The Henry George Theorem

Textbooks in public finance and urban economics sometimes contain a topic known as the “Henry George Theorem.”  It states that the public revenue that provides for the collective goods of an optimally‑sized community equals the land rent of that community.  As presented in Atkinson and Stiglitz (1987, 523-5), the representative agent’s utility function is U(G,X), where G is a collective and X a private good.  Output Y is a function of N workers:

Y = f(N) = XN + G.

X = {f(N)‑G} / N

The wage is the marginal product of labor:

Mf/MN = X

Therefore,

Mf/MN = {(f(N)‑G)/N}

G = f(N) ‑ Nf’(N)

With land and labor the ultimate and original factors of production, rent (R) is the difference between total product Y and total wages:

R = f(N) ‑ Nf'(N)

Therefore,

R = G.

The Henry George Theorem is so named because it echoes Henry George's (1879) single‑tax proposal, that not only should land rent be the only general tax, but that it will be adequate to finance public goods.