UK Climate Change Policy – A Critical Analysis (2)

The second of this series of posts focuses on carbon pricing in the UK, on policies for those sectors not currently subject to a carbon price, and on the integration of housing policy with climate change mitigation policy.

The UK has established a carbon price on significant parts of its economy via its Emissions Trading System (ETS), an example of what is sometimes termed a cap-and-trade system. In outline, the government sets an annual cap on the total emissions of firms within the scope of the system and issues emissions permits up to the amount of the cap.  Some permits are issued free and some are auctioned, the latter having raised government revenue of just over £4 billion in 2021 (1).  Firms within the scope of the scheme must limit their emissions according to the number of permits they have, but trading of permits between firms is allowed and this secondary market determines the carbon price, which is currently around £80 per tonne CO2 equivalent (2).  Firms therefore have an incentive to reduce their emissions up to the point at which the marginal abatement cost equals the carbon price. 

Such a trading system has the important property of economic efficiency.  The carbon price induces firms with lower abatement costs to reduce their emissions by more than those with higher abatement costs.  The total reduction in emissions across firms within the scope of the scheme is therefore achieved at least cost.

The fact that some permits are issued free should not limit the effectiveness of the ETS in reducing emissions.  Firms which receive free permits still have an incentive to reduce their emissions if they can do so at a cost less than the market price of permits, because they can then sell any unused permits.  More fundamentally, the cap applies to all permits, whether auctioned or issued free.  The effect of free permits is just distributional: to reduce government revenue while limiting costs to some firms and as a consequence helping to maintain their international competitiveness. 

For electricity generation only, the ETS is supplemented by a tax known as Carbon Price Support (CPS) at a current rate of £18 per tonne CO2 equivalent (3).

An alternative way to establish a carbon price, advocated by many (4), is via a carbon tax.  This has the same efficiency property as a cap-and-trade system.  A possible advantage over a trading system is that it could realistically be applied to small firms and individual households, many of which would have difficulty in coping with the complexities of permits and trading.  In principle, therefore, a carbon tax could provide a more comprehensive incentive for emissions reduction.  To help understand how big an advantage this might be, Table 1 below shows an analysis by sector of UK emissions and indicates which sectors are within the scope of the ETS or taxes providing an incentive to reduce emissions.

Table 1 is simplified in a number of respects, both in the classification of sectors and in the choice of taxes and similar instruments mentioned.  Because its data are for 2020, when passenger flights were greatly reduced due to the covid pandemic, the emissions figure for international aviation is much lower than for a normal year.  Apart from that, I believe the broad picture it presents is fair.  A couple of points merit explanation.  For electricity generation (fossil fuel) there is no mention of the significant addition to electricity bills for “environmental and social costs”.  The reason for this is that the policy instruments referred to in the third column are only those which provide an incentive for firms to reduce their emissions.  It is true that, within these environmental and social costs, a large element relates to climate policy costs, such as obligations under the contracts for difference scheme to subsidise wind and solar power.  However, the environmental and social costs are a levy on all electricity bills, not just those for electricity from fossil fuels, so they do not provide any incentive to electricity consumers to choose low-carbon electricity. 

The inclusion of Fuel Duty, a tax introduced to raise revenue long before climate change had become an issue, may appear puzzling. Let me offer here the following principle, which I have not seen stated as such, although I think most economists would agree.

People respond to the actual incentives created by a tax in the circumstances in which they find themselves, regardless of the intentions of the authorities in introducing and retaining the tax.  

Applied to Fuel Duty which raises the cost of running a petrol-driven car, and given that electric vehicles are now available as an alternative bearing no equivalent tax, the implication is that the duty provides an incentive to decarbonise personal transport. What’s more, the incentive is surprisingly large, as the following calculation shows.  The current rate of Fuel Duty on petrol is just over £0.50 per litre, but effectively £0.60 per litre because VAT at 20% is added to the duty (5).  When burnt, a litre of petrol yields about 2.4 Kg of CO2 (6). The implicit carbon price is therefore £0.60 / 2.4 or £0.25 per Kg, or £250 per tonne.  This is much higher than most estimates of the appropriate current carbon price to optimally address climate change, or the current price of ETS permits.  Even for the much lower rates of Fuel Duty applying to fuel for some agricultural uses (marked gas oil or “red diesel”) and shipping (fuel oil) (7), the implicit carbon price is a far from insignificant £40 per tonne. 

Let’s now consider the implications of the analysis in Table 1.  Of the total estimated emissions of 426 (MtCO2e), 257 are from sectors that are either wholly or mainly within the scope of ETS or subject to Fuel Duty.  The main potential benefit from a comprehensive carbon tax is that it could bring carbon pricing to the sectors responsible for the remaining 169 and so provide an incentive for decarbonisation in those sectors.  However, of this 169, 58 relates to sectors with mainly short-lived emissions such as methane and hydrofluorocarbons.  A carbon tax, understood as a tax on all emissions of greenhouse gases aggregated using the GWP100 metric, is not the most effective way to deal with such emissions.  As explained in my previous post, this metric significantly underweights their short-term warming effect.  Policy for these sectors should reflect the particular nature of their emissions. 

That leaves 111 (MtCO2e) of which the majority (65) relates to the residential combustion sector.  This sector consists of the burning of gas and other fuels for domestic heating and cooking (it excludes domestic use of electricity from fossil fuels because in that case the combustion takes place at the power station).  I will focus on gas since well over 80% of homes have gas central heating (8).  Taxes and levies on gas for domestic use are very low and provide little incentive to users to decarbonise.  Gas prices do include an element for environmental and social costs, but these are at a current rate of only about 3%, as compared with about 12% for electricity, including low-carbon electricity (9).  There is also VAT at 5%, but that also applies to electricity, again including low-carbon electricity (10).  In principle, there is a strong case for establishing a significant carbon price on residential gas use as an incentive to households to reduce their emissions.

At the time of writing, however, the price of gas to households has more than doubled in the last year, largely as a result of changes in global supply and demand.  This is one of a number of reasons for what has been termed a “cost of living crisis” in the UK.  If the price of gas should in due course fall back to the sort of level seen prior to 2021, then there may be a suitable opportunity to introduce a tax on residential gas use.  But to introduce such a tax at the present time would inflict significant hardship on poor households: politically it would be a non-starter. 

