An Unnecessary Book on Environmental Economics?

In the internet age, a collection of fine articles may not make a worthwhile book.

Edward Elgar Publishing have recently published a seventh edition of Economics of the Environment: Selected Readings (1), a collection of 34 articles on a wide range of topics in environmental and natural resource economics, edited by Robert Stavins.  According to the publisher, it “serves as a valuable supplement to environmental economics textbooks and as a stand-alone reference book of key, up-to-date readings from the field”. 

A virtue of the book is that, while the articles are all republished from academic journals, most of them are towards the more readable and less mathematical end of the spectrum of academic writing on economics.  I will comment briefly on a few.

Article 2 – Coase’s The Problem of Social Cost (1960) – is a seminal work in which he challenges the view that the appropriate policy response to a negative externality is either a Pigovian tax or regulation. Instead, he lays emphasis on a comparison of the overall economic effects of alternative social arrangements defining the respective rights of the parties, and on the transaction costs which arise if a party attempts to negotiate agreement with another party to infringe their rights in return for payment.  His numerous detailed examples illustrate the range of circumstances to which his arguments apply – but many readers will probably prefer to skip some sections in order to focus on the main points.

Articles 5 to 7 by, respectively, Carson, Kling et al and Hausman (2012), set out alternative positions on the contentious issue of the role of the contingent valuation method for valuing non-market environmental goods.  They focus especially on the conditions under which contingent valuation studies may be subject to hypothetical bias, where individuals overstate their willingness to pay for an environmental good.  I discussed these articles in this post.

Article 12 by Schmalensee & Stavins (2017) is a useful and fairly concise analysis of the performance of and lessons from seven cap and trade (marketable permit) systems intended to reduce emissions at a lower cost than would a command-and-control approach.  It considers six US systems differing in type of emission addressed and regional scope – notably the national Sulphur Dioxide Allowance Trading Program that began in 1995 –, as well as the EU Emissions Trading System, a multi-country system focused on CO2 emissions which started in 2005.  Among the lessons identified are a) not to require prior approval by a central authority of trades in emissions allowances; b) to establish rules and obtain accurate data well before the start of the first compliance period; c) to limit price volatility by price collars and by permitting allowances to be carried forward to the following period (allowance banking).

Article 16 by Covert, Greenstone & Knittel (2016) asks whether natural supply and demand forces (that is, without policy intervention) can be expected to significantly reduce fossil fuel consumption and so help to mitigate climate change.  They consider two kinds of such forces: increases in the costs of extracting fossil fuels; and technological advances improving the energy efficiency of existing technologies and developing new carbon-free technologies.  Their conclusion that fossil fuels will remain the primary energy source without policy intervention may not be a surprise, but it is useful to have the evidence for this set out in detail.

Article 24 by Tol (2018) considers the overall economic effects of future climate change, drawing on the conclusions of many previous studies of general and specific effects of climate change, and also considers recent estimates of the social cost of carbon (which should inform the welfare-maximising rate of a carbon tax).  As might be expected, he concludes that the overall effects of climate change in the long run are negative.  On the crucial issue of quantifying the negative effect, he suggests that the welfare effect of a century of climate change is unlikely to exceed that of losing a decade of economic growth.  But this conclusion is importantly qualified by recognition both that the effect on poor tropical countries is likely to be especially large and that the range of uncertainty is very wide.

Article 30 by Shogren & Taylor (2008) assesses the relevance of behavioural economics to environmental and natural resource economics, referring to much previous literature on this topic.  One of various arguments considered is that markets tend to encourage rational behaviour, in aggregate if not at the level of individual participants, and that the insights of behavioural economics are therefore especially relevant to behaviour in respect of non-market environmental goods. The conclusions reached are in my view balanced: neither dismissing the behavioural approach, nor over-stating the extent to which it requires modification of conventional analysis and policy recommendation based on an assumption of consistently rational behaviour. 

Although the book certainly contains some fine and mostly recent articles, I find it difficult to see who would want to buy it at a (current online) price of £130.50 (hardback) or £35.96 (paperback).  The world of publishing has changed since the first edition (1972).  Those affiliated to an academic institution will probably have free access to most if not all the articles via institutional arrangements with the original journals.  Moreover, nine articles are from the Journal of Economic Perspectives, an open access journal.  Another four (articles 3, 12, 24 & 27) I found to be freely accessible on the websites of the Review of Environmental Economics and Policy and the American Economic Review, subscription journals which however make the full text of selected articles freely available.  The Coase article is available within the open-access part of JSTOR.  So even without an institutional affiliation, it is possible to obtain free (and legal) access to at least 14 of the articles. 

