## Housing Reform in England

Housing in England is under-supplied, resulting in high costs.  The government’s proposed reforms to address the problem are a step in the right direction but do not go nearly far enough.

I don’t usually engage in autobiography, but it so happens that my own case illustrates the problems of housing in England rather well.  I left university in 1978 and started work in London.  At first I lived in rented accommodation, but by 1983 I was in a position to buy a house – a fairly typical 3-bed terraced property in outer London, only a few minutes walk from my work.  The house cost £24,500, which I funded via a mortgage of two and a half times my then annual salary as a part-qualified accountant of £8,600 together with £3,000 savings accumulated while I had been renting.  The annual interest on the mortgage, at a rate of 10%, was £2,150 or 28% of my income.

I wouldn’t be able to do that now.  The current estimated value of that house is £400,000 (1).  The current salary for an equivalent job in London would be unlikely to be much more than £30,000.  So the value of the house is more than sixteen times larger than in 1983, while the salary is only about four times larger.  To buy the house with that salary, assuming an equivalent proportion (12% or £48,000) from savings, would require a mortgage of more than eleven times salary.  No mortgage lender would agree to that: the risk of default would be too great, since the annual interest, at a current variable rate of around 4%, would amount to some £14,000 or almost 50% of income.

Because homes in London and some other parts of England are so expensive, many young adults face a choice between unsatisfactory options: live with parents; club together with friends or rely on help from parents to buy a property; live where property is less expensive but suitable jobs are hard to find without a long commute; or rent forever at an annual cost that may be no less than that of buying.  The current average monthly rent for a one-bedroom flat in London is £1,250 (2), equivalent to 50% of an annual salary of £30,000.  Renting a room or studio apartment is cheaper, but few would consider it satisfactory as a long-term arrangement.  Sharing a larger rented property can also reduce costs, but is not for everyone.

Most informed observers consider that the main reason why housing costs are so high is that supply is constrained by the limited quantity of land with approval for housing development (3).  Such approval may be granted  by local authorities acting within a framework of law created by the Town and Country Planning Act 1947 and much subsequent legislation.  But even if a proposed development is well-designed, a local authority may gain little from allowing it to proceed, and by doing so will become responsible for much of the initial cost of associated roads and other infrastructure, and the ongoing cost arising from the extra population including children’s education and care for the elderly. It may also face campaigns from local people opposed to the development for reasons which may include loss of countryside, pressure on local services, the possibility of undesirable neighbours, and loss in value of their properties.  Furthermore, much land around London and other cities is protected from development by national designations such as Green Belt.

The government (4) now proposes a reform of the planning system in England.  Details have been published in a White Paper Planning for the Future (5).  The Prime Minister, in his foreword, introduces the proposals as (6):

“Radical reform unlike anything we have seen since the Second World War.  Not more fiddling around the edges … a whole new planning system for England.”

He concludes that:

“… what we have now simply does not work.  So let’s do better.  Let’s make the system work for all of us.  And let’s take big, bold steps so that we in this country can finally build the homes we all need and the future we all want to see.”

Consultation on the proposals, inviting general comments and answers to specific questions, is open for 12 weeks from 6 August 2020.  I set out below the response I have submitted.  Questions are shown in bold with, in some cases, my brief explanatory comments in italics (for fuller context, reference should be made to the White Paper itself).  My responses are in plain text.

The Prime Minister’s foreword quite rightly identifies the need for radical reform of the planning system.  It states that the new system should provide “the homes we need in the places we want to live at prices we can afford, so that … we can connect our talents with opportunity”.  The Secretary of State’s foreword quite rightly refers to “the present generational divide”: the fact that many young adults, even those on above-average incomes, are unable to buy their own home in the way that their parents’ generation were, and have little option but to pay high rents or else live with their parents.  The Introduction (on p 14) quite rightly refers to “long-term and persisting undersupply” of housing, and to the fact that housing in England can be much more expensive than in other European countries. Two points which might have been added are:

1. The high cost of housing is a major contributory factor to poverty for families with moderate earnings whose rent is a high proportion of their income, and indirectly adds to government expenditure via the provisions for housing costs within Universal Credit.
2. The average number of persons per household in the UK (2.4) is higher than in many other European countries (cf Germany 2.0) (7).  This has probably facilitated intra-household transmission of Covid-19 and may be a contributory factor to the UK’s relatively high death rate from the virus.

Although the White Paper contains many sensible proposals, these fall well short of what is needed to address these problems.  In particular:

1. The annual target of 300,000 new homes is far too small.  It represents annual growth in housing stock per capita of about 0.75% (see answer to Q5).  That’s not big and bold. What is needed is a target supported by careful economic analysis showing that, over a period of 5-10 years, it can be expected to result in a substantial reduction in the cost of housing.
2. Although the proposed designation of Growth areas is welcome, it needs to be accompanied by measures to ensure that such designation does not result in huge gains to existing landowners with little benefit to developers or potential residents.
3. The White Paper offers little to discourage the speculative element in demand which is one reason why housing is so expensive.  People expect an upward trend in the price of houses, and this may lead them to buy more, or larger, homes than they require for their own use. When many people do this, prices do indeed rise.  Reform of the planning system offers an opportunity to break this cycle of expectation.  Two measures that would be desirable in themselves and also help to change expectations include increasing the annual target for new homes to considerably more than 300,000, and allowing development on some Green Belt land.

Although outside the scope of the White Paper, it should be recorded that, to be most effective in addressing the problems of England’s housing, reform of the planning system should be accompanied by:

1. Cessation of the Help to Buy scheme which increases demand for housing and so tends to raise house prices;
2. Appropriate reform of taxation relating to housing, including:
1. Ending the anomaly under which VAT is charged on major renovations and extensions to existing homes but not on construction of new homes, so discouraging an important means of maintaining and expanding housing space;
2. Bringing main homes within the scope of Capital Gains Tax (perhaps with the charge rolled up over a lifetime), so removing the current tax incentive to treat housing as a speculative investment;
3. Policies to ensure an adequate supply of skilled labour to the building industry (including via immigration), and to support the development and application of building methods with reduced labour requirements such as modular construction.

Q5 Do you agree that Local Plans should be simplified in line with our proposals?

