# Why can we collect more Ricardian Rent than the land has to offer?

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?

• Please edit your question to display formulas in Mathjax. – Giskard Jun 3 at 5:19