The Henry George theorem, named for 19th century U.S. political economist and activist Henry George, states that under certain conditions, aggregate spending by government on public goods will increase aggregate rent based on land value more than that amount, with the benefit of the last marginal investment equaling its cost. This general relationship, first noted by the French physiocrats in the 18th century, is one basis for advocating the collection of a tax based on land rents to help defray the cost of public investment that helps create land values. Henry George popularized this method of raising public revenue in his works, which launched the 'single tax' movement. In 1977, Joseph Stiglitz showed that under certain conditions, beneficial investments in public goods will increase aggregate land rents by at least as much as the investments cost. This proposition was dubbed the "Henry George theorem", as it characterizes a situation where Henry George's 'single tax' on land values, is not only efficient, it is also the only tax necessary to finance public expenditures. Henry George had famously advocated for the replacement of all other taxes with a land value tax, arguing that as the location value of land was improved by public works, its economic rent was the most logical source of public revenue. Although the conditions specified in Stiglitz's paper do not strictly exist in reality, actual conditions are often close enough to the theoretical ideals that the great majority of government spending does indeed appear as increased land value. Subsequent studies have generalized the principle and found that the theorem holds even after relaxing the assumptions. Studies indicate that even existing land prices, which are depressed due to the existing burden of taxation on labor and investment, are great enough to replace taxes at all levels of government More recent economists have discussed whether the theorem provides a practical guide for determining optimal population sizes of cities and private enterprises. Mathematical treatments of the theorem suggest that an entity obtains optimal population when the opposing marginal costs and marginal benefits of additional residents are balanced.