It is proposed that Local Plans should identify three types of land: Growth Areas suitable for substantial development, with automatic outline approval for development; Renewal Areas suitable for smaller scale development such as densification and infill of existing residential areas, with a statutory presumption in favour of suitable development; and Protected Areas, including Green Belt and Areas of Outstanding Natural Beauty, which justify more stringent development controls to ensure sustainability.

My response:  Yes (in part).  I agree that the role of land use plans should be simplified and with the proposed definitions of Growth areas and Renewal areas.  Automatic outline approval for development within the former and a presumption in favour of development within the latter would simplify and accelerate the process of obtaining approval for development.  However, consideration should be given to the effect on the market value of land within Growth areas especially.  Existing landowners, who would not have had to apply for permission to develop or indeed to do anything at all, could be expected to enjoy very large gains if they then sell their land.  There is a risk that too much of the economic benefit from automatic outline approval would accrue to existing landowners and not enough to either developers or potential residents.  In other words, there is a risk that the designation of Growth areas might make more land available for development, but only at a cost to developers that would make it unprofitable to undertake development unless homes could be sold at prices at least as high as at present.  Taxation (via Capital Gains Tax or otherwise) of the undeserved gains made by existing landowners would be justifiable but do nothing to help developers or residents.  A much more constructive approach to the problem is suggested in the Letwin Report on Build Out (8).  In outline, if designation of land as Growth area comes with an automatic requirement that development of that land must provide for diversity of housing in respect of type, size, style and tenure, including a minimum proportion of affordable homes,  then the residual land value will be much less than it would have been with unconstrained development permission, allowing both lower prices or rents to potential residents and reasonable profit for developers.  The Report’s recommendation that residual land values be capped at around ten times existing use value seems very appropriate for greenfield sites, still allowing the landowner a very worthwhile gain.  There may also be a role for compulsory purchase powers, particularly in assembling large sites with multiple existing landowners where an individual landowner is holding out in the hope of a larger gain at a later date.

The third land type would more logically be divided into two (making four types altogether). Distinguishing the following types would help to promote public understanding of the varied reasons for restricting development and to raise awareness of the extent of land at risk of flooding.

• One type (“At-risk areas”?) would be land which is unsuitable for development because of its current or likely future exposure to environmental hazards including coastal and river flooding.  Identification of such land should have full regard to the best available predictions of the effects of climate change, including sea level rise, over the next 100 years and beyond, and to realistic assessments (having regard to cost as well as technical feasibility) of the scope for mitigation of risk.   Land potentially at risk of flooding should not be considered suitable for development just because the risk can be fully mitigated in the short term.
• The second type (“Protected areas”?) would be land which should be protected from development because it has environmental qualities sufficiently valuable to be worth preserving even at the price of restricting development.  Such land may provide direct benefits to visitors via opportunities for recreation and the enjoyment of natural beauty.  It may also provide ecosystem services yielding more indirect benefits such as drainage, water and air purification, biodiversity and (of especial importance in mitigating climate change) carbon sequestration by forests and woodlands.   This could include Areas of Outstanding Natural Beauty and Local Wildlife Sites.  As many people are coming to realise, however, it is not appropriate that all of the very large amount of land designated as Green Belt should continue to be protected (9).  Green Belt land is very varied in quality and much of it is inaccessible to the public. An effect of the London Green Belt is that much development is located beyond the Green Belt but occupied by people who work in London, whose resulting long commutes are harmful both to them and to the environment.  Allowing development on perhaps 10% of Green Belt land, chosen for its limited environmental value and proximity to existing transport links, would enable provision of many new homes in places where people want to live, such as around London, Oxford and Cambridge.

Q8a Do you agree that a standard method for establishing housing requirements (that takes into account constraints) should be introduced?

By a standard method is meant a means of distributing the national housebuilding target of 300,000 new homes annually.  It would make it the responsibility of individual planning authorities to allocate land suitable for housing to meet their share of the total.  They would be able to choose how to do so via a combination of more effective use of existing residential land, greater densification, infilling and brownfield development, extensions to existing urban areas, or new settlements.

My response:  Yes.  To secure an adequate rate of provision of new homes, it is essential that binding targets are imposed on planning authorities.  However:

• These targets should be part of a framework which also provides incentives to planning authorities to approve more new homes and leaves meaningful scope for local input to the planning process. This will minimise the risk of conflict between central government and local communities, allow planning authorities to innovate with successful practice being copied by others, and ensure a genuine role for local democracy.
• The overall planning framework should prioritise number of new homes and quality of individual homes and appropriate infrastructure provision and placemaking.  Enforcement of the first should not implicitly downgrade the others.
• The overall annual target for new homes in England should be considerably more than 300,000.  Given existing stock of c 24 million, and even if all of that stock remains in use, it represents annual growth of just 1.25%.  With likely population growth of 0.5% (10), this is equivalent in per capita terms to 0.75%. It is not credible that such a modest rate of growth, even if sustained over several years, can do much to mitigate what the White Paper itself (p 14) describes as a situation in which housing space in the UK can be twice as expensive as in Germany or Italy.  An OBR Working Paper (11) estimates the price elasticity of demand for housing in the UK at -0.92, suggesting that annual growth in per capita housing stock of 0.75% would reduce house prices annually by just 0.82%.
• Targets should allow for development of selected Green Belt land.  Not to do this would unduly restrict home provision in areas where people want to live (see answer to Q5).

Q8b Do you agree that affordability and the extent of existing urban areas are appropriate indicators of the quantity of development to be accommodated?

My response:  Yes (in part).  Requiring more development in areas where property is more expensive, other things being equal, establishes a crucial link to the signals provided by the market, ensuring that development occurs where people want to live.  However, a link to the extent of existing urban settlement is more problematic and a simple algorithm, attempting to spread development “fairly” between planning authorities, would probably yield some bizarre results.  More important than such fairness is the need to ensure that new or expanded settlements are of a sufficient size to support a good range of local services, rather than requiring residents to make frequent car journeys to a neighbouring large town.

Q9a  Do you agree that there should be automatic outline permission for areas for substantial development (Growth areas) with faster routes for detailed consent?

Approval for development is often in two stages, outline approval being the first stage.

My response:  Yes, for the reason given in answer to Q5.

Q14 Do you agree that there should be a stronger emphasis on the build out of developments?  And if so what further measures would you support?