The conclusion I draw from this review of the main sectors for which no significant carbon price has been established, those outside the scope of both the ETS and Fuel Duty, is that to introduce a comprehensive carbon tax would be far from optimal as a means of mitigating the UK’s contribution to climate change, and – especially in view of its implications for the cost of gas to households – politically infeasible at the present time.  Hence:

Proposal 6:  Reductions in emissions in those sectors outside the scope of the ETS and Fuel Duty should be sought by suitable sector-specific policies (and not by a comprehensive carbon tax).

A number of sector-specific policies are already in place.  For waste disposal, the Landfill Tax, introduced in 1996 and progressively increased in real terms, is a major reason why methane emissions from landfill have fallen from 60MtCO2e in 1990 to 13MtCO2e in 2020 (11).  Rather than being the normal means of disposing of waste, landfill is increasingly regarded as a last resort where it is impracticable to use other waste management techniques such as recycling, incineration or generation of biogas.

The use of fluorinated gases including hydrofluorocarbons in refrigeration and air-conditioning has been regulated in the European Union since 2006, and since Brexit equivalent regulations have continued to apply in the UK (12).  Regulation is a more suitable instrument than taxation for this sector because emissions are difficult to measure: most occur not during the operation of equipment in good condition, but during manufacture or disposal of equipment, or during operation of poorly maintained equipment.  Hence measurement of emissions as a basis for taxation would be difficult, and the more effective approach adopted is regulation to specify which of the many types of these gases are permitted, to limit the total quantity of such gases used, and to promote good practice in manufacture, maintenance and disposal of equipment.

Fugitive emissions arising in the extraction, processing and distribution of oil and gas are difficult to measure for similar reasons.  These may be due to leakage at joints or valves, venting and flaring of waste gas, equipment failure and accidents.  A variety of regulations and regulatory bodies apply to different parts of the supply chain, with the North Sea Transition Authority (also known as the Oil and Gas Authority), the Environment Agency and the Health and Safety Executive all playing important roles.  Despite this, a study in 2021 by CATF, a campaign group, found numerous examples of poor practices resulting in methane emissions (13). This is perhaps unsurprising given that the relevant regulations and regulatory bodies have a variety of objectives of which climate change mitigation is just one.  In particular, the North Sea Transition Authority, according to its website:

“… has discretion in the granting of licences to help maximise the economic recovery of the UK’s oil and gas resources, whilst supporting the drive to net zero carbon by 2050” (14)


Proposal 7: Regulation and enforcement relating to fugitive emissions from the oil and gas industries should be reviewed to ensure that it gives adequate focus to climate change mitigation and takes due account of the powerful greenhouse effect of methane emissions.

While the raising of livestock is strongly regulated in respect of animal welfare, the UK has no significant policies designed to reduce the methane emissions arising from the digestive process of ruminant animals including cattle and sheep.  As Table 1 shows, this is the UK’s largest source of short-lived emissions.  Comparing different forms of meat in terms of the methane emissions associated with production of one kilogram of meat, these are highest by far for beef, much lower for lamb, and much lower still for pork and chicken (pigs and chickens not being ruminants) – see Table 2 below.  This is partly because beef cattle are typically slaughtered at around two years, as against about six months for sheep and pigs.  While other greenhouse gases also need to be considered, especially nitrous oxide from livestock waste, the conclusion remains that beef cattle make by far the largest contribution of any livestock to climate change per kilogram of food produced.  The contribution of dairy cattle is much less because of the very large quantity of milk that a dairy cow can yield over its lifetime.

Although the amount of a cow’s methane emissions depends on various factors – its breed, diet and age at slaughter – it is significant for all cows (15).  Measurement of emissions from a single cattle farm appears impracticable.  It is difficult to see how either an emissions tax or regulation could significantly reduce emissions while maintaining beef output.  It seems possible that developments in breeding or dietary science will eventually lead to beef production that could genuinely be considered low-methane, and without adverse effects on productivity or animal welfare.  For the time being, however, the only practical way to achieve a substantial reduction in emissions is to reduce beef production.  Fortunately, many consumers regard beef and other kinds of meat as near substitutes, implying that a small increase in the price of beef would probably lead them to reduce their consumption of beef and increase their consumption of alternatives.  This creates an opportunity for a significant contribution to climate change mitigation at the price of a small loss in consumer welfare.  Hence:

Proposal 8: The sale of beef should be taxed at a moderate rate with the aim of reducing beef production and so reducing methane emissions from cattle.

Several features of this proposal should be noted.  Firstly, while the policy may result in a  reduction in total meat production, it is not essential that it should do so. Even if a reduction in beef production were exactly offset by increased production of other meat, a reduction in methane emissions would still result.  Secondly, I refrain from making the claim that measures needed for climate change mitigation will, as an additional benefit, promote the adoption of healthier diets.  That may be so, but most people I think will want to take advice on diet from experts in that field, rather than as part of an argument about climate change.  Thirdly, the policy leaves even those consumers who do not eat pork for religious or cultural reasons with a reasonable choice of other meats: lamb, poultry and – at a somewhat higher price – beef.  Fourthly, beef production, especially when the cattle are mainly grass-fed, is land intensive: a reduction in beef production is likely to free some land for other uses.  Finally, a tax on the sale of beef will impact not only domestic production but also overseas production of beef for import to the UK, thus making a small contribution to reducing methane emissions abroad and so to Proposal 2 in my previous post.

Policy on emissions from international aviation is constrained by the Chicago Convention and other international agreements which, it is understood, do not allow the taxation of aviation fuel (IATA).  As a permitted alternative, in 1994 the UK introduced Air Passenger Duty, a tax per passenger per flight at a rate currently depending on the class of travel and whether or not the distance is more or less than 2,000 nautical miles, with exemption for children under 16 travelling by economy class (16).  Since the total tax due in respect of a fllght is therefore roughly correlated with the number of passengers and distance travelled, and since international airliners are mostly fairly similar (given current technology) in their fuel consumption, Air Passenger Duty can be considered a very imperfect substitute for a tax on aviation fuel.  In addition, flights to destinations in the European Economic Area are within the scope of the ETS (Airport Watch).  The combination of these measures provides little incentive to reduce emissions on long-haul flights, which account for the bulk of emissions (17).

