This paper estimates the Brazilian Amazon’s carbon-efficient forest cover – i.e. when farmers internalize the social cost of carbon. We propose a dynamic discrete choice land-use model and estimate it using a panel of land use and carbon stock of 5.7 billion pixels between 2008 and 2017. The business-as-usual scenario implies an inefficient release of 42 billion tons of CO2 in the long run resulting from the deforestation of an area twice the size of France. A carbon tax that makes farmers internalize the social cost of carbon would implement the efficient allocation and generate welfare gains exceeding 1.6 trillion dollars. Responses from a carbon tax are highly convex: a carbon tax of only $10/ton would preserve 95% of the efficient carbon stock. An excise tax on cattle ranching, a second-best policy, achieves at most 87% of the first-best welfare gains.