‘Build out’ refers to the building of homes once approval has been granted. Build out of large developments can be slow due to low market absorption rates, with some sites taking over 20 years to complete.

My response:  Yes.  Slow build out has a direct effect in limiting the rate of provision of new homes.  It also invites the widespread mis-perception that under-supply of housing is the fault of developers and nothing to do with any deficiencies of the planning system.  Requiring diversity of housing within large developments so that provision more closely matches the range of housing demand, as recommended in the Letwin Report, should encourage faster build out by developers in the knowledge that homes are unlikely to remain unsold or untenanted.  Consideration might also be given to some form of penalty, such as a surcharge on the Infrastructure Levy, where the time taken to complete developments is determined (under suitable rules) to be excessive.

Q17  Do you agree with our proposals for improving the production and use of design guides and codes?

Design guides and codes record architectural and other features of developments that have been judged successful in the past.  They can be used by architects as an alternative to original design, and by planning authorities in specifying the type of development they are prepared to approve.

My response: No.  The proposals tend to suggest that planning authorities would be required to comply with the National Design Guide, National Model Design Code and Manual for Streets.  Making individual planning decisions rules-based rather than discretionary is highly desirable since it will create greater certainty for developers and lead to faster decisions with reduced costs for all parties. However, each planning authority should be free to adopt its own rules via design codes, etc., adapting national guidance to their local circumstances as they judge appropriate.  For example, authorities may reasonably take different views regarding the balance in their areas between car use and public transport, with different implications for car parking provision and housing density.

Q18 Do you agree that we should establish a new body to support design coding and building better places, and that each authority should have a chief officer for design and place-making?

My answer: Having a central body to support design coding and building better places is a sensible proposal, provided that its role is limited to support and planning authorities are free to adapt its output as they see fit.  While design and place-making are very important, a requirement for each planning authority to have a designated chief officer for these functions would limit the freedom of authorities to determine their own best arrangements having regard to financial constraints.  An authority might for example wish to provide training in design and place-making for a number of officers contributing to the planning process rather than appoint a single designated officer.  Such freedom enables authorities to try different arrangements and to learn from each other’s experience, and is more likely to lead to successful results than a uniform approach.  A requirement for authorities to have regard to design and place-making would be sufficient.

Q20 Do you agree with our proposals for implementing a fast track for beauty?

My response: No.  While there are many excellent suggestions in the report of the Building Better, Building Beautiful Commission (12), its emphasis on “beauty” as an overarching concept is liable to mislead and to be interpreted differently by different parties.  A development I happen to have visited – Great Kneighton, pictured on p 50 of the White Paper – appears to be well planned and well constructed, a good place to live, but I would not call it beautiful.  What is needed is not a fast track for a specific category of developments judged to embody beauty but a general acceleration of the planning process for all housing developments of sufficient quality.

Q22a Should the government replace the Community Infrastructure Levy and Section 106 planning obligations with a new consolidated Infrastructure Levy, which is charged as a fixed proportion of development value above a set threshold?

This question concerns the resourcing of the roads and other infrastructure required by new housing development.  The current Community Infrastructure Levy is a charge that local authorities may choose to levy – about half do – based on the floorspace of new development.  Section 106 (of the Town and Country Planning Act 1990) enables authorities to set conditions when approving a development, requiring the developer to do certain things or to pay money to the authority.

My response:  Yes.  Negotiations over Section 106 cause delay in obtaining approval for development and may deter small builders from submitting applications at all.  A consolidated Infrastructure Levy at a rate known in advance would avoid such delay and provide certainty for applicants.

Q22b Should the Infrastructure Levy rates be set nationally at a single rate, set nationally at an area-specific rate, or set locally?

My response: Nationally at an area-specific rate.  I suggest a uniform rate for most areas but higher rates for areas where development now requires or may in future require works to mitigate flood risk or maintenance of existing flood defences.  Such higher rates are justified because areas exposed to flooding are unlikely to have lower needs for non-flood-related infrastructure than other areas.  They would also provide some incentive for builders to prefer development in areas not exposed to flood risk.  Where such higher rates are charged the extra sums should pass to the appropriate bodies responsible for flood defence.

Q22c Should the Infrastructure Levy aim to capture the same amount of value overall, or more value, to support greater investment in infrastructure, affordable housing and local communities?

My response: More value.  This is one way in which planning authorities can be incentivised to approve more new homes (as proposed in answer to Q8a).  However, the overall situation faced by developers, including the price at which development land is available and the sale price of new homes as well as the Levy, should provide reasonable scope for profit.

Q24a Do you agree that we should aim to secure at least the same amount of affordable housing under the Infrastructure Levy, and as much on-site affordable provision, as at present?

My response: No.  As explained in answer to Q5, the provision of affordable housing within a diverse development should be automatically required at the point that land is designated as Growth area.  Such a development can be profitable for the developer because that requirement will substantially lower the price which the existing landowner can obtain for the land and so its cost to the developer.  Under this approach, there should be no need for affordable housing to be funded from the Infrastructure levy, which should be reserved to meet the costs of infrastructure provision and placemaking.

Notes and References

1. From Zoopla’s online property valuation tool.
2. Valuation Office Agency  Private Rental Market Summary Statistics – April 2018 to March 2019  Read from Chart 3 https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/809660/PRMS_Statistical_Release_20062019.pdf
3. The economics of housing in England (and elsewhere) is complex.  For a concise and fairly orthodox account, identifying causes and effects of under-supply, see Barker K (2014) Housing: Where’s the Plan?  London Publishing Partnership.  A dissenting view (arguing that under-supply is not the problem) is set out in Mulheirn I  (2019) Tackling the UK housing crisis: is supply the answer? https://housingevidence.ac.uk/publications/tackling-the-uk-housing-crisis-is-supply-the-answer/   An international perspective is given by Davies B, Turner E, Marquardt S & Snelling C (2016) German Model Homes: A Comparison of UK and German Housing Markets  https://www.ippr.org/files/publications/pdf/German-model-homes-Dec16.pdf
4. The UK government is responsible for housing policy in England, while housing policy in Wales, Scotland and Northern Ireland is the responsibility of their devolved administrations.
5. Ministry of Housing, Communities and Local Government  Planning for the Future  https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/907647/MHCLG-Planning-Consultation.pdf
6. As (5) above, p 6.
7. Euromonitor International https://www.euromonitor.com/united-kingdom/country-factfile gives UK population 2019  66.65M and number of households 28.02M implying population per household 2.38; and https://www.euromonitor.com/germany/country-factfile gives Germany population 83.02M and number of households 41.58M implying population per household 2.00.
8. Rt Hon Sir Oliver Letwin MP  (2018) Independent Review of Build Out  https://www.gov.uk/government/publications/independent-review-of-build-out-final-report   See especially paras 3.3, 3.8, 4.3. 4.4, 4.16 & 4.17.
9. Those advocating selective relaxation of Green Belt to allow housing development include:
10. ONS: National Population Projections: 2018-Based, Main Points (5% growth over 2018-2028 implies an annual average rate of 0.5%) https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationprojections/bulletins/nationalpopulationprojections/2018based#main-points
11. Auterson T (2014)  Forecasting House Prices, OBR Working Paper No. 6, para 3.14 p 23 https://obr.uk/docs/dlm_uploads/WP06-final-v2.pdf
12. Building Better, Building Beautiful Commission (2018) Living with Beauty: promoting health, well-being and sustainable growth  https://www.gov.uk/government/publications/living-with-beauty-report-of-the-building-better-building-beautiful-commission

