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1MM, ideal tax-independent property value = $P_p$

1% tax rate, x, on market tax-dependent property value, $P_t$

$0.01 * P_t = tax revenue = T_r$

$T_r$ over real interest rate, $R_r = M_p$, market value of that perpetuity

$P_p - M_p = P_t$

sub

$P_p - \frac{T_r}{R_r} = P_t$

$P_p - \frac{P_t * x}{R_r} = P_t$

$P_p = P_t + \frac{P_t * x}{R_r}$

$P_p = \frac{P_t * R_r}{R_r} + \frac{P_t * x}{R_r}$

$P_p = \frac{P_t * R_r + P_t * x}{R_r}$

$P_p = \frac{P_t(R_r+x)}{R_r}$

$P_p * R_r = P_t(R_r+x)$

$\frac{P_p * R_r}{R_r+x} = P_t$, the market value of property, is the ideal value of the property times the real interest rate, all over the real interest rate plus the tax rate.

Tax revenue, $P_t * x = \frac{x(P_p * R_r)}{R_r+x}$, hits a ceiling no matter how high x goes.

A Georgist 100% tax rate, where $x=1$, is where market value and tax revenue intersect. $\frac{P_p * R_r}{R_r+1}$ gives us the Ricardian Rent value of the property.

We can see what percent of a land plot's Rent we collect at any tax rate x:

$ = \frac{T_r}{Rent}$

$ = \frac{T_r}{\frac{P_p * R_r}{R_r+1}}$

$ = \frac{x * P_t}{\frac{P_p * R_r}{R_r+1}}$

$ = \frac{\frac{x(P_p * R_r)}{R_r+x}}{\frac{P_p * R_r}{R_r+1}}$

$ = \frac{\frac{x(P_p * R_r)(R_r+1)}{R_r+x}}{P_p * R_r}$

$ = \frac{x(P_p * R_r)(R_r+1)}{(R_r+x)(P_p * R_r)}$

$ = \frac{x(R_r+1)}{R_r+x}$

Looks like it's possible to collect more Rent than the land has, but it flattens out. How is this possible?

Also, we collect 50% of the Rent already?

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    $\begingroup$ Please edit your question to display formulas in Mathjax. $\endgroup$ – Giskard Jun 3 at 5:19

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