The UK consulted in 2021 on a strategy to decarbonise aviation known as Jet Zero.  It includes some sensible ideas on improving fuel efficiency, improving management of airports and airspace, and developing low-carbon aviation fuels.  However, none of its scenarios show  aviation emissions reducing to zero by 1950 (18).  To get to net zero, they all rely on what it terms “abatement outside aviation sector”, that is, technologies yet to be identified for the removal of greenhouse gases from the atmosphere (19).  A common feature of all the scenarios is that demand reduction due to carbon pricing is estimated to lead to only a 9% reduction in emissions.  That I submit suggests a lack of seriousness about tackling climate change and perhaps a lack of willingness to make the case for discouraging international air travel and reducing the size of the aviation industry.

Having argued above that it would be inappropriate at present to bring residential gas consumption within the scope of carbon pricing, I will not make the same argument for aviation.  There is a fundamental difference between the two cases: home heating is an essential while international air travel in most cases is a luxury.  Most journeys from UK airports are either for holidays or to visit friends and relatives: less than 20% of journeys in 2019 were for a business purpose (20).  To create a stronger incentive to reduce aviation emissions, the practicable and sensible approach in the short term is to increase Air Passenger Duty on long-haul flights.  Hence:

Proposal 9: Rates of Air Passenger Duty on long-haul flights should be raised so that the overall structure of rates relates more closely to flight distance and therefore to fuel consumption.

A small – much too small – step in this direction has been taken by the introduction from 1 April 2023 of a slightly higher rate of duty for journeys over 5,500 miles.

Although taxes and levies on gas for domestic use are very low, a number of policies are in place or proposed with the aim of reducing emissions from domestic combustion.  The Heat and Buildings Strategy envisages gradual progress towards a future in which buildings are better insulated and heated mainly by electric heat pumps, with heat networks and hydrogen-powered boilers as alternatives in some circumstances (21).  Specific policies include:

  • The Social Housing Decarbonisation Fund: £800 million for social landlords (local authorities and housing associations) to carry out energy efficiency upgrades (eg insulation) in their tenants’ homes.
  • Phasing out the installation of new natural gas boilers from 2035.
  • The somewhat misleadingly named Boiler Upgrade Scheme: £450 million offering grants to households to contribute to the cost of installing heat pumps and, in limited circumstances, biomass boilers.
  • The Heat Pump Ready Programme: £60 million to support innovation in heat pumps and improve consumer experience in installation.
  • In due course, rebalancing energy prices so that heat pumps will be no more expensive to buy and run than gas boilers.
  • Ensuring that from 2025 all new homes are ready for net zero so that they will not need to be retro-fitted later.

The Strategy also indicates an ambition of both greatly expanding UK production of heat pumps and reducing their cost, although the specific policies to achieve this are not entirely clear.

The case for promoting the installation of heat pumps on a very large scale in place of gas boilers is twofold.  Firstly, heat pumps are powered by electricity, so are a zero-carbon source of heating provided the electricity is itself from a zero-carbon source.  Secondly, they are an extremely efficient source of heat. For other forms of heating such as gas boilers and conventional electric heaters, efficiency, measured as the ratio of heat energy output to energy input, cannot exceed 100%.  A heat pump, however, because it uses electricity to draw in heat from the air or ground outside a building, can achieve efficiency of 400% or more (22).  Additional benefits are that heat pumps, once installed, require little maintenance, and some models have the facility, when needed, to go into reverse and act as air-conditioners, a consideration that may became increasingly important as we need to adapt to climate change.

However, heat pumps also have disadvantages. The initial cost of purchase and installation depends on circumstances, but can easily be more than £10,000 (23), as against typically £2,000 to £3,000 for a gas boiler.  Costs may fall somewhat in future as an expansion of heat pump manufacturing in the UK yields economies of scale.  But it would be over-optimistic to expect a dramatic fall in costs such as solar power has experienced over the last decade.  The  unfamiliarity of heat pumps to many people in the UK may suggest that they are a relatively new technology with plenty of scope both for improvement and cost reduction.  In fact, the first heat pump was built in 1856 (24).  In the UK in 1945, an engineer named John Sumner developed a large-scale heat pump to heat the premises of the Norwich City Council Electrical Department, and later installed a heat pump in his own home.  Subsequently, the technology was adopted in some other countries much more widely than in the UK: the US is estimated to have had 750,000 heat pumps in operation by 2008.  By 2020, almost 180 million heat pumps were in use worldwide, the majority having been installed in new buildings (25). Considerable numbers were in countries colder than the UK, including Norway, Sweden and Finland. Two conclusions should be drawn from this. One is that there has already been plenty of opportunity across the world for innovation to improve the performance of heat pumps and reduce costs, suggesting that the benefits of further innovation may be only marginal.  The idea that heat pumps will eventually be no more expensive than gas boilers appears rather optimistic.  The other is that there is a lot of experience worldwide of installing heat pumps in different circumstances, and the UK should be drawing on that experience as much as possible (an example of Proposal 4 in my previous post).

To heat a home of any size, a heat pump alone is insufficient. The heat pump itself simply draws in heat from outside, but that heat then needs to be distributed to all parts of the home.  A variety of systems are in use, but to illustrate some potential complications I will refer to what is termed an air-to-water heat pump (26).  In outline, an outdoor unit takes in heat from the air and transfers it via a heat exchanger to a hot water tank.  Hot water is then circulated via a network of pipes to radiators located in the rooms of the home.  Suppose now that such a system is to be installed in a home which previously used a gas-powered central heating system. The conversion might seem fairly straightforward: the pipe network and radiators can be retained, the hot water tank can go in the space previously occupied by the boiler and, assuming the boiler was next to an external wall (as is likely for release of its waste gases) the outdoor unit can be fitted on the external side of the wall.

In practice, however, there can be various difficulties which will make the installtion of a heat pump system more complicated,  more costly, and perhaps impossible.  In some homes, especially flats, the boiler is not on the ground floor.  It may then be possible to fit an outdoor unit outside an upper floor, but it will need suitable physical support, and in a block of flats will probably require the landlord’s permission which could be refused, if only to preserve the external appearance of a block.  Even if the boiler is on the ground floor, the ground outside the wall may not be a suitable place to locate an outside unit.  In my home, for example, the boiler is next to an external wall, on the other side of which is a public pavement: an outside unit would have to go somewhere else, requiring fitting additional pipework to connect to the existing network with disruption to another ground floor room.  A further complication is that the existing radiators may not be suitable: a heat pump system will not heat water to as high a temperature as a gas boiler, and therefore larger radiators may be needed to yield the same heating effect (27).  Fitting larger radiators may in turn require changes to the location of furniture, and make it difficult to fit, say, a bed and a wardrobe into a small bedroom.  This helps to explain why some heat pump systems avoid radiators and instead use underfloor heating, but that further adds to the installation cost.