## Some Carbon Tax Scenarios

How does a competitive industry respond to an emissions tax in the short run and the long run?  What if the industry is a monopoly?

In this post I bring together two standard pieces of microeconomic analysis: the effect of an emissions tax to address a pollution externality; and the behaviour of profit-maximising firms in different market structures.  It’s a straightforward exercise, but some of the results may be found a little surprising.

My method here is the exploration of numerical examples.  Therefore the only claim I make for the results is that they demonstrate possibilities: to infer any sort of generalities would be an obvious fallacy.  The numbers from which the examples begin have been chosen for ease of calculation: it is no accident that many of the output and other figures to which they lead are round numbers.

I consider two industries, one with many firms in perfect competition, and one a monopoly.  The following assumptions are common to both:

1. Emissions are uniformly mixed and very large in total (as is the case for CO2 and some other pollutants).  Hence the damage due to any one firm’s emissions is independent of its location, and its contribution to total emissions is too small to affect the marginal damage per unit of emission.
2. Marginal damage m from the pollutant (in terms of the local currency) is 1 per unit of emission.
3. In the absence of an emissions tax, with firms taking no particular measures to limit their emissions, the emissions ratio e (the ratio of emissions to output) is assumed to be 4.
4. The emissions tax is introduced with minimal notice.  Therefore all adjustment to the tax takes place after its introduction.
5. Firms’ costs consist of four components: a) a fixed component; b) a component proportional to the square of output (in conjunction with (a) this yields the characteristic U-shaped average cost curve); c) a component reflecting, for any level of output, higher costs for a lower emissions ratio; d) a component for the cost of the tax, where applicable.  I take costs to include ‘normal’ profit: all references below to profit should be understood to mean economic or supernormal profit.

Outcomes are assessed from several points of view, of which perhaps the most important is net welfare, calculated as consumer surplus plus producer surplus minus damage due to emissions plus tax receipts.

An Industry in Perfect Competition

The industry is assumed to be a constant-cost industry, that is, the entry or exit of firms does not affect the cost functions of its firms.  Writing q for output volume and t for the tax rate, the cost function per period of each firm is:

$c(q,e) = 10 + 0.1q^2 + 4q/e + qet$

Writing P for the market price and Q for total industry output volume, the market demand function per period (in inverse form) is:

$P = 11 - 0.01Q$

Initial Position with No Emissions Tax

We assume that the industry is in equilibrium, with competition having driven the market price to the minimum point of the firms’ average cost (AC) curves so that their profit will be zero.  We have to find the output q of each firm at which average cost is minimised. Price P is then equal to average cost at that point.  Using the market demand function we can then find industry output Q, from which we can infer the number of firms (Q/q) and the total value of the industry’s sales (PQ).  We can also calculate the industry’s total variable costs excluding tax, which is of interest as an indicator of the total employment supported by the industry and its suppliers.

The industry’s emissions are simply Qe.  To calculate producer surplus we need the average variable cost (AVC) of one firm at the output determined above.  We then have everything needed to calculate the components of net welfare.

With Emissions Tax: Short Run

I take the short run to be a period in which no firm has changed its emissions ratio or exited the industry.  Thus any reduction in emissions resulting from the tax must be due to a reduction in output.  In a previous post, I noted that a reduction in emissions in response to a tax could be due to the introduction of abatement technology, to a reduction in output, or to a combination of the two.  Here I consider the implications of the timing of such a combined response: a reduction in output can usually be almost immediate, but the introduction of abatement technology will normally take time.

In the short run, having not fully adjusted to the tax, firms will not set their output to the minimum point of their average cost curves.  Instead, we must start from the more fundamental principle that they will set their output to the point at which their marginal revenue (the market price P) equals their marginal cost.  So from the cost function we obtain marginal cost in terms of firm output q and set this equal to P: this yields the inverse supply function for a firm.  Since the number of firms is known from the initial position, we can infer the market supply function relating P and Q.  From this in conjunction with the market demand function we can infer the values of P and Q, and hence q.  The remaining calculations are just as for the initial position.

With Emissions Tax: Long Run

I use the term ‘long run’ in a special sense: a period in which all firms have adjusted to the tax as fully as possible by changing their emissions ratio or exiting the industry.  This is not quite the Marshallian long run since the fixed component of the firms’ cost functions is assumed unchanged from the initial position (I leave for another day the important case in which abatement of emissions involves investment in fixed capital).

The method of calculation is as for the initial position except that the average cost curve now contains two unknowns: firm output q and the emissions ratio e.  So we must find the combination of values of those two variables which minimises average cost. Once we have found that minimum point, yielding q, e and P, the calculations proceed in the familiar way.

Results

Table 1 below sets out the results of the above calculations.  It can be seen that the industry’s emissions are reduced in the short run and further reduced in the long run.  Thus the primary purpose of the tax is achieved.  Also on the positive side, net welfare is increased in the short run and further increased in the long run.

Output per firm in the long run is the same as in the initial position.  Thus the long run reduction in emissions is achieved via a combination of a lower emissions ratio and a reduction in the number of firms.