Notes & References

  1. R N Stavins (ed) (2019)  Economics of the Environment: Selected Readings, 7th edition,  Edward Elgar Publishing   https://www.e-elgar.com/shop/economics-of-the-environment
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Some Thoughts on this Blog

When I started this blog in 2012, I considered – having looked at many other blogs – that posts should be short and frequent, and my early posts were all well below 1,000 words.  But it gradually became apparent that for many topics I could not present the sort of sustained argument I wanted to make within that limit. I do aspire to persuade, and not just address readers who already agree with what I say.  Hence my posts became longer and less frequent.   Many are in the region of 2,000 to 3,000 words, and the longest – a review of Dieter Helm’s Natural Capital: Valuing the Planet – extends to some 8,000 words.

Through WordPress I can access statistics giving some idea of which of my 54 posts have received most views.  The statistics are not as helpful as they could be, with a high proportion of views classified under the catch-all category of “Home page / Archives”.  Based on the classification of the remainder, some posts have been viewed far more times than others.  The ten most-viewed posts are as below, in descending order of views (counted from the date of posting to the end of 2018).

  1. The Economics of a Carbon Tax (20/2/2013)
  2. Of Fish, Fishers and Consumers (23/6/2013)
  3. Explaining Environmental Policy Failure (1/12/2017)
  4. Pollution Control and Output (30/12/2016)
  5. A Valuation Case Study: The Great Barrier Reef (15/7/2017)
  6. Green Space: An Important Use of Urban Land (28/7/2013)
  7. Net National Product and Sustainability (17/5/2017)
  8. In Defence of the Linear Demand Function (21/6/2016)
  9. Reducing Pollution with a Combined Tax and Subsidy (6/9/2012)
  10. Lessons from the Industrial Revolution (7/3/2013)

Of the less-viewed posts, the following are some with which I am especially pleased:

While some posts relate to matters that were in the news at a particular time, all are intended to address or illustrate more general issues in the field of environmental and natural resource economics and related disciplines.  I’m not trying to build up an encyclopaedia – which would be absurdly ambitious -, but I hope that some may find my posts, including some of the older ones, a useful resource.  With that hope comes a responsibility to try to improve older posts where possible, which may include explaining points more clearly, improving layout and – yes – on occasion correcting errors.  In that spirit I have recently made substantial amendments to Net National Product and Sustainability and minor changes to several other posts.

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Fish Imports, Tariffs and Conservation

A recent paper proposes that, post-Brexit, the UK should lower tariffs on imported fish to benefit consumers.  That may be a good idea, but the effect on fish stocks in the regions of origin should also be considered.

The Institute of Economic Affairs has published Plan A+: Creating a prosperous post-Brexit U.K. by Singham and Tylecote (1).  The paper is wide-ranging, but of particular interest from an environmental perspective is a short section on fish and fisheries (2).  It includes a proposal that tariffs on certain imported fish should be lowered once Brexit allows the UK to do so (3).  That set me thinking. Generally I favour free trade so that countries can gain from specialising in industries in which they have a comparative advantage, but sometimes short-term gains from trade must be weighed against long-term costs. When the traded good has been harvested from a renewable natural resource such as fish, there clearly is a possible long-term cost in that the quantity of fish imported could contribute to over-exploitation and depletion of the resource.

A little background.   Currently, fish imported into the UK from outside the EU are subject to the EU’s common customs tariff.  Imports of Pacific bluefin tuna, for example, carry a tariff of 22% (4).  Once the UK leaves the EU, and subject to the terms of any Brexit agreement, it will be free to set a lower tariff, or none at all.  Arguments regarding import tariffs typically focus on the protection they offer to domestic producers and the costs they impose on domestic consumers.  The UK fishing industry contributes £1.4 billion annually to the UK economy and employs some 24,000 people (5).  But tuna in recent years has been rare in UK waters (6).  Commercial fishing of tuna by UK fishers is virtually non-existent, and the same goes for some other fish types.

Singham and Tylecote’s proposal to lower tariffs on imported fish relates specifically to those types of fish that are consumed but rarely caught in the UK.  Reduced tariffs, they state, would benefit consumers but have little effect on the UK fishing industry.