The conclusion to be drawn is that, although heat pump systems are an excellent option when included from the outset in designs for new homes, retro-fitting them into existing homes is in many circumstances awkward and expensive, and in some cases practically impossible.  It would not be surprising if some home-owners are induced by unscrupulous or poorly-trained salesmen in conjunction with government financial help to accept the installation of systems which turn out to be less satisfactory than their previous gas central heating.

A further feature of heat pump systems – although it may seem counterintuitive – is that they require coolants, typically hydrofluorocarbons or similar chemicals (28).  That means that, just as explained above for refrigerators and air-conditioners, heat pump systems may contribute to the atmospheric concentration of short-lived greenhouse gases.  Hence:

Proposal 10: The government’s aims of encouraging the installation of heat pump systems and reducing their cost should not be at the price of weakening measures to limit emissions of fluorinated gases.

The essential problem with the Boiler Upgrade Scheme is that it is not technology-neutral.  The government has picked its winners – heat pumps and, in limited circumstances, biomass boilers – and other low-carbon heating technologies do not qualify for financial support.  Why should equivalent financial support not be available for a household which replaces a gas-powered central heating system with modern electric heaters and also improves its insulation?  Provided the electricity is from a low-carbon source, such a system is just as low-carbon as a heat pump system, and has the advantage of avoiding any risk from fluorinated gases.  If storage heaters are used it can also contribute to balancing the timing of supply and demand for electricity – of which more in another post.  For the household, the capital cost may be much lower than for a heat pump system, and installation much less disruptive.  Hence:

Proposal 11:  Eligibility for the Boiler Upgrade Scheme should be extended to any household conversions from fossil-fuel heating systems to electric or other low-carbon heating systems, subject to defined standards of loft and wall insulation and glazing so as to limit energy consumption for heating.

Other low-carbon systems would include those powered by hydrogen (if and when hydrogen replaces natural gas in the local or national gas grid) and by solar thermal.  The Heat and Buildings Strategy notes the possible potential of hydrogen as a heating fuel which does not produce CO2 emissions because its combustion yields water vapour only (29).  Provided hydrogen can be produced in a zero-carbon way and distributed safely, it appears to offer an attractive heating solution for homes currently heated by gas central heating which for whatever reason are unsuitable for a heat pump, with only the boiler needing to be replaced while pipework and radiators could remain.  However, experience worldwide with hydrogen as a home heating fuel is very limited (30), and the Heat and Buildings Strategy sensibly plans safety and feasibility testing leading to a “village scale” trial by 2025 (31). 

Some other aspects of the Heat and Buildings Strategy are also questionable.  The date of 2035 for phasing out the installation of new natural gas boilers is explained in the Strategy as being 15 years before 2050, around 15 years being the lifetime of such a boiler (32).  That is presumably just an average: some will last longer and, if installed just before 2035, may continue, if permitted, to contribute to carbon emissions beyond 2050.  Furthermore, even if every gas boiler lasted exactly 15 years, many boilers might be contributing to carbon emissions right up to 2049, which would be consistent with the 2050 target but hard to reconcile with the plan of steadily reducing carbon budgets over the whole period to 2050.  Also, the “phasing out” wording leaves it unclear what exactly the government intends, and seems to represent a retreat from earlier statements referring to a “ban” which prompted strong reactions in some quarters.  There is clearly a dilemma for the government in trying to promote the installation of heat pumps and development of the heat pump industry to that end while avoiding the opposition that could be generated by perceptions of high costs for households and (even if some years away) compulsion.  Its hope, presumably, is that potential opposition can be overcome by a combination of innovation leading to cost reductions, support for improvements in consumer experience, financial support for early adopters, and a rebalancing of prices between electricity and gas. Whether that approach will be successful appears far from certain.  Hence:

Proposal 12:  Progress in phasing out the use of fossil fuels for home heating should be carefully monitored, and consideration given to a ban on new fossil-fuel systems (in addition to financial support for alternatives) should progress be insufficient.

It might be asked why it should be required that all new homes from 2025 be net zero ready.  Clearly, it is much cheaper to install zero-carbon heating when a home is built than to install a conventional heating system and then retro-fit later.  But is that a sufficient reason to ban anyone from building or buying a new home that has, say, gas central heating, at a time when such heating is still widely used in older homes?  Why not rely on the good sense of buyers to understand that, given the broad direction of climate change policy, buying a home that will need to be retro-fitted later represents a poor long-term investment unless the price is at an appropriate discount relative to a net-zero-ready but otherwise similar home, and on the recognition by developers that they will not make profits by selling new homes at such a discounted price?  One reason is that buyers may be unaware of the need for subsequent retro-fitting, or have no clear idea of how much it might cost or how much disruption it might involve.  But even if they are well-informed on these points, the need for retro-fitting may have little salience for them relative to other points they have to consider when choosing a new home, such as number of bedrooms, location, transport links, and local facilities.  It seems quite possible, therefore, that in the absence of government intervention, developers would still find a profitable market for new homes that were not net zero ready.

There is a further reason for government intervention which also illustrates a more general point about the political economy of climate change.  I referred above to the broad direction of climate change policy as a “given”.  But it isn’t a given: whether policies designed to progressively reduce emissions leading to net zero by 2050 will receive sufficient political support to enable them to be delivered is far from certain (33).   Even if bringing climate change to a halt is in the long-term interests of all, and even if many people are willing to accept some degree of sacrifice to that end, there are bound to be groups seeking to oppose particular climate change policies which would adversely affect their interests in the short and medium term.  Effective government in respect of climate change mitigation is not only about adopting the ‘right’ policies: it is also about building support for those policies by strengthening supportive interest groups and weakening opposition (34).  The large number of households with gas central heating is a substantial interest group, and I have already noted above that to put a significant carbon price on domestic gas use in current circumstances would be a political non-starter.  Financial support for the installation of heat pumps is one policy which will tend to weaken that interest group, by reducing its numbers.  Requiring new homes to be net zero ready may not reduce by very much the absolute number of households with gas heating: probably most new homes will be a net addition to the housing stock, rather than replacing existing homes.  It will however increase the proportion of homes that are net zero ready, and so gradually weaken potential opposition to measures that are likely to be needed eventually such as a carbon price on domestic gas and a ban on new gas heating installations.

