What “certain conditions” are applicable on Henry George Theorem?

Question

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 (land rent) 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 (especially in Progress and Poverty), which launched the 'single tax' movement.

Source: Wikipedia

Obviously government can be very inefficient. Government can spend trillions of dollars building landfill or creating even bigger problems. So we would need at least some "benevolent" dictator and that's not reasonable "conditions".

So what's the conditions?

Answer 1

The original paper lists several situations where it does not hold:

1. In planned Economies if either

   a. The opportunity cost of land is differential depending on where on the city boundary you are.

   b. The city is small.

2. In competitive economies the above is true, but also the theorem is violated in the event that population is not distributed Pareto optimally (which it generally is not). This condition can be substituted by lump sums--if individualized lump sums are used to redistribute wealth, the theorem holds. When indirect subsidization or sums based on group membership are used instead, it generally does not hold.

The paper claims that the theorem holds for any optimal (utility maximizing) city with a population distribution determined by outside factors, and for any polity in general that has public goods, constant returns to production, and no externalities (these conditions are never exactly true).

The theorem also has implicit assumptions that are generally not accurate when taking into account behavioral results (e.g. completeness of preferences).