Although the tax reduces the volume of output and increases its price per unit, these may be regarded as necessary side-effects of the emissions reduction.  However, the fact that both these changes slightly overshoot in the short run may be considered to impose an unnecessary (albeit temporary) detriment on consumers.  The need for the losses incurred by firms in the short run is questionable: by providing an incentive for firms to exit the industry they hasten the arrival of long-run equilibrium with few firms and profits restored to nil, but perhaps that process could be facilitated by other means.  These features of the short-run position after introducing a tax with minimal notice suggest that there could be advantage in giving a longer period of notice allowing firms to adjust before the tax comes into effect.  However, the way in which firms would respond during such a notice period would be difficult to predict.  It would depend on, among other things, the degree of certainty with which firms believe that the tax will be introduced, and the judgments firms make as to how many of their competitors will exit the industry.

It is important to note that the industry will not leave the short run one day and arrive at the long run the next.  Between the two is a transitional process in which some firms introduce abatement technology and others exit the industry.  Again, firms’ behaviour during this period is difficult to predict.  Perhaps some firms will make an early strategic decision to exit.  Alternatively, all firms may begin incurring the extra costs of abatement technology, and only as losses accumulate will some firms decide to leave the industry.

How does the tax effect employment in the long run?  To the extent that industry variable costs excluding tax are a good proxy for the employment supported by the industry, the direct effect is only a small reduction. Although many firms leave the industry, the effect on employment is largely offset by the extra costs per firm of reducing their emissions (staff made redundant by exiting firms may be re-employed by other firms).  Taking a broader view, however, the significant increase in industry sales value implies, given constant aggregate demand, a corresponding reduction in demand for other goods, adding to any reduction in employment.  Much therefore depends on how the government uses the tax receipts. If it uses them in ways which raise employment, either via government expenditure on goods and services, or via a cut in another tax, then the overall effect on employment could be neutral or even positive.

A Monopoly

The single firm’s cost function is:

$C(Q,e) = 800 + 0.01Q^2 + 4Q/e + Qet$

Its inverse demand function is:

$P = 13 - 0.01Q$

Initial Position with No Emissions Tax

Here e = 4 and t = 0.  Using the demand function we can express profit Pr as a function of Q only and then find the level of Q that maximises profit.  Price P, sales value and profit follow immediately.  We can also calculate variable costs, emissions (Qe), and then the components of net welfare.

With Emissions Tax at Rate Equal to Marginal Damage: Long Run

For this industry I omit the short-run analysis and proceed directly to the long run.  Here t = 1 while e, along with Q, is an unknown to be found.  So we find the levels of Q and e which maximise profit.  The only other difference from the calculations for the initial position is that we need both total variable costs (in order to calculate producer surplus) and variable costs excluding tax (as an indicator of employment).

With Emissions Tax at a Rate Less Than Marginal Damage: Long Run

We take the case t = 0.7.  The method of calculation is exactly as for t = 1.

Results

Table 2 shows the results of the above calculations.  As expected, the tax reduces emissions, partly by reducing output and partly by reducing the emissions ratio, and the higher tax rate reduces emissions by more.

The tax considerably reduces the firm’s profits, but they are still positive, and a reduction in the profits of a monopoly may be considered of little concern.  The small increase in price represents only a modest additional burden to consumers.  Since the reduction in sales value exceeds that in variable costs excluding tax, the net effect on employment may well be positive, even before consideration of how the government uses the tax receipts.

Net welfare is increased at either of the two tax rates, but is slightly higher when the rate is somewhat lower than the rate of marginal damage.  The reason for this is that, leaving aside the emissions damage, the initial position is sub-optimal relative to what could be achieved if output were set to equate price and marginal cost, rather than restricted so as to maximise the monopolist’s profit.  The theory of second best implies that a policy measure that would otherwise be optimal to address a market failure may not be optimal if another form of market failure is also present (1).  For a theoretical treatment of taxes to address externalities in the context of monopoly see Barnett (1980) (2).

A policy-maker selecting a tax rate in this situation might nevertheless want to look not only at net welfare but also at its separate components.  These are shown in Table 3 below.

It can be seen that the extra net welfare at the lower tax rate is due to an increase in producer surplus plus a smaller increase in consumer surplus, offset by an increase in damage due to emissions and a reduction in tax receipts.  The increase in producer surplus is exactly reflected in increased profits.  A policy-maker might reasonably conclude that, although it does not maximise net welfare, the tax rate equal to the rate of marginal damage is to be preferred.

The workings supporting the above results may be downloaded below (MS Word 2010 format).

References

1. Wikipedia Theory of the Second Best  https://en.wikipedia.org/wiki/Theory_of_the_second_best
2. Barnett, A H (1980) The Pigouvian Tax Rule under Monopoly  American Economic Review 70(5) pp 1037-41

## Covid-19 and Household Size

Differences in national rates of Covid-19 infection may be partly due to differences in household sizes.

While many questions about the Covid-19 virus are currently unanswered, one point on which there has been wide agreement is that transmission is more likely indoors than outdoors (1,2).  If therefore we are to explain differences in national rates of infection, an obvious place to look is differences in indoor environments.  A plausible hypothesis is the following:

Rates of Covid-19 infection will be higher, other things being equal, in larger households, that is, households with more occupants.

The thinking behind this is simple.  If one member of a household becomes infected, and unless there is effective self-isolation within that household, then it is quite likely that their infection will transmit to other members. The larger the household, the more people they can infect.  The hypothesis does not imply that household size is the sole or main reason for differences in rates of infection, merely that it is one contributory factor.

If correct, the hypothesis suggests a possible link between housing policy and rates of Covid-19 infection.  Countries (such as the UK) with restrictive planning policies that have limited the supply of land for building new homes will have fewer homes than they would otherwise have. This reduced supply of housing will lead to higher costs (whether for ownership or renting).  As a consequence, fewer people will be able to afford their own home, and (other things being equal) average household sizes will be larger: young adults, for example, will tend to stay longer with their parents before setting up their own home.  Larger households in turn will create more scope for transmission of infection.

But is the hypothesis correct?  An ideal test would require large sample data on household size and numbers infected at individual household level.  Here I present the results of a ‘quick and dirty’ test based on data currently available at national level.