Let’s examine these claims.  For any fish type, UK demand is only a small proportion of world demand.  Whether or not the UK levies a tariff therefore has only a small effect on the world price (7).  If a tariff is levied, then it raises the price to UK consumers by most of the amount of the tariff.  Conversely, starting from the UK’s current position, lowering the tariff will reduce prices by most of the amount of the tariff reduction.  That’s a clear benefit to UK consumers.

The claim that there would be little effect on the UK fishing industry is more problematic.  Singham and Tylecote’s point is that the fish types mainly caught by UK fishers – cod, haddock, mackerel, etc – are not those on which they advocate a lowering of tariffs.   But the relevance of this depends on consumer behaviour  in respect of fish purchases, which can usefully be described in terms of the cross-elasticity of demand, a measure of how a change in the price of one good affects demand for another.

Suppose cod and tuna can be taken as representative respectively of UK-caught and imported fish.  If the cross-elasticity of demand between cod and tuna were close to zero – that is, a change in the price of one would have very little effect on demand for the other – then Singham and Tylecote’s argument would be valid.  But it would fail if there were a large positive cross-elasticity of demand, implying that consumers regard cod and tuna as good substitutes. The reality is probably somewhere in between, a situation sometimes described by saying that the goods are weak substitutes. Cod is a white fish while tuna is an oily fish, an important distinction for consumers in terms of both taste and nutrition.  So far, then, Singham and Tylecote’s claim that there would be little effect on the UK fishing industry seems to have a degree of validity.

However, about one third by value of the UK catch consists of oily fish such as mackerel (8). The cross-elasticity of demand between tuna and mackerel seems likely to be fairly high.  If so it would further weaken Singham and Tylecote’s claim.

It might also have been suggested that the interests of millions of fish consumers should take precedence over those of the relatively small number of people employed in the UK fishing industry, but that is not an argument used by Singham and Tylecote.

The above analysis is entirely within a comparative static framework, which is fine so far as it goes.  When considering the economics of a natural resource at risk of depletion, however, it can never give the full picture.  It has no regard to the importance of conservation of fish stocks so as to ensure continuing catches for the benefit of future consumers. This prompts me to pose the following question:

If country A imports fish caught by country B within B’s waters (eg its Exclusive Economic Zone (EEZ)), should A’s policy on fish imports have regard to the conservation of B’s fish stocks?

Admittedly the scenario posited by the question is only one of several possibilities: imported fish might be caught (under agreed arrangements) in a third country’s EEZ, or in international waters.  It does I believe present the issue I want to consider in its simplest form.  Here are some arguments that might be adduced.

The sovereignty argument: No
Management of the fish stocks within B’s waters is entirely a matter for B.  Whether it chooses to conserve or to over-exploit is its own decision.  It is no business of A’s to interfere, and to do so could infringe B’s rights under the UN Convention on the Law of the Sea (9).

The laissez-faire argument: No
The fact that there is, and will probably continue to be, a market for exports of fish caught in B’s waters provides B with an incentive to conserve its fish stocks.  Although A has an interest in continuing to have the opportunity to import fish from B, there is no need for it to take any particular steps to that end.

The second-best argument: Yes
B may not be managing its fish stock in a sustainable manner, as evidenced by declining fish populations in its waters.  By limiting its fish imports from B, A can help to limit demand for B’s fish.  Other things being equal, reduced demand will reduce the quantity of fish that B’s fishers can profitably catch in its waters and so contribute to conservation of its fish stock for the benefit of future consumers, including those in country A.

The public choice argument: Yes
B’s government may understand the long-term benefits of conservation, but find it politically impracticable to override a fishing industry lobby defending its short-term interests.  A’s government, however, may find it relatively easy to limit its fish imports, imposing a small cost on each of a very large number of consumers.

All these arguments could have a degree of validity, subject to the detailed circumstances. But the applicability of the sovereignty argument is I suggest very limited indeed.  The UN Convention on Law of the Sea does indeed assign sovereign rights to a coastal country within its 200 nautical mile EEZ.  Those rights, however, are not the equivalent of the sovereignty a country exercises over its land territory: they do not amount to the right to do almost anything it likes. Article 56 specifies that, within its EEZ, a country has:

“sovereign rights  for the purpose of exploring and exploiting, conserving and managing the natural resources, whether living or non-living, of the waters …” (9)

Article 61 explictly forbids over-exploitation of living resources:

