Rethinking the Theory of Differential Rent, and How it Affects the Demand for Leverage

Ricardo’s theory of rent, still in the text books, denies that rent enters into prices.  It holds that rents are high because profits are high and not vice versa.

When challenged that this concept may hold for differential rent (that is natural differences in land, Ricardo stressed differing fertility), but it did not apply to extensive rent (that is application of capital to land to improve yields) he responded that this makes no difference as a ‘dose’ of added capital to land not at the margin of cultivation was substitutable for an extension at the margin of cultivation.  If the latter had no rent then the former could charge no rent either or else investment would go to the intensive margin..

The theory was ingenious, much misunderstood and often only taught in part, that is the differential rent aspect, because the argument that extensive rent is equivalent is accepted without question.

Last week in a brief post I outlined a theory regarding extensive rent that challenged whether all of extensive rent is price taking.  The fallacy often made is that an added dose of capital can be applied to land without labour, and similarly that the capital itself is not the result of prior land and labour.   When one considers rent in value terms then the addition of value must affect price. It does not matter what precise cause of value you hold, at this level of abstraction all is necessary is that an increase in value must affect long run price.  Ricardo’s original argument regarding differential rent was that natural differences was not an addition of value and so could not add to price,  Anwar Shaikh contacted me to say that he had developed a very similar theory on his forthcoming book.

Today I want to consider to what extent this applies to differential rent.

Ricardo had a number of prior assumptions.

1) That where there was free uncultivated land, labour could move to it preventing the landowner charging more rent than the value of the natural differential that this land provided.

In cases though where all feasible land was cultivated landlords can charge an additional rent monopoly rent.  This is the origin of the concept in Smith and Rodburtus of Absolute Rent, later developed by Marx.  The level of such rent being the minimum level of wages required to hire (reproduce) the labour force – assumed to be a subsistence level.  Ricardo did take this assumption from Malthus, but did not elucidate the concept of absolute rent that underlay it or set out that the margin of reproduction of an agricultural labour force depended on the  availability of non-agricultural work.

2) ‘Fertility’ was used as a cipher for all natural productivity of land.  Ricardo stressed soil fertility  but other authors have stressed other aspects of natural productivity including location and transport to market (Von Thunen).

The theory can easily be extended to include the full range of these differences as a number of Ricardo’s contemporaries pointed out (Scrope has the most useful generalisation of the ricardian theory).

3)  Ricardo did not consider the capital and labour cost of first reclaiming land at the margin of cultivation.  It is the converse of the problem covered before, you cannot create land without capital and labour.  This omission laid him open to criticism from Carey who argued that the most fertile land was often not first settled because of such costs.  It also led Carey to claim that rent was the return to those who reclaimed the land and inputted capital and labour to maintain the lands fertility.

From these three points almost all of the objections to the Ricardian theory derive.  The theory survives the first two as explained if we include absolute rent and a broad definition of natural differentials.  The problem is the third objection which is at least partially right.  Here is a case of Ricardo not following the rigorous and consistent logic of his modelling through.  If there is a difference in costs and returns at extensive and intensive margins simulataniously what are those differences?

Consider a sum of accumulated capital and a possible decision either to invest it on the extensive margin or to improve productivity of existing land.  Even if land at the margin of cultivation is free it will have a capital cost to reclaim, and an ongoing capital cost to maintain.  Now consider two such pieces of land at the extensive margin each with different costs. The owner of the less costly land will be able to charge a rent equal to the difference in reclamation costs.   This is a form of absolute rent – price setting as it arises from the addition of value to the land.  It is a form of access charge.      If there is no free land the access charge from monopoly increases accordingly.  Absolute rent is price setting not price taking.  Once land is reclaimed and costs of maintenance and reclamation deducted the proportion of rent that arises from natural differentials is pure differential rent, does not result from addition of value, and is not price setting.  Absolute rent on the other hand is a transfer of value to landowners.

One can calculate this addition to differential rent through the method of perpetuities set out in the previous post.  Once land is improved then providing it is maintained then it will permanently grant a yield.  Using the perpetuity formula one can calculate the maximum value of all rent that can be charged on the land.  Providing interest rates are positive the NPV of this addition to value will be finite.  This is will be the maximum capital cost of the land.  The area between this perpetuity curve between two points in time is the yield of services of the rent – the maximum rent that can be charged.

Not all of this rent will be realisable.