At the present time, reliable data on total rates of infection since the start of the outbreak is not available.  National totals of confirmed cases are incomplete because many cases have not been confirmed by testing, and international comparisons of those totals reflect differences in rates of testing as much as in rates of infection.  I therefore used national rates of death from Covid-19 as an, admittedly imperfect, proxy for rates of infection.  Even such death rates are unlikely to be perfect for international comparison, since practice in recording the cause of death of patients with multiple conditions may vary.  As a proxy for rates of infection, death rates suffer from the limitation that they are also influenced by differences in health systems between countries.  Nevertheless, it seems reasonable to assume, at least for the developed countries of Western Europe, that official figures on deaths from Covid-19 are at least of the right order of magnitude.

Average household size was calculated from national statistics for population and numbers of households.

A regression was estimated for the model:

DP  =  C  +  (B x PH) + E

where:  DP is death rate from Covid-19 per million population; C is the regression constant; B is the slope coefficient; PH is average population per household; and E is the error term.  The regression was run on data for 14 Western European countries: Austria, Belgium, Denmark, France, Germany, Italy, Ireland, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.

Estimation of the regression was by weighted least squares, with weighting by population (implying that the fitting of the regression line takes more account of data points for countries with larger propulations).  The justification for the weighting is that a local random factor affecting the death rate within a region with a population of a few million could have a large effect on the overall death rate of a country with a smaller population.  Within a larger country, however, the effect of such a local factor would be less, and different random factors within different regions of the country would probably tend to offset each other.  It is proper to record that the choice of weighted least squares, rather than ordinary (ie unweighted) least squares, makes a large difference to the result.

The estimated regression line was:

DP  =  -1,334 + (770 x PH)

The precise values of the estimated coefficients, which rather implausibly imply a nil death rate at a household size of about  1.7, are not important. What does matter is that the estimated slope coefficient is positive, consistently with the hypothesis (and is sufficiently large that the null hypothesis that its true value is zero or less is rejected at the 5% significance level (3)).

I would describe this result as ‘interesting’. But no more conclusion should be drawn than that the hypothesis merits further research.

Notes and References

1. Sandhu, S (11/5/2020) Why you are less likely to catch coronavirus outside than indoors, according to experts  i   https://inews.co.uk/news/coronavirus-catch-outside-indoors-why-get-covid-19-explained-2848865
2. Moffitt, M (28/4/2020)  China study suggests outdoor transmission of COVID-19 may be rare  SFGATE   https://www.sfgate.com/science/article/China-study-suggests-outdoor-transmission-of-15229649.php
3. This can be inferred from the fact that the 95% confidence limits of the estimated slope coefficient are both positive.

## Urban Wildlife – An Exploration

In many cities around the world, there are wild animal species whose presence is enjoyed by some and a nuisance to others. Management of such species should be informed by economic analysis as well as ecological, ethical and animal welfare considerations.

I had better say this right away: this post was prompted not by the current Covid-19 pandemic, but by repeated sightings last summer of a fox around my London home.  Nevertheless, the pandemic does show that the proximity of wild animals can in certain circumstances have enormous adverse consequences for humans.  At the time of writing, the precise source of the initial outbreak in Wuhan, China, is not known, but it appears that the virus was transmitted from wild animals to humans at a market.  Quite possibly, however, it was a wild animal farmed outside the city and brought to market for sale, and not therefore urban wildlife in the sense considered in this post.

Human attitudes to wildlife depend greatly on its nature, location and behaviour.  Large carnivores in what remains of their natural habitats are widely considered worthy of conservation efforts, but if such a creature should be on the loose in a city, as happens occasionally (1), then most people would  support its killing in the interests of public safety if other options are impractical or ineffective.  Very small animals encountered in or near people’s homes may evoke little affection or sympathy: many who would never harm larger animals will happily swat a fly or lay a mouse trap.

Between these extremes are medium-sized wild animals present in and adapted to life in cities about which people may have differing or complex attitudes – animals not large or dangerous enough to present a major physical risk to human life, but capable of being a considerable nuisance while also evoking human sympathy and the protection of custom or law.  Table 1 below lists some examples (this has been compiled from numerous online sources which it would be tedious to list in full).

Trying to be objective, I have avoided any reference to animals “attacking” humans, as it is apparent that what one source considers an attack, another may view as defensive action in response to human provocation or to protect young.  In the same spirit, I have not stated that any of the animals “spread” human diseases.  Undoubtedly many urban wild animals carry pathogens that are potentially harmful to humans (2).  The questions then are the likelihood of transmission to humans, and whether transmission can be prevented by simple precautions such as washing hands after contact or requires more elaborate preventive measures.  It is also pertinent to consider whether or not the risks to humans are greater than those already encountered from pets and domestic animals.

There seems to be little literature on the application of economics to the management of such urban wildlife.  What literature there is on the economics of wildlife management focuses mainly on rural wildlife, as is apparent from the highlighting of costs from harm to livestock and crops, and benefits from hunting and recreation (11).  Nevertheless, the insight that there may exist an optimum population size which maximises benefits less costs (12) appears relevant to urban as well as rural wildlife.

Before pursuing this argument, I will briefly address some lines of thought that seem unlikely to be helpful in informing management strategies for species of the sort listed in the table.  Firstly, conservation is not normally an issue for such species.  It may be that their adaptation to urban environments is to some extent a response to loss of their natural habitats.  But all the listed species are classified by the International Union for the Conservation of Nature as of least concern (13), implying that their populations are large enough that they are far from any risk of extinction.  Secondly, and as a consequence of the above, a focus on such species’ contribution to biodiversity, and on the economic value of that contribution, is unlikely to yield useful information.  There is no foreseeable risk that that contribution will be lost.

Any attempt to measure the benefits and costs to humans of an urban wildlife species would require application of a judicious selection of non-market environmental valuation techniques.  Benefits from observing animals might be measured by adapting the travel cost method, typically used in valuing parks and other recreational sites, to allow for the fact that the animals are not concentrated at one site but spread out across an urban environment.  Thus the relevant travel costs are not those incurred in getting to a particular site but those incurred in getting to wherever, at a particular time, an animal can conveniently be observed.  The “travel” required to make such an observation when at home might be no more than getting up and coming to a window when alerted to an animal’s presence by a family member.  The fact that such “travel” may involve very little cost – the value of perhaps just a minute or two of a person’s time – does not mean that the benefit is correspondingly low.  This is because the travel cost method measures value in terms of consumer surplus – in simple terms the difference between the cost a person would have been willing to incur to view an animal and the cost they actually incur.  The cost they would have been willing to incur might be assessed from the costs actually incurred to view an animal by other people who happen to live where such animals are not present.