“The coastal state, taking into account the best scientific evidence available to it, shall ensure through proper conservation and management measures that the maintenance of the living resources in the exclusive economic zone is not endangered by over-exploitation.” (10)

If B – like most countries (11) – has ratified the Convention, then for A in its policy on fish imports to have regard to the conservation of B’s fish stocks could hardly be described as interference.  It would be helping B to fulfil its treaty obligations.  Even if B were not a party to the treaty, no one would suggest that for A to adopt a trade policy such as an import tariff would in itself amount to interference or an infringement of sovereignty. Any such claim would have to refer to the intentions underlying A’s policy.  There is a subtle difference between a country adopting a trade policy to advance its own interests, without particular regard to its effects on another country, and adopting perhaps the same policy with the intention of affecting another country in a specific way.  Trade sanctions would be an extreme case of the latter.  A policy intended to help conserve another country’s fish stocks would be, at worst, a very mild form of interference.

The laissez-faire argument would be a good one in circumstances in which B is effectively managing its fish stock in a sustainable manner, with regard to its long-term commercial interests.  However,  there are many fisheries for which this is not the case.  The FAO estimated that in 2013 31% of the world’s marine fish stocks were fished at a biologically unsustainable rate (12).

Where, for whatever reason, B is not managing its fish stock sustainably, the second-best argument becomes relevant.  For country A through its trade policy to try to contribute to conserving B’s fish stock is an inferior approach to effective management by B itself, but it may be better than nothing, especially if A’s policy can be coordinated with that of other importing countries.  A coordinated tariff could ensure a significant lowering of the world price of the fish, resulting in a worthwhile reduction in the quantity demanded and so make a material contribution to conservation of B’s fish stock.  It could also avoid the objection that a tariff adopted by one country alone would impose a cost on its consumers but do little towards conservation and therefore little to safeguard continuing imports of the fish for its consumers in future.

Where the reason B is not managing its fish stock sustainably relates to the lobbying power of its fish industry, the second-best argument may be complemented by the public choice argument.  What is envisaged here is far from the situation in which a powerful producer lobby achieving gains for itself at the expense of many dispersed consumers.  In the right circumstances, perhaps via coordination with other importing countries as above, the cost to consumers would be in return for a benefit to future consumers via conservation of B’s fish stock and continuing imports.

In conclusion, my main concern about Singham and Tylecote’s proposal to lower tariffs on certain imported fish is that it is presented without any consideration of the possible effects on fish stocks in the marine regions of origin.  Whether detailed information on the state of those fish stocks and the way in which they are managed would strengthen or weaken the case for their proposal is beyond the scope of this post.  But it would be unwise – an application of the precautionary principle – to lower tariffs without a careful examination of what the full effects might be.

Addendum 27 November 2018: WTO Rules and Fish Conservation

Would the imposition of a tariff with the aim of conserving fish stocks in another country’s waters be consistent with WTO rules?  Such a policy would carry a risk of non-compliance with GATT Article I (13), which requires that any advantage granted to one country must be granted to all others.  The logic of setting a tariff with a conservation aim would suggest that, if country B’s fish stocks are more depleted than country C’s, then a higher tariff should be levied on fish imports from country B.  But that is just what Article I prohibits.  The most that could be done, consistently with Article I, would be to set a uniform tariff having regard to the average conservation status of fish stocks in all relevant fish-exporting countries.

However, WTO rules do permit certain exceptions to Article I.  The most relevant appears to be Article XX(g) which permits measures:

“relating to the conservation of exhaustible natural resources if such measures are made effective in conjunction with restrictions on domestic production or consumption” (14)

Fish as a natural resource are normally described as “renewable” rather than “exhaustible”, but in the US-Shrimp case it was held that in certain circumstances a living species could be considered exhaustible (15).  The clause about domestic restrictions requires “even-handedness” (16) in promoting conservation domestically as well as abroad.  Where a type of fish is both imported and caught in a country’s own waters, this requirement could perhaps be met by combining a tariff on imports with a tax on domestic production.

Paragraph (g) is subject to the overriding condition in the preamble of Article XX that such measures:

“are not applied in a manner which would constitute a means of arbitrary or unjustifiable discrimination between countries where the same conditions prevail …”.

To demonstrate that this condition is satisfied would seem to require, as a minimum, very good scientific evidence regarding the conservation status of fish stocks in different countries, together with a clear link between the scientific findings and the tariff rates both across countries and between fish species.

