Can Land Tax Remove Land Values?

Neil Gilchrist

[date of publication unknown]

Many Georgists repeat a truism stated by Henry George giving it a meaning it does not have. Henry George said that if the full economic rent were taken by the government land would have no selling price. As Henry George equated economic rent with land values, to state that taking the whole land value would leave nothing, is stating the obvious. The mistake is to believe that the full land value can be easily taken. The mistake is amplified when it is assumed that a tax rate of 5 to 10 percent would reduce land values to zero.

It is agreed that you cannot tax land without the value of land being affected. The question is how much is the value affected? (Some will take issue and say that the value of land is unchanged, it is only the price that is affected. However, the value of land is all the costs and benefits, present and future, associated with it, including the tax liability. While land may be valued differently by different people, the only meaningful value to talk about is its value in the market place, that is the price.)

The Value Of Future Liabilities

As the value is not affected only by the current tax liability but also by the anticipated liability for future years one has to estimate how the market values that projected tax liability. I will assume that the market would expect the prevailing tax liability to continue indefinitely. An annual payment of a fixed amount is known as an annuity. Accountants have arrived at the following formula for the present value of an annuity: P = 1/i{1-[1/(1+i)n]} where P is the present value of an annuity of $1, i is the average anticipated interest rate for the period and n is number of periods.

While very few in the market would use the present value of an annuity formula, most would follow informed advice while the intuition of others would be close to the mark. Using this formula for a period of 40 years and an interest rate of 4 percent gives a multiplier of 19.7928, while an interest rate of 10 percent gives a multiplier of about 9.7791. That is a dollar a year for 40 years, at an interest rate of 4 percent is equivalent to $19.79 or at 10 percent $9.78. I have chosen a period of 40 years because that is as far as my table goes, after 40 years there is little change in the value anyway and realistically few people attach any value to money that far in the future.

In the case of an annual tax liability the present value is negative to the tax payer and reduces the value of any investment the tax applies to by that amount. Land values will be reduced by the present value of the projected tax liability, that is the current liability multiplied by a factor to allow for the future liability. What then, will be the land value for a given tax rate?

There are two ways of looking at the problem. You can assume a steady but small increase in the rate over a number of years or you can choose a rate and assume that it applies for a number of years.

Steady Increase Method

If one assumes a steady increase then the Value for a given rate Vr is the Value at a slightly lower rate Vr-1 minus the Value at the lower rate multiplied by the current rate R multiplied by an annuity factor P. The formula is Vr = Vr-1 - (Vr-1 x R x P). For this formula to be accurate the increments (the change in R) must be small. Figure 1 is a graph of this formula assuming an initial land value of $100,000 and an interest rate of about 10 percent (P = 10) and changes in the rate of .1%.

A number of observations can be made from Figure 1:

The land value is asymptotic with zero; The tax value is asymtotic with the untaxed value divided by the annuity factor P; 1. At a rate of 100 percent the tax liability is equal to the land value.

While this formula enables the change in land value and tax liability to be graphed, relative to the rate, to calculate the land value and tax value for a particular rate you calculate all the values for lower rates.

Constant Rate Method

Assuming a particular rate applies for a number of years and that each year the land value is based on the current rate and not anticipated rates enables the value for a particular rate to be calculated without calculating all the intervening rates.

Again I assume an initial land value of $100,000 and an interest rate of about 10 percent (P = 10) and this time an interest rate of 1 percent. Table 1 shows the Land Value, Tax Liability, Change In Tax Liability, and the Change In Tax Liability as a percentage of the original value.

LAND VALUE	YEAR	TAX LIABILITY	CHANGE IN TAX LIABILITY	CHANGE AS PERCENT OF ORIGINAL VALUE
100,000.00	1	1,000.00	1,000.00	1.00000
90,000.00	2	900.00	-100.00	-0.10000
91,000.00	3	910.00	+10.00	0.01000
90,900.00	4	909.00	-1.00	0.00100
90,910.00	5	909.10	0.10	0.00010
90,909.00	6	909.09	0.01	0.00001
90,909.10	7	909.09	> 0.00	> 0.00000

Table 1.

The land value and tax liability continue to gravitate in ever decreasing amounts to a point where they remain constant. In each successive year the change in tax liability is equal to the original value multiplied by the tax rate to the power of the number of years. For example in the second year the change in liability is 100,000 x .12 . The equilibrium tax liabitity of $909.09 cents is equal to the sum of the changes in the tax liability $1,000 - $100 + $10 - $1 + 10c - 1c. The general formula is Vr = V0 - (V0 x P x (r - r2 + r3 - r4 + r5 - r6 ...) where V0 is the initial value. I assumed that the market was not anticipating shifts in land value due to the tax liability. In reality the market would quickly move to the equilibrium land value based on the formula above.

Both formulas gives the same results up to a rate of 100 percent provided that the increments are sufficiently small in the first and that the rates in the second is extended to a high enough power. The second formula does not work for a rate of 100 percent or greater. 1, that is 100/100, to any positive power is 1. Greater than 100 percent the values become meaningless.

All Else Equal?

The above changes in land values assume that all else remains equal (ceteris paribus). However, even if no other taxes were removed you would expect an increase in economic activity. As the rate of land tax increases those land holders that under- utilise their land will want to generate an income to cover the tax by applying higher levels of capital and/or labour. An increased level of economic activity is another way of saying there will be more wealth. Higher levels of wealth will be reflected by an upward pressure on land values.

The revenue raised from land value taxation will enable the removal or reduction of other taxes. The removal of stamp duty will remove an up front cost of purchasing property and this will be reflected directly in land values. The removal of payroll tax will result in more demand for labour. Increased demand will reflect in higher wages and in more people having wages. The removal of income tax will directly increase the after tax income of everyone who currently pays it.

Furthermore, as the cost of production and exchange is reduced by the removal of taxes and the costs of complying with tax laws, the price of goods and services will fall. Increased buying power is the same as having an increased income. All this additional wealth will be reflected in land values.

A society that taxes capital and labour less than another, even to the point of not taxing them at all, will attract labour and capital from outside. This inflow of labour and capital will increase the demand for land and will be reflected in land values.

The Right Message

Georgists should not argue that land values will disappear if land value taxation is extended to a broader base and increased to a higher rate. They should not do so for two reasons. One, it is not true. Two, it is poor sales technique to tell over 70 percent of Australians that own land that their most valuable asset would disappear if our policies were followed. What is true is that land would become more affordable and the whole population wealthier!