Firstly rent is payable in advance typically so the cash flow will need to be discounted over the rental  period (month, quarter, year) according to the prevailing interest rate.  This discount is the difference between the value of the perpetuity in advance, measured at the start of the rental period, and the value of the ordinary perpetuity at the end of it.    If the period is short enough, and real interest rates (after accounting for inflation) low enough it can be disregarded.The resulting differential rent then is the area between the ‘in advance’ and ‘ordinary’ perpetuity curves.

Secondly costs of value added need to be deducted in the manner above.  If a certain capital is invested it will have a payback period.  From the rate of interest and the results of the perpetuity calculation above one can calculate the length of this payback period.  One can then use the annuity formula over this period to calculate the value added.

Even if this land is at the margin of cultivation and the cheapest parcel of land to reclaim and maintain over this payback period there will be alternative potential investments both from the intensive margin and other investments.  Both the return on the capital advanced for improvements and to buy the land must meet the prevailing rate of profit to secure investment.  The yield differential between the least costly piece of land to reclaim and the next least costly will add to absolute rent and so to price.  The upfront capital temporarily and capital of maintenance permanently.

Consider then a case of where the cost of reclaiming the least costly piece of land to reclaim is 10,000 per hectare and the next least costly piece of land 9,000 per hectare.  The absolute rent here would be 1,000 per hectare, the investor however would need to invest 10,000 to reclaim.   This means that land investments will often have a very long payback period, especially where land is not highly differentiated and absolute rents are high.  However where opportunities for investing to create new margins (extensive or intensive) are limited yields on land can be attractive enough for this investment to take place.

This leads to a puzzle, if new capital has to be raised to pay for the improvements but only part of this new capital leads to higher prices of land where does the additional value go?  The answer is that the difference as part of the gross surplus is distributed between holders of capital as money leant – as interest payments, and owners of land (if leased) as differential rent.  The capitalist will be prepared to take a below average profit for a time period to pay back capital invested in return for the perpetuity of creating new land of higher than average profit.  If the land is leased there will be no incentive to do so unless the owner strikes land reclamation and maintenance costs from rent so an average profit is earned for the undertaker throughout – hence the concept of full repairing leases and rent free periods during initial investment periods.

So in many cases of highly differentiated land and where significant opportunities to create new land yield exist the extent of this ‘new land yield’ rent will not be high and can be disregarded.

However where land is not highly differentiated and opportunities to create new land yields are limited the extent of this ‘new land yield’ rent may be very high.  Consider a case for example where there is only one site to extend a town, or only one building where an additional story may be added.  This theory explains why in these cases the rents for this new land is so high and why this rent is added to the price of the land and raises land prices, relative to incomes, overall.

The ‘margin of development’ then, both extensively and intensively, is not absolute it depends on viability.  After all the sea may be reclaimed, mountains may be levelled and additional story’s added to buildings to the limits of engineering but it is rarely viable to do so.  If the costs of such capital improvements fall, due to new techniques ,falling interest rates or regulatory changes then the margin of development can shift.

To give one example Hong Kong has a fixed land mass and regulatory restrictions on reclamation in the harbour.  Recent increases in disposal costs of construction wastes in the PRC has led the government to consider using it instead for land reclamation.

So with this significant modification the ricardian theory of differential rent survives, providing you separate from it intensive and absolute rent and the impact of value creation separately on land price and money price. Carey was wrong in that costs of reclamation and maintenance do not explain all of rent only part, there still remains an underlying natural differential rent.

Though not the conventional ricardian story of the text books this reflects much of the valuation practice in real estate where cost of reclamation is considered a cost which comes off the residual price of land – the widely used residual method.  Indeed we have now a more sophisticated method for calculating the price of land that properly takes into account interest costs of different elements. These differential costs of interest are not considered in standard valuation practice probably because of the assumption of a perfectly differential and infinite land stock which will not occur in many markets.

The theory is able to explain for example why there are real estate booms at times of very low interest rates and available bank lending power. It is also able to explain why there are rapid increases in land prices once opportunities for ‘new land’ are restricted and why this leads to significant increases in demand for leverage.

This argument can also be extended to extensive rent in terms of different methods for upgrading the same piece of land.  The obvious case would be between developing agricultural land between alternative land uses, say housing and industry.  This case deserves its own article as its shines a different light on neoclassical.

In the next post I will explain the broad theory mathematically and graphically.


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