Notes and references

  1. Singham S & Tylecote R (2018) Plan A+: Creating a prosperous post-Brexit U.K. , IEA Discussion Paper 95 https://iea.org.uk/publications/plan-a-creating-a-prosperous-post-brexit-uk/
  2. Singham & Tylecote, as 1 above, pp 64-67.
  3. Singham & Tylecote, as 1 above, p 66.
  4. European Commission Market Access Database http://madb.europa.eu/madb/euTariffs.htm?productCode=03023599&country=US
  5. Ares E, Rhodes C & Ward M (2017) The UK Fishing Industry House of Commons Library Debate Pack 2017/256
  6. Although it is beginning to become slightly more common. See https://phys.org/news/2018-04-experts-team-bluefin-tuna-uk.html
  7. Suranovic, S M International Trade Theory and Policy Trade 90-5 http://internationalecon.com/Trade/Tch90/T90-5.php
  8. UK National Statistics (2017) UK sea fisheries annual statistics report 2016 https://www.gov.uk/government/statistics/uk-sea-fisheries-annual-statistics-report-2016 See Chapter 3 Table 3.2.
  9. UN United Nations Convention on the Law of the Sea http://www.un.org/depts/los/convention_agreements/texts/unclos/unclos_e.pdf  p 40
  10. UN, as above, p 46
  11. Wikipedia UN Convention on the Law of the Sea – Parties https://en.wikipedia.org/wiki/United_Nations_Convention_on_the_Law_of_the_Sea#Parties
  12. FAO (Food and Agriculture Organisation of the United Nations) The State of World Fisheries and Aquaculture 2016  http://www.fao.org/3/a-i5555e.pdf  p 38.
  13. GATT Article I https://www.wto.org/english/docs_e/legal_e/gatt47_01_e.htm#articleI.  Note that the original GATT 1947 agreement has been incorporated into subsequent GATT / WTO agreements.
  14. GATT Article XX https://www.wto.org/english/docs_e/legal_e/gatt47_02_e.htm#articleXX
  15. WTO Trade Report 2010 E.Natural resources, international cooperation and trade regulation p 168 https://www.wto.org/english/res_e/booksp_e/anrep_e/wtr10-2e_e.pdf
  16. WTO Trade Report, as above, p 168
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Housing, Countryside and Economic Welfare

If we can value ecosystem services, then the “housing v countryside” debate can be treated as an optimisation problem.

Cities often expand laterally to provide housing for an increasing population. This usually involves a loss of surrounding farmland, woodland, wetlands or other countryside, and consequent loss of the ecosystem services they used to provide.  Opinions on housing and the countryside often tend towards one of two extreme positions.  There is the view that land must always be made available to meet some conception of “housing need”, regardless of the resulting destruction of the countryside.  At the other extreme is the view that countryside around cities (Green Belt as some is designated in the UK) should be inviolable, implying that “urban sprawl” should always be prevented.

An Economic Model of Land Use In and Around a City

Economic analysis offers a way to articulate a third view.  To anyone with a little economic training the following formulation may seem quite natural, a straightforward application of the equimarginal principle of optimisation to the case of different land uses:

Overall welfare is maximised if housing extends up to, but not beyond, the point at which the marginal value of housing per unit of land equals the marginal value of an undeveloped unit of land.

This is represented in Diagram 1 below.  Line MVH shows the marginal value of housing, falling as housing area is increased. Line MVU shows the marginal value of undeveloped land, rising as housing area is increased and therefore less undeveloped land remains.  In the case shown, the area occupied by housing is H0, the red area represents the total economic value of housing, and the green area the total economic value of undeveloped land within the relevant area.  However, overall welfare is maximised where the respective marginal values are equal, that is, at the intersection of the marginal value lines, with housing area H*, and declines with distance from H* on either side.  With housing occupying area H0, therefore, welfare is less than it might have been by the amount represented by the blue triangle (though more than it would have been if H0 had been even further to the left of H*).

Welfare Effect of Urban-Rural Boundary

Now I do indeed think that this is a useful model to have in mind when considering policy towards housing development. Nevertheless, the assumptions on which it relies are considerable.  Awareness of those assumptions can help to ensure that we do not misapply the model.