Benefits from controlling species regarded as harmful might be measured using a combination of ecological and economic analysis.  Ecological analysis would attempt to quantify the effect of the population of the beneficial species on the population of the harmful species, and the relation between the population of the harmful species and specific forms of harm (theft of unprotected food, dispersion of pathogens, dropping of faeces, chewing of materials, etc).  It would then be for suitable economic analysis to attempt to value the benefit from a reduction in the relevant forms of harm.

The costs attributable to urban wildlife include numerous components.  Theft of food that would otherwise have been available for human consumption can as a minimum be costed at its market value or, where prepared at home from bought-in ingredients, at the market value of the ingredients plus the opportunity cost of the preparation time.  The cost of overturned bins might be taken to be the opportunity cost of the time spent in cleaning up, and that of disturbance to gardens and damage to buildings the cost of reinstatement or repair.  In the case of damage to overhead power lines, the cost of the power outage should be added to the repair costs.  Power outage costs will depend on how many users are affected and what they use electricity for, but can be very large (14).  The cost of injury or ill-health attributable to urban animals should include the costs of associated healthcare and of lost income (to employees) or lost production (to employers) due to time off work.  Given suitable information about the effect of education on children’s employment and earnings prospects, one might also include a cost element for time off school.  Estimating the costs of ill-health of retired people raises issues beyond the scope of this post (15).

Where nuisance attributable to animals is recurrent, further costs may arise. Various forms of avertive behaviour may be adopted in an effort to minimise the nuisance.  These may include: never eating out of doors; keeping windows closed (even in hot weather); buying larger or more secure waste bins; fitting spikes where birds might want to perch; setting deterrents  such as motion-sensitive lights, chemical sprays and imitation snakes; and going out of one’s way to avoid certain locations.  All these have costs: either direct monetary outlays, or time costs, or costs of restrictions on life-style. The last-named costs might be estimated using the hedonic property method, requiring comparison of house prices in locations with and without the need for such restrictions.

None of this is easy.  Even an apparently simple case such as theft of purchased food  requires reliable data on the quantities and types of stolen items, and the species responsible for theft.  Although the economics of environmental valuation has made great strides in recent decades, its application to the full range of benefits and costs of particular species, and collection of the necessary data, would present enormous challenges.

It is plausible to suppose that a higher urban population density of a wild species will not imply proportionately higher benefits to humans.  The principle of diminishing marginal utility suggests that someone who enjoys seeing a fox or a monkey is unlikely to obtain ten times as much enjoyment from seeing ten foxes or monkeys, or from seeing just one ten times as often.  That could be tested empirically by observing how much time and effort a person incurs to view such animals, and how that time and effort varies with the number of known opportunities for views.

The costs to humans of a higher urban population density of a wild species, however, may be more than proportionately higher.  One overturned waste bin in a street may be seen as an exception. Many such bins not only create proportionately more clean-up work, but may also be perceived as lowering the tone of the neighbourhood, and may prompt efforts to address the problem by deterrent measures or obtaining more animal-proof bins. Occasional animal noises may be a minor issue, but persistent noise, especially at night when it may disturb sleep, can be a serious problem.  Similarly, occasional theft of food may be tolerable, but routine thieving may force changes in life-style, such as never eating out of doors, keeping windows closed even in hot weather, and abandoning businesses selling food at outdoor market stalls.

If these suggestions are broadly correct, then we can represent the situation in terms of the sort of diagram familiar from, for example, the economics of pollution control.

As in other contexts, net benefit is maximised when marginal benefit equals marginal cost.

However, such an approach should not be the sole determinant of how a species should be managed.  It is also important to consider, from the perspectives of effectiveness, cost and ethics, the means of getting from the current to the optimum population.  More fundamentally, an animal rights perspective would suggest that an approach based solely on benefits and costs for humans is to be rejected as an example of human supremacism (16).

What would be missing, in an approach that only takes account of benefits and costs for humans, is consideration of animal welfare.  That implies, as a minimum, avoidance of direct cruelty to animals including, in particular, avoidance of practices such as blocking of dens and use of poisons that subject animals to lingering and unnecessarily painful deaths.  The importance of animal welfare in this narrow sense is widely recognised: in the UK, for example, use of such practices to kill foxes is illegal (17).

However, appropriate management of urban wildlife requires a much broader conception of animal welfare that has regard to the extent to which animals lead worthwhile lives with a positive balance of well-being over suffering, and to how humans and the urban environment they create can affect that balance.  Positive features of an urban habitat may include a plentiful food supply and an absence of natural predators.  Negative features may include intense competition for territory and the risk of death or injury in road accidents.  The balance might be expected to vary between species and locations.

Ideally, management of an urban species should be informed by knowledge not only of the actual welfare of its members but also of how their welfare might change if its population density were to increase or reduce, or if features of its environment were to change.  But rarely if ever do we have such knowledge (18).  Even our knowledge of actual welfare is very limited.

There is a further difficult and contentious issue.  Philosophers have explored, in respect of humans, the ethics of policies that affect the size of the future population.  How should we choose between scenarios A and B, if people in A have greater well-being but people in B are more numerous?  Totalism asserts that we should maximise total well-being, calculated as population multiplied by average quality of life (19).  Averagism holds that we should maximise average quality of life, without regard to size of population.  Both these positions, and others, have been shown to have counter-intuitive implications.  A considerable literature in this field has not led to anything approaching a consensus.  The point here is this: the same ethical issue arises in respect of actions or policies which affect the size of an animal population.

A plausible assumption is that the average well-being of an animal species is greatest when its population density is neither too small nor too large.  If it is too small, then it may be very difficult for individuals to learn behaviour from others or to find mates.  If it is too large, then competition for territory may become severe, diseases may spread more easily, and the available food supply may be inadequate.  Rather more speculatively, it might be argued that if population expands beyond the level that its food supply can support, then average well-being will decline so rapidly as to render the debate between totalism and averagism irrelevant (because total welfare will fall despite the extra population).  If so, then the relation between population density and welfare, according to whatever is our preferred measure of overall welfare of an animal population, could be represented as in the diagram below.