The impact of the requirement will depend on how many new homes are built.  Average annual UK housing completions over the five pre-pandemic years 2015-19 were about 190,000 (35).  At that rate, completions during the whole period 2025-49 would be just under 5 million, about one-sixth of the current total housing stock of 29.5 million (36).  The impact would be much larger if annual completions were to increase to 300,000, a target indicated in the 2019 Conservative manifesto (37).

A faster rate of homebuilding would have two significant advantages in respect of climate change mitigation, over and above the general economic advantages of lowering housing costs by increasing supply and of facilitating labour mobility.  One would be to increase more rapidly the net zero ready proportion of the total housing stock.  The other would be, by increasing overall housing supply, to lower housing costs and so increase the proportions of household incomes available for other expenditure.  This in turn would increase the willingness of households to bear the costs needed to address climate change.  Putting the point another way, it is likely to be difficult to secure political acceptance for extra costs on households to reduce the UK’s emissions, let alone to provide generous financial help for poor countries in respect of climate change, while many households have little choice but to spend a large proportion of their incomes on housing, leaving them in the position of just managing – or not managing – in respect of other essentials such as food and fuel.

The rate of homebuilding could be increased with minimal public expenditure, simply by relaxing planning restrictions which can make it difficult for developers to obtain approval for new housing in areas where people want to live.  It is unfortunate that the government appears to have abandoned the main thrust of its White Paper Planning for the Future (2020), considered in this post, which included a proposal to designate growth areas within which outline approval for suitable housing development would be automatically secured.  It is also unfortunate that, despite the current intense concern and interest regarding the cost of living crisis, the cost of housing seems to be the elephant in the room, rarely mentioned despite being for many households by far the largest element in their spending. 

It has to be acknowledged that there is currently a substantial carbon footprint associated with the building of a new home, arising mainly in the manufacture of materials such as bricks, tiles, glass and cement.  The quantity, sometimes termed the embodied carbon, depends on the type of home and materials used, but for an average house is of the order of 60 tonnes CO2 equivalent (38).  To put that figure into perspective, annual emissions from an average house heated by gas central heating are about 2.4 tonnes.  We can infer that, in a scenario where an average gas-heated house is replaced by a new zero-carbon house, the ‘carbon payback period’, that is, the period it takes for the embodied carbon to be offset by the avoidance of ongoing emissions from gas heating, is 25 years (60 / 2.4).  The conclusion to be drawn is that, considered purely as a means of climate change mitigation, and even before consideration of cost, replacing old homes with new is a rather poor approach. 

Unfortunately, current VAT rules tend to favour new buildng over renovation.  VAT is not chargeable on the construction of new homes.  Under rules introduced in the April 2022 Budget, VAT is also not chargeable in most circumstances on the installation of energy-saving materials including heat pumps, insulation and solar panels.  However, there is no general VAT exemption for home repairs and refurbishments.  If therefore a home is in very poor condition but capable of being refurbished to a good standard, the extra VAT cost could tip the balance in favour of demolition and rebuilding, despite the much larger embodied carbon that would result.

Most demand for new homes is for reasons unrelated to climate change mitigation, including population growth, employment opportunities in particular regions, and (perhaps becoming increasingly significant in future) adaptation to climate change via replacement of homes lost or uninhabitable due to sea level rise, coastal erosion or frequent flood risk.  In such cases the carbon payback period is less relevant, but the issue of embodied carbon remains.  Indeed, those keen to maintain current planning restrictions might deploy the argument that such restrictions contribute to climate change mitigation.  However, such restrictions are not the best way to address the carbon footprint of building new homes.

Like all greenhouse gas emissions, the embodied carbon associated with new homes is a form of market failure, a negative externality consisting in the fact that, without government intervention, developers and home buyers do not bear the cost of the damage the emissions cause.  There are three reasons why is it better to address that externality via a carbon price on building materials than by stringent planning restrictions with the effect of limiting the number of homes built.  Firstly, a carbon price on building materials at the same rate as on other goods within the scope of the ETS will enable the market to find the best trade-off between building new homes and producing other goods, subject to the ETS cap on emissions.  More formally, it will ensure that profit-maximising developers build homes up to the point at which the marginal benefit per unit of emission from new homes equals that from other goods, assuming that benefit is reflected in the prices buyers are willing to pay.  Current planning restrictions, by contrast, yield a rate of homebuilding that depends on the vagaries of separate decisions by local planning authorities having little regard either to national housing needs or to climate change mitigation.  Secondly, the carbon price on materials is location-neutral: unlike planning restrictions, it has no bearing on developers choice of where to build new homes. Other things being equal, therefore, it enables developers to choose to build homes in areas where people want to live. Thirdly, the carbon price provides an incentive to design new homes, in terms of size and choice of materials, with less embodied carbon.  Strategies for limiting embodied carbon include avoiding sites requiring deep foundations, choosing simple, compact shapes (eg rectangles rather than L-shapes), and using timber-framed structures where possible.

Summarising the above, I propose the following package of measures to integrate housing development policy and climate change mitigation policy:

Proposal 13: To facilitate an appropriate trade-off between the economic benefits of housing development and the need to mitigate climate change:

  1. Planning restrictions on housing development should be relaxed, broadly along the lines of the White Paper Planning for the Future (2020);
  2. All new homes put on sale from 1 January 2023 should be required to be net zero ready;
  3. Repair and refurbishment of existing homes, including installation of insulation and low-carbon heating systems, should have the same VAT status as construction of new homes;
  4. The manufacture of materials used in building new homes and associated infrastructure should be subject to a carbon price at a rate consistent with the UK’s carbon budget at the time.

All these points require changes from current policy, although the changes needed are largest for (a) and (c). Point (b) implies bringing forward to 2023 the date of 2025 specified in the Heat and Buildings Strategy. There is no justification for allowing homes that will need retro-fitting to be sold for a further two years.

Point (d) is largely implicit in the ETS, which applies to the large-scale manufacture of, among other materials, bricks, tiles, cement, glass, metals and plaster board (39).  However, the scope of the ETS in many sectors is limited by thresholds.  Where production involves fuel combustion, the threshold is often 20 MW.  Other sectors have thresholds in terms of daily production capacity, including bricks and tiles (75 tonnes), glass (20 tonnes), and cement clinker (500 tonnes if from rotary kilns, 50 tonnes if from other furnaces).  Hence:

Proposal 14:  The various sector thresholds set out in Schedule 2 of The Greenhouse Gas Emissions Trading Scheme Order 2020 should be reviewed to ensure that they are no higher than necessary.