I begin with some general remarks about assumptions in relation to economic models.  Some assumptions are just convenient simplifications, useful for presenting a model but readily replaced by more realistic descriptions in empirical work that pretends to any degree of accuracy.  Others are more essential to the model, indicating limitations in scope beyond which it would not work or be fundamentally altered. In the present case, the assumption of  linearity of the marginal value lines is just a convenient simplification.  The fact that these lines are monotonic (downward sloping in one case and upward sloping in the other) is more essential: if instead the lines were complex curves with both downward and upward sloping regions, then there could be multiple local optima at which the marginal values were equal, and welfare would not always be lower if H0 were further from the global optimum.

The spatial and temporal frameworks of the model require comment.  The assumption that all relevant land is either undeveloped or used for housing ignores other urban land uses (businesses, roads and railways, urban parks, etc) but is a convenient simplification.  The same can be said of the assumption that there exists a fixed area of “relevant land” in and around a city. What matters for the model is that it considers the respective marginal values over the range of areas of land relevant to a particular question. In terms of the diagram, moving A a little to the left or right will not change either the position of H* or the area of the blue triangle.  Similarly, it could be acceptable to truncate the diagram at the left, setting the origin at, say, 500 hectares rather than at zero area. This would change the position of H* only in the trivial sense that it would be closer to the new origin.  Its true position relative to the area indicated by the horizontal scale would be unaffected.

A measure of welfare should relate to a defined period.  It is convenient to take the period to be short (one year at most), since then in most circumstances we can ignore additions to the housing stock during the period.  This is a reasonable assumption because additions to housing in any period are usually only a very small proportion of total stock. Policy on housing development relates to the model in that the housing stock reflects policies in many past periods, which may or may not have changed the quantity or character of housing development from that which would have been delivered in a free market.  Thus the model relates welfare in a period to the outcome of policy and market forces in many previous periods.  What the model does not do, and it is a significant limitation, is draw out the full consequences of policy at any time for welfare extending over many periods.

Nor is the model designed to show the welfare effects of possible additional housing development.  That would require consideration of housing construction costs, which do not feature in the model (the assumption of no additions implies that all construction costs were incurred in past periods and are therefore sunk costs, irrelevant to welfare in the period of interest).  Any welfare comparisons inferred from the model are not comparisons before and after new development.  They are comparisons involving one or two hypothetical alternatives to the actual situation in the period, based on counterfactual assumptions about the quantities of housing development in past periods.

The Value of Land with Housing

Consider now the marginal value of housing line.  Because the horizontal axis measures land area, the line must be taken to mean the marginal value of housing per unit of land area.  A simple interpretation of the line starts from assumptions of uniform housing density and uniform utility to residents per home.  Given these assumptions, residents have no reason to prefer one home to another.  Ignoring externalities (which we will consider below), the marginal value of housing line would therefore be a pure price-quantity relation, its downward slope reflecting the greater quantity demanded of housing of uniform utility when the price of housing is lower.

Suppose that, with a view to greater realism, we drop the uniform utility assumption and take it instead that, although housing is of uniform density, homes differ in attributes such as quality and location which determine their utility to residents.  Then we must expect the price of housing in a particular location per unit of land to depend upon both its attributes and the total quantity of housing.  But if homes are not equivalent, on which land shall we take the marginal unit of housing to be?  For the purposes of economic welfare analysis, we should ignore geographical considerations, such as distance from the city centre, and take units of land in descending order of utility of their housing.  Thus the marginal unit of land with housing is that at which the homes offer the least utility.

Table 1 below shows how this would work for a very simple case with just three land units, identified in descending order of utility as L1, L2 and L3.  H is the number of units occupied by housing and, given uniform housing density, also measures the quantity of housing.  The locations have demand functions with the same downward slopes with respect to housing quantity, but different choke prices reflecting their different utility.  In the demand columns, an entry of “na” against an area indicates that it would have no housing at the relevant value of H.

Derivation of MV of Housing

The entries in red trace the marginal value of housing line: if for example H = 2, then the marginal unit is L2 for which demand is 11.  Note that, unlike in the case of uniform utility, this line is not a pure price-quantity relation.  Of the fall in marginal value of 7 from H = 2 to H = 3, for example, 2 is due to the higher quantity of housing and 5 to the lesser utility of L3 than L2.

Thus we can derive a downward-sloping marginal value of housing line without assuming uniform utility, at least within the area of existing housing.  To extend the line into the area of undeveloped land, we would need to make an assumption about the quality of the homes that might be built on that land.

