally, produced a biodiverse landscape and limited greenhouse gas emissions. When the parameters of the model are changed to reflect the current institutional realities of reduced access to the land, and less direct dependence on it, traditional Aboriginal burning is prevented or delayed, fuel loads build up and uncontrolled fires are more likely to occur, damaging previously protected species. If Aboriginal burning is to be used to control fires successfully in a modern resource management context, it is necessary to adjust for changes in the institutional incentive structure. Payments for carbon offsets are an example of replacing lost incentives with new ones.