There is still much that this analysis leaves out.  It passes over the issue of what in an animal’s environment we are regarding as held constant as its population density varies.  Whatever management method might be chosen – for example shooting, poisoning or sterilization for a reduction in population, and providing extra food or nesting opportunities for an increase – would in itself amount to a change in the environment.  It also omits the ecological consequences of a change in the population density of an animal species.  Through food chains and in other ways, there are likely to be effects on the populations of other animal species, and so in turn on the welfare of those species.

Nevertheless, it is I believe of interest to consider the implications of putting together the economic analysis summarised in Diagram 1 and the animal welfare analysis summarised in Diagram 2.  I assert the following:

Proposition 1: There is no reason to suppose that the population density of an urban animal species that optimises its net benefit to humans is the same as, or even close to, the population density that optimises its own overall welfare.

The justification for Proposition 1 is simply that the bases of the optimum for humans and the optimum for the animal species are entirely different.  It would be entirely coincidental if these optima happened to be the same or close.

For the next proposition it is convenient to represent the actual current population density of an urban animal species in a particular location as A, its optimum density for humans as OH, and its optimum density for animal welfare as OA.  We can then state:

Proposition 2:  For any urban animal species, there are 6 possible orderings by increasing animal population density of A, OH and OA.  For 4 of these orderings, there is available what might be termed a Pareto improvement (20), a change in population density that would yield a net benefit for humans and raise the overall welfare of the animal species.  For the other 2 orderings, a change in animal population density that was advantageous to humans would be disadvantageous to the animal species, and vice versa.

The 6 possible orderings are: 1) A < OA < OH ; 2) A < OH < OA  ; 3) OA < OH < A ; 4) OH < OA < A ; 5) OA < A < OH ; 6) OH < A < OA .

For ordering 1, an increase in population density from A to OA would optimise the overall welfare of the animal species, but also bring the net benefit for humans closer to that at OH.  For ordering 2, an increase from A to OH would optimise for humans but also raise overall welfare for the animal species.  For orderings 3 and 4, a suitable reduction in population density would be beneficial for both humans and the animal species.  It is only for orderings 5 and 6, in which A is between OA and OH, that a change in density can be beneficial for humans or for the animal species, but not for both.

Proposition 2 should not be taken to imply that the 6 orderings are equally likely: such a claim would be way beyond what can be supported by current knowledge.  What it does suggest, however, is that, in the management of an urban animal species there is not necessarily a conflict between what is good for humans and what is good for the species.  Where an urban animal species is, on balance, a nuisance to humans, it is possible that a reduction in its population would also be good for the species.

However, that is just a possibility.  It is also possible that a reduction in the population of an urban animal species would be good for humans but bad for the species.  Much more research is needed to enable us to make well-supported decisions on the management of urban animals.

Notes & References

1. The Guardian (29/9/2016) Lion shot dead at Leipzig zoo after escaping from enclosure https://www.theguardian.com/world/2016/sep/29/two-lions-escape-from-leipzig-zoo-enclosure
2. “Pathogen” is a general term for micro-organisms that can cause disease, including viruses, bacteria, fungi, protozoa and worms.
3. Metro (8/9/2018)  Inside the secret world of London’s urban foxes  https://metro.co.uk/2018/09/08/inside-the-secret-world-of-londons-urban-foxes-7923273/
4. Aberdeen City Council  Living with Urban Gulls  https://www.aberdeencity.gov.uk/sites/default/files/2018-05/Living%20with%20Urban%20Gulls.pdf
5. Reuters (11/12/2018)  Monkeys run amok in India’s corridors of power  https://uk.reuters.com/article/us-india-monkeys/monkeys-run-amok-in-indias-corridors-of-power-idUKKBN1OA01R
6. East Coast Radio (30/8/2017) Monkey-ing around – harmless or menace?  https://www.ecr.co.za/shows/terence-pillay-iinvestigates/monkey-ing-around-harmless-or-menace/
7. San Francisco Animal Care and Control  Coyotes  https://www.sfanimalcare.org/living-with-urban-wildlife/coyote-sightings/
8. The Humane Society of the United States  Coyotes and people: what to know if you see or encounter a coyote   https://www.humanesociety.org/resources/coyotes-people-encounters
9. The Guardian (3/9/2019)  Swooping magpie shot by Sydney council after ‘particularly aggressive’ attacks  https://www.theguardian.com/environment/2019/sep/03/sydney-council-shoots-aggressive-swooping-magpie
10. The Guardian (10/12/2017)  Magpie edges out white ibis and kookaburra as Australian bird of the year  https://www.theguardian.com/environment/2017/dec/11/magpie-edges-out-white-ibis-and-kookaburra-as-australian-bird-of-the-year
11. See for example Gren I-M, Haggmark-Svensson T, Eloffson K & Engelmann M (2018)  Economics of Wildlife Management – an overview  European Journal of Wildlife Research 64:22  https://link.springer.com/article/10.1007/s10344-018-1180-3  – start of Introduction
12. See for example Gren et al as 12 above, p 3
13. This can be confirmed at the IUCN Red list website https://www.iucnredlist.org/, entering in turn the names of the species.
14. Trotti, J 9/7/2018 The Human and Economic Costs of Power Cuts and Blackouts https://www.distributedenergy.com/home/article/13034360/the-human-and-economic-costs-of-power-cuts-and-blackouts
15. See for example Huter K et al 2016 Economic evaluation of health promotion for older people – methodological problems and challenges BMC Health Services Research 16 (Suppl 5) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5016726/
16. Positive.News 8/3/2017  Are you a human supremacist?  https://www.positive.news/environment/are-you-a-human-supremacist/
17. UK Government  Foxes, moles and mink: how to protect your property from damage  https://www.gov.uk/guidance/foxes-moles-and-mink-how-to-protect-your-property-from-damage
18. Hecht, L (2019) Optimal population density: trading off the quality and quantity of welfare   https://www.wildanimalinitiative.org/blog/optimalpopulationdensity   See especially the final paragraph.
19. Wikipedia  Population Ethics https://en.wikipedia.org/wiki/Population_ethics
20. I use the term Pareto improvement here in a specialised sense.  It is not implied that such a change would leave each individual human and each individual animal no worse off, only that overall welfare for humans and overall welfare for animals would both be improved.