Even within the area of existing housing there are further issues with the concept of the marginal value of housing line.  We have noted that location is an attribute that can affect the utility offered by a home.  Some characteristics associated with location, such as risk of subsidence or flooding, may be permanent.  Within a city, however, most of the utility associated with a home location relates to ease of access to and quality of shops, schools, transport links, employment opportunities, business and social networks, parks, and so on.  Importantly in this context, differences in housing quantity at the margin can be associated with differences in the locational attributes of intra-marginal homes.  In other words there can be positive or negative externalities associated with particular homes, that is, social benefits or costs not accruing to or borne by residents of those homes.  Comparing situations with larger and smaller numbers of residents, the former may for example have more or better shops, different social mixes in schools, more congestion on roads and public transport, and more networking opportunities. Such externalities imply that the utility of any one home is not fixed but may depend upon the quantity and location of other homes.  Consequently, an ordering of land units defined in terms of housing utility may itself not be fixed.

In most cities the density of housing is far from uniform (with the inevitable consequence that there is no simple relation between housing area and quantity of housing (whether measured as number of homes or as floor space).  One way to handle this within the model is to treat density as another characteristic of location.  Thus demand for housing on a unit of land on which there is a tower block containing many flats will be the sum of the demands for the individual flats.  Subject to quality, that housing will have a much higher value per unit of land than land with low-rise homes, and so feature earlier in the ordering of land units.

Another approach starts from the observation that, in some cities, most high-rise housing developments are towards the centre.  For such cities, it may be a reasonably good approximation to reality to treat the outer suburbs as being of uniform density.  One might then exploit the possibility noted above of truncating the model at an area chosen so as to exclude most high-rise developments.

Unfortunately these approaches, though consistent with our model, are unsuited to addressing the important practical issue of selecting the appropriate density for new housing developments.  As many have pointed out, building housing at fairly high densities, either on undeveloped land or by redevelopment of urban sites, can limit the extent to which cities impinge on their surrounding countryside.  In this context, we really need a more complex model which considers how welfare can be maximised when both the area of land used for housing and the density of housing on that land are considered variable.  That is beyond the scope of this post.

A further issue concerning the marginal value of housing line is the definition of the underlying concepts of demand and price.  Since the model relates to a period, demand must be taken to mean demand for the use of housing for the period by both tenants and owner-occupiers, sometimes termed demand for housing services. Tenant demand can be equated with willingness to pay a period’s rent for a home.  Owner-occupier demand for a period’s use of housing is a theoretical construct that would have to be inferred from market data, with suitable adjustments to exclude the effect of any speculative element in market values.  That has its complications, but without such a concept of housing demand it is hard to see how economic welfare analysis can be applied to housing.

The Value of Undeveloped Land

The economic value of the undeveloped land is the total value of the various ecosystem services it provides over the period.  It includes the market value of the agricultural products of farmland less the costs of inputs other than land.  Often more important, however, are the values of non-market services including water purification, drainage, support for biodiversity, carbon sequestration, and opportunities for outdoor recreation. These values would have to be estimated using suitable non-market environmental valuation techniques (1). Some of these techniques are contentious, and none can be expected to yield more than very approximate value estimates.

If we assume that the ecosystem services are uniform across the land, then we can interpret the marginal value of undeveloped land line as a pure value-quantity relation.  Whether such a line would be upward-sloping would depend on the type of land use.  If the undeveloped land were all used for agriculture and were all of similar quality for that use, then its value might be roughly proportional to its area. Agricultural products from farmland may be sold on markets supplied by many regions, and the small changes in total market supply that would result from changes in the amount of farmland around one city would not significantly affect prices.  Proportionality would also probably apply to woodland if its main value elements were timber sold on markets supplied by many sources, and carbon sequestration contributing through atmospheric mixing to mitigation of the global increase in atmospheric greenhouse gases.  The model will work with a horizontal marginal value line for undeveloped land, provided that the marginal value of housing line slopes down so that the lines meet only at one point.

For some other land uses, the marginal value will be greater if there is less undeveloped land.  This applies especially to recreation.  If there is much open-access countryside within easy reach of a city’s inhabitants, then a little more or less would be unlikely to be of much consequence, but if only a little remains, then its marginal value would probably be considerable.  Recreational land much further from the city could not be considered an adequate substitute, given the greater travel costs city residents would have to incur to enjoy it (2).  It could also apply to aspects of biodiversity.  An animal species usually needs to forage or hunt for food, and this may be impossible if the remaining area of otherwise suitable habitat is too small, leading to loss of the species from the locality.   For such land uses, the marginal value of undeveloped line might be expected to slope upwards with increasing use of land for housing.

