A Chinese mayor problem

We solve an optimal land sale problem for a mayor who sells public land and uses the land sale revenue to finance infrastructure. Over an infinite horizon the mayor chooses land sale and infrastructure in each period to maximize the market value of the city net of the spending on infrastructure. The infrastructure spending is bounded by the land sale proceeds of the previous period. We show the optimization problem can be solved analytically. If it is profitable to sell land then it is profit-maximizing to sell it as early as the finance constraints permit. Finance constraints reduce the total size of land eventually sold.