# Chapter C: Land and resources taxes

## C2. Land tax and conveyance stamp duty

## Annex C2: Relationship between the rate of tax on land and a tax on economic rent

The economics of land tax can be analysed using a relatively simple model (adapted from Oates and Schwab 2009).

Assume that the value of land (L) depends on the rental income (r) and an interest rate (ρ) over n years, so that:

*L*=

*r*

_{}

*ρ*)

^{ }

*r*

*ρ*)

^{2}

*r*

*ρ*)

^{3}

*r*

*ρ*)

^{n}

^{n}

∑

^{s=1}

*r*

*ρ*)

^{s}

Since land does not depreciate with time, it is reasonable to assume that the value depends on the cash flows into infinity so that:

*L*=

*r*

*ρ*

This means that when market interest rates are at 5 per cent, land that returns a rental income of $30,000 will sell at $600,000 in the market. Now assume that a tax on land value (t_{L}) is introduced and because it is broad (and land is in fixed supply), there is no way for the landowner to pass it onto the tenant. The annual rental income to the owner (r) is reduced by (r — t_{L}L). Substituting this into (3) we find:

*L*=

*r*

*ρ + t*

_{L}

The market value of land has been reduced. For example, a land tax rate of 1 per cent would see the value of land fall to $500,000; that is, equivalent to the present discounted value of the tax liability of $100,000. Any new buyer of the land will receive a rental income of $30,000, out of which a tax of $5,000 would be due. But because they only paid $500,000, they still earn an post- tax return equivalent to the market return of 5 per cent (that is $25,000). The purchaser is effectively compensated for the tax payments by the fall in the price of land.

This model allows the rate of a land value tax (t_{L}) to be compared against an equivalent tax directly on economic rent (t_{r}). If the two revenues are equal, then r t_{r} = L t_{L} and equation (4) implies:

*t*=

_{r}*t*

_{L}*t*

_{L}+ ρ

So at a 5 per cent interest rate, a 1 per cent land tax is equivalent to a 17 per cent tax on economic rent.

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