In most circumstances, however, the mix of ecosystem services provided by a unit of land will differ between units.  Provisioning services such as food crops and timber may relate to clearly delineated subsets of the total undeveloped area.  The rate of carbon sequestration is likely to be highest in areas of woodland, lower in areas with fewer trees, and close to zero in some other areas.  Support for biodiversity, which embraces many different plants and animals requiring different habitats, will vary according to the characteristics of different locations, and in some cases (eg where agricultural pests are present) could include negative value elements.  The effectiveness of water purification and drainage services will vary with geological and soil characteristics.

This leads to a problem analogous to that encountered above in respect of housing.  Where units of undeveloped land differ in ecosystem services and therefore in value, which piece of land should be taken to be the marginal unit?  Again, the economic approach is to take units of undeveloped land in descending order of value, reading in this case from right to left in our diagram.  As with housing land, the slope of the marginal line may then reflect a combination of differences in ecosystem services between land units and quantity effects.

Does the Model Identify the Welfare Optimum?

Let’s now bring together our analyses of the two marginal value lines.  Given the ordering approach to the construction of the two marginal curves, we can identify the marginal unit of undeveloped land and, in terms of the housing land ordering, the first extra-marginal unit of undeveloped land suitable for housing.  Suppose, to keep things simple, that the undeveloped land in Diagram 1 has been divided into just three units, X, Y and Z (and take the sloping marginal value lines as approximate representations of the step functions which such large units would require).  We might then identify X as being both the marginal unit of undeveloped land and the first extra-marginal unit of undeveloped land suitable for housing.  Since the marginal value of unit X as land for housing is greater than its marginal value as undeveloped land, we might infer (as suggested by the blue triangle) that welfare would be higher if X had been developed for housing.

But this is a fallacy.  Our orderings for housing and for undeveloped land are based on different principles. To make even partial sense of our diagram in circumstances of non-uniformity, we must specify that units of land with housing (to the left of H0) have been ordered according to value as housing, while units of undeveloped land (to the right of H0) have been ordered according to value as undeveloped land.  We cannot assume that the units of undeveloped land have the same ordering according to value as housing.  Table 2 below shows two (of several) possible ways in which the respective orderings of the undeveloped land might relate to each other.  Note that both possibilities have the same three values in the “Value as housing” column: only the orders differ.

Possible Relations between MV Lines

Possibility 1 is the interpretation which Diagram 1 invites, with unit X having a higher value as housing.  But Possibility 2 is entirely plausible.  For example, unit Z might be attractive green space close to the edge of the city and have the highest value as undeveloped land because it receives many recreational visitors, but also because of its closeness to the city  have the highest value as housing.

Conclusion

The model clearly has many limitations.  I would justify the claim that it is nevertheless useful in the following ways.  Firstly, it offers a principled intermediate position on housing and the countryside as an alternative to the two extreme views outlined at the start of this post.  Even if it is challenging to estimate the marginal value lines for a particular city, the idea that welfare is maximised when the marginal values are equal is an important one whose recognition could raise the level of public debate on proposed housing development.  Secondly, the possibility of truncating the scope of the model – applying it to a relatively small area of land at the urban-rural fringe rather than to a whole city and a large area of surrounding countryside – could in some circumstances enable it to be applied in a relatively simple form because assumptions of uniformity would approximate to reality fairly well within that limited area.  Thirdly, it may be found that for some cities the difference in estimates of the marginal value of housing and undeveloped land is so large that – notwithstanding limitations of the model and the approximate nature of such estimates – a conclusion that welfare is far from being maximised would be hard to dispute.  That would not lead directly to a policy conclusion – whether or not to permit housing development on undeveloped land – but it would give a strong pointer suggesting a need for more detailed studies of particular sites near the urban-rural boundary.

Notes and References

  1. For an overview of such methods see Joint Nature Conservation Committee – Ecosystem Services Valuation http://jncc.defra.gov.uk/default.aspx?page=6383.   I have discussed some of these methods in previous posts: see especially here re the travel cost method and here re contingent valuation.
  2. Re the value of recreational land near to urban centres see Bateman I et al (2013) Bringing Ecosystem Services into Economic Decision-Making: Land Use in the United Kingdom Science Vol 341 Issue 6141 pp 45-50 (section headed National-Scale Implications)  http://science.sciencemag.org/content/341/6141/45
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