Farmers on the economic frontier often do not have clear titles to their land. Therefore, using an infinite-horizon representative agent model calibrated with data for the Brazilian Amazon, this paper analyzes how improved property rights influence the frontier farmer's investment in the land, as well as the farmer's consumption and debt. Three channels through which property rights affect these variables are identified in the analysis. Two involve the expenditure the farmer incurs to defend the land claim, and the third involves the interest rate premium the farmer faces when borrowing without a clear title to the land. Variants of the model allow for labor to defend the land claim and for endogenous property rights. The findings suggest a need and direction for further, empirical research, particularly with regard to informal institutional arrangements, measures of property rights and the means by which they are defended.