# Why doesn't land value go to 0 when tax rate goes to 100%?

I'm looking at this equation here:

$$y = \frac{ra}{r+x}$$

Where:

• $$y$$ = market value of land
• $$r$$ = real interest rate, set at 0.01
• $$a$$ = land value, set at 1
• $$x$$ = tax rate

I don't really understand this equation conceptually.

• The easiest way to think about this is to consider the fact that you obtain value from land ownership that is not taxable. – 123 Dec 28 '18 at 16:05
• And this extra value left over after a 100% tax rate is that untaxable value? Can you explain? – AntiTruthist Dec 28 '18 at 16:17

## 1 Answer

The correct answer is that it does not. It goes to zero as tax rate increases to infinity.

The reason for that is that the rent derived from land (assuming away any necessary land maintenance) can be thought of as a windfall gain. As a result all incidence of burden from such tax must fall on the holder of the land. Already If the tax is equal or above 100% the whole rent is confiscated and hence the holder of land would be willing to sell it away for nothing, although in the model you shown 100% tax rate would not reduce the property value to zero but to:

$$y=\frac{ra}{r+1}=\frac{0.01}{1.01}\approx0.0099>0$$