A threshold might be considered necessary if, for production at any scale below the threshold, the costs of compliance and enforcement, including measurement of emissions, would be  disproportionate to any benefit from abatement of emissions.  The logic behind the various current thresholds is far from clear; one suspects that they were arrived at partly as a result of lobbying by firms or industry bodies.  What’s more, the threshold quantities are quite large.  The power rating of a central heating boiler for an average house might be about 30 kW (40).  The 20 MW threshold is therefore equivalent to about 670 (20 x 1,000 / 30) such boilers.  For cement clinker, the daily 500 tonnes threshold is equivalent to about 180,000 tonnes annually, which is about 2% of total annual cement production (9 M tonnes (41 Statista)).  Because of these thresholds, some of the embodied carbon in new homes, and more generally much small and medium scale industrial production, is not currently subject to a carbon price. 

Notes and References

  1. ICAP  Factsheet 99 – United Kingdom  p 3
  2. EMBER  Carbon Prices
  3. HM Treasury  Spring Statement 2022 – Policy Costings  p 31
  4. Economists’ Statement on Carbon Dividends Organized by the Climate Leadership Council
  5. HM Government  Tax on Shopping and Services – Fuel Duty
  6. Carbon Independent,1%20gallon%20is%204.546%20litres).
  7. HM Government (17 May 2022)  Excise Duty hydrocarbon fuel rates
  8. English Housing Survey: Energy Report 2019-20  p 18
  9. Ralston J, ECIU (2022)  Energy bills: getting the balance right
  10. SSE Energy Services  Costs that make up your gas and electricity bills
  11. DBEIS  Final UK greenhouse gas emissions national statistics 1990-2020  Table 1.4 Row 75
  12. The Fluorinated Greenhouse Gases (Amendment) (EU Exit) Regulations 2021 (SI 2021/543)
  13. Clean Air Task Force (2021)  New evidence of UK methane pollution uncovered ahead of COP26;swpmtxnonce=4b770f2d2f
  14. North Sea Transition Authority – Licensing & consents – Overview
  15. Dewhurst R & Miller G (2019)  How do different livestock types, sizes and breeds differ in their greenhouse gas emissions?  pp 3-4
  16. H M Revenue & Customs  Rates for Air Passenger Duty
  17. Dept for Transport (2021)  Jet Zero Consultation para 3.14 p 26
  18. Dept for Transport, as (17) above  pp 13-15
  19. Dept for Transport, as (17) above  pp 35-36
  20. Statista  Purpose of air travel at airports in the United Kingdom 2002-2019,to%2017%20percent%20in%202019.
  21. DBEIS (2021) Heat and Buildings Strategy
  22. Pears A & Andrews G (2016)  Back to Basics: Heat Pumps
  23. EDF Energy  A complete guide to air source heat pumps
  24. Finn-Geotherm  The History of Heat Pump Technology
  25. International Energy Agency  Heat Pumps
  26. Idronics  Air-to-water heat pump configurations
  27. Kensa Heat Pumps – Radiators,efficiency%20of%20the%20heating%20system.
  28. WSP (2018)  The importance of refrugerants in heat pump selection
  29. DBEIS, as (21) above  p 82
  30. International Energy Agency (2021)  Hydrogen
  31. DBEIS, as (21) above  p 233
  32. DBEIS, as (21) above  p 20
  33. Lockwood M (2013)  The political sustainability of climate policy: the case of the UK Climate Change Act  Global Environmental Change 23 (2013) pp 1339-40
  34. Lockwood M, as (33) above  pp 1340-41
  35. Statista  New homes completed … in the UK from 1949 to 2019
  36. ONS  Dwelling stock by tenure, UK, 2020 edition  Table 1 row 25
  37. Conservative Party Manifesto 2019 p 31
  38. Barrett J & Wiedmann T (2007)  A Comparative Carbon Footprint Analysis of On-Site Construction and an Off-Site Manufactured House p 9
  39. HM Government  The Greenhouse Gas Emissions Trading Scheme Order 2020  Sch 2 Table C
  40. PlumbNation (2021)  What size boiler do I need for my home?
  41. Statista  Cement production volume in Great Britain from 2001 to 2019,levels%20seen%20prior%20to%202009.
Posted in Climate change | Tagged , , , , , , , , , | Leave a comment

UK Climate Change Policy – A Critical Analysis (1)

In the first of a series of posts, I focus on objectives and some issues regarding technology.

Anyone who takes seriously the task of analysing climate change policy is liable to be daunted by what they find.  The literature is vast, embracing many disciplines – climate science, technology, economics, behavioural science, international relations – and many sources – governments, inter-governmental bodies, academics, think tanks, campaign groups, industry bodies.  Just to understand the elements of current policy is a challenge, as my previous post – and the many sources I had to refer to to put it together – shows.  Then there is what might be termed the problem of numbers.  On the one hand one cannot get very far in policy analysis without considering numbers – to assess the importance of issues, to distinguish the possible from the unrealistic, and to compare the costs of different approaches.  On the other hand the literature abounds in numbers that for one reason or another are not useful, ranging from the poorly defined, the excessively detailed and the out of date to the incorrect and the just plain silly (a favourite from the last category: “recycling just one banana skin generates enough energy to charge your smartphone twice” (1)).

The complexity of the issues surrounding climate change policy perhaps invites the taking of short cuts.  In terms of the classification of thinkers into hedgehogs – those who view the world through one big idea – and foxes – those influenced by a variety of ideas (2) -, it seems that many of those who offer opinions on climate change policy have what may be called hedgehog tendencies.  The prisms through which different groups view climate change policy are varied: environmentalism; criticism of profit-seeking corporations; faith in free markets to deliver innovative solutions;  inequality (both between and within countries); general distrust of experts; and (at a more technical level) lively appreciation of the merits of a uniform carbon price.  Each of these prisms brings something useful to the policy debate, but is too narrowly focused to offer anything like a sensible overall policy package.  Climate change policy analysis – perhaps even more than most policy areas – needs foxes as well as hedgehogs.

I start with objectives.  The objective of net zero by 2050 is the centrepiece of current UK policy.  In recommending this objective, the Climate Change Committee referred to the Paris Agreement aims of limiting the increase in global average temperature to well below 2°C and pursuing efforts to limit it to 1.5°C.  It also noted the Agreement’s emphasis on equity and expectation that developed countries should take the lead.  Against that background the Committee considered that “an appropriate UK contribution … should go beyond what is required for the world overall” and recommended a path leading to net zero by 2050 as “towards the high end of the estimated range of necessary reductions for a limit of 1.5°C” (3).

The Committee also argued that “setting and pursuing [the net zero target] will confirm the UK as a leader among the developed countries on climate action” (4). It noted that several other climate leaders had set or were considering net zero targets by 2050 or earlier, and warned that for the UK to adopt a weaker or later target would undermine these moves towards a broader international consensus.  This is a most important point. The UK’s territorial emissions are only about 1% of the global total, so any influence it can exert, via its policy towards the 1%, on other countries’ policies towards the remaining 99%, represents a significant outcome of UK policy.  As it happens, a large number of countries have now committed, either in law or as government policy, to a target of net zero by 2050 or earlier, including Australia, France, Germany, Japan, South Korea, Spain and the US (5).

A possible criticism of the net zero target is that it is not grounded in economic analysis seeking to find the optimal balance between the harm done by climate change, including in the very long term, and the costs of mitigation.  A number of economists have developed Integrated Assessment Models which, in principle, can be used to determine mitigation paths which maximise welfare over time.  Such paths are typically characterised in terms not of carbon budgets progressing towards a net zero target at a certain date, but of a gradually increasing social cost of carbon.  For example, one version of the DICE model developed by Nordhaus and others implied a social cost of carbon to maximise welfare of $43 in 2020 rising to $105 in 2050 and $295 in 2100 (6).  In my view these models do not provide a suitable basis for setting climate policy.  One problem is that they depend on numerous assumptions, some based on less than conclusive evidence, and some involving contentious ethical judgments.  Perhaps the most contentious issue is what discount rate, if any, should be used in comparing costs of mitigation with the harm they are expected to avoid in the distant future.  Nordhaus (2018) states that “the debate on discounting … is just as unsettled as it was when first raised three decades ago” (7).  A matter on which economists are far from agreed is not an adequate basis from which to try to build a national and international consensus on climate policy. 

I readily accept that 2050 may not be the optimal date for the net zero target.  If it were possible to specify a suitable model and resolve all necessary issues regarding assumptions, the optimal date might well be found to be a few years either earlier or later.  But the nature of the climate change problem is that it requires global action.  To achieve a consensus around an easily understood objective which may only approximate to optimality would be a fairly good outcome.  To lose the opportunity for such a consensus by focusing on the possible sub-optimality of the 2050 date would not. 

However, acceptance of the net zero target should not be taken to imply that any methods of reducing emissions are acceptable.   Net zero is not an ultimate objective but a means to the end of limiting climate change.  Climate is influenced not only by the quantity of greenhouse gases in the atmosphere but also by the reflectivity (albedo) of the earth’s surface.  The widespread view that planting trees helps to mitigate climate change is an oversimplification: in some circumstances, especially at high latitudes, the effect of trees in sequestering carbon can be outweighed by their effect in absorbing more sunlight than lighter surface covers such as grass or snow (8).  Although the Climate Change Committee’s recommendations on the Sixth Carbon Budget include increasing the rate of afforestation to 50,000 hectares (about 190 square miles) per year by 2035 (9), I could not find any mention of reflectivity in the Committee’s very detailed supporting methodology document (10).  Hence my first proposal:

Proposal 1: Emissions-reducing projects involving large-scale changes in land use such as afforestation should be adopted only if careful assessment of their total effects, including their effects on reflectivity, clearly demonstrates a mitigating effect on climate change.

Subject to that caveat, I support the UK’s maintenance of the net zero by 2050 target. But I am not persuaded by all the points made by the Climate Change Committee in recommending that objective.  In arguing that the the UK should go beyond what is required for the world overall, the Climate Change Committee noted that the UK has “a significant carbon footprint attached to imported products” (11) (ie consumption emissions, which are not included within the UK’s net zero target and carbon budgets).  While that is a correct statement, the unstated suggestion is that the UK’s consumption emissions are a relatively minor issue which is adequately addressed by adopting a challenging net zero target.  It is hard to measure consumption emissions with great accuracy, given the the impracticability of determining the emissions from production of many different goods from many countries (and this may become even harder in future as some production processes in some countries become decarbonized).  However, it is estimated that 43% of the emissions associated with UK consumption are embedded in imports (12).  Reducing its consumption emissions is potentially therefore a very significant way in which the UK can contribute to mitigation of global climate change, requiring an objective of its own.  Hence:

Proposal 2: The UK should adopt an objective of substantially reducing the emissions embodied in its imports

Whether such an objective is best expressed as a quantified target is debatable, given the difficulty of accurate measurement.

The Climate Change Committee presented as a merit of the net zero target that it applies to all greenhouse gases, aggregated using the GWP100 metric (13). This is another oversimplification.  The GWP100 metric weights different gases according to the contributions which 1 tonne of a gas would make to global warming over 100 years (14).  Thus it provides a good measure of the long-term warming effect of a cocktail of gases.  However, policy also needs to consider the short-term effect of greenhouse gases, which can be crucial in determining whether and when warming will reach 1.5°C or 2°C, and in that context GWP100 is a poor measure because it gives insufficient weighting to the warming effect of short-lived greenhouse gases, primarily methane.  Sun et al (2021) state:

“… current net zero targets do not inherently call for early action on short-lived GHG’s, which a growing body of research shows is a key strategy to slow down global warming in the near-term.  Emissions of short-lived GHG’s account for nearly a third of today’s gross warming, and … emissions reductions in these GHG’s can quickly lead to slowing down the global-mean rate of warming” (15)

In conjunction with substantial global reductions in carbon emissions, early reductions in methane emissions can reduce by about 0.2°C the peak of global warming, which could make the difference between success and failure in meeting the Paris objective of keeping the increase in global mean temperatures below 2°C (16).  Hydrofluorocarbons – a large group of mostly short-lived greenhouse gases (17) widely used in refrigeration and air-conditioning – can also contribute to this effect.  Hence:

Proposal 3: The UK should supplement its net zero target with specific legally binding targets for reductions in short-lived greenhouse gas emissions including methane and hydrofluorocarbons

Although the UK has regulations in place regarding fluorinated gases including hydrofluorocarbons, these do not include a specific focus on short-lived hydrofluorocarbons (guidance relies on the flawed GWP100 metric (18)).  So far as methane is concerned, the UK (along with over 100 countries) has signed the Global Methane Pledge aiming to cut global methane emissions by 30% by 2030 (19), but has not yet adopted a legally binding target for reductions in its own emissions.

In arguing that the net zero objective is achievable, the Committee stated that its scenarios for reaching the target are based on “known” (or “existing”) technologies (20).  This again is an oversimplification.  I am struck by the contrast with Bill Gates’ book (reviewed in this post), which lists numerous technologies needed to achieve net zero (21).  Admittedly Gates was addressing the problem of getting the whole world to net zero.  But the main reason for the difference is surely the vagueness of claiming that a technology is “known”?  A widely used framework for assessing the status of a technology is the 9-point Technology Readiness Level scale (22), where Level 1 is “basic principles observed” and Level 9 is “actual system proven in operational environment”.  Technological innovation is often a gradual process, and the suggestion that technologies are either known or unknown is not helpful.  Research, development and innovation have a crucial part to play in getting the UK to net zero.

Sensible policy on technology for climate change mitigation requires an appropriate balance in several respects: between the roles of the government and the private sector; between technologies already at an advanced state of readiness and those which are more speculative; and between making new things possible, reducing the cost of what can already be done, and facilitating and promoting uptake of proven technologies. There is a risk however that policy may be distorted by over-ambitious aspirations to make the UK a global leader in climate-related technologies. In the introduction to his Ten Point Plan for a Green Industrial Revolution (2020), the Prime Minister wrote:

“We will turn the UK into the world’s number one centre for green technology and finance, laying the foundation for decades of economic growth by delivering net zero emissions in a way that creates jobs” (23).

The UK has indeed been a global leader in some aspects of climate change mitigation: for example in being one of the first countries to adopt a legally binding target for emissions reductions.  As a developed country with one of the world’s largest seven economies, and with a relatively long history of industrial emissions, it has a responsibility to act as a leader.  In respect of technology, it can reasonably aspire to technological leadership in fields where it has or can develop a comparative advantage, because of either its natural resources and geography or its stock of physical and human capital. Offshore wind energy is perhaps such a field. 

It would, however, be a mistake for the UK to attempt to become a technological leader in every climate-related field.  The likely outcome would be that resources for innovation would be spread too thinly to be effective, with the UK’s efforts in many fields dwarfed by those elsewhere.  Furthermore, an obsession with leadership may result in opportunities to learn from other countries being missed.  Hence:

Proposal 4: The UK government should accept that, for some technologies needed for climate change mitigation, its main focus should be on encouraging and facilitating the application and adaptation to the UK’s circumstances of what has been learned through innovation and experience in other countries.  It is neither necessary nor advantageous for the UK to try to achieve global leadership across the full range of climate-related technologies. 

My final proposal in this post concerns the assessment of progress towards net zero. The progressively reducing carbon budgets are important because mitigation of climate change depends not only on the level of emissions at 2050 and beyond but also on the pathway of emissions between now and 2050 (24).  These budgets also serve as a measure of progress towards net zero, but only in a very imperfect way.   Currently, the UK is towards the end of the third budget period, for which the budget, likely to be achieved, is equivalent to a reduction in emissions of about 34% relative to 1990.  That indicates progress in a sense.  But it is misleading to assess progress towards net zero without regard to the degree of readiness of the technologies that will be needed to complete the transition.  Have the technologies needed to secure the remaining 66% reduction been demonstrated to work, in the particular circumstances in which they need to operate in the UK, at reasonable cost?  And if not what are the innovations that are needed? 

I cannot find answers to these questions in the Climate Change Committee’s latest progress report to Parliament.  In fact, although the report runs to more than 200 pages, it contains very little about technology.  For example, a lengthy chapter entitled “Underlying progress on key enablers of the path to Net Zero” is divided into sections headed, respectively, “Governance and delivery”; “People and public engagement”, “Just Transition – who pays and who gains?”, “Just Transition – workers and skills”, and “Other key drivers of progress” (25).  Within the latter, there is a short subsection (26) on innovation and infrastructure.  Hence:

Proposal 5: The annual progress reports to Parliament by the Climate Change Committee should focus in more detail on the extent of the UK’s technological readiness to achieve the net zero target by 2050.

Cement production is an example of a sector in which the UK (and indeed the world) appears to lack  the technology needed for net zero, in the sense that the reasonable cost requirement has not yet been met.  One way to express the cost issue is what Gates calls the green premium – the percentage by which the cost of producing a good using the cheapest available zero-carbon technology exceeds the cost of conventional production (27).  For cement, he quotes (for the US) a range for the green premium of 75% to 140% (28). The equivalent range for the UK will probably be slightly different, but in any case that’s a large extra cost, given that cement is an essential input to concrete which is used in very large quantities in buildings and infrastructure. 

The Climate Change Committee uses the more conventional concept of abatement cost – the cost per tonne of CO2 of reducing emissions to zero.  I could not find in its publications an abatement cost for cement production, but for the whole of the manufacturing and construction sectors, of which cement production is an important part, it indicates a cost of c £100 per tonne (29).  Gates’ figures however are equivalent to £150 to £280 per tonne (30).  These are not necessarily inconsistent with the Committee’s figure since the abatement cost may be much lower for other parts of the manufacturing and construction sectors.  But it does highlight the need for more detailed information on technologies and costs to give credibility to the Committee’s claims about the feasibility and costs of attaining net zero.

Notes and References

  1. Seen in a leaflet about food waste recycling distributed in the Merton area of south west London.  The connection with climate change is that the processing of the food waste to produce fertiliser and gas which is used to generate electricity results in much less CO2 equivalent emissions than would taking the waste to landfill.
  2. Wikipedia – The Hedgehog and the Fox
  3. Climate Change Committee (2019)  Net Zero – The UK’s contribution to stopping global warming  p 19
  4. Climate Change Committee, as (3) above  p 21
  5. Energy & Climate Intelligence Unit – Net Zero Scorecard
  6. Nordhaus W D (2018)  Climate change: The Ultimate Challenge for Economics  Nobel Prize Lecture  p 454              
  7. Nordhaus, as (6) above  p 455
  8. Popkin G (2019)  How much can forests fight climate change?  Nature 15 January 2019  p 281
  9. Climate Change Committee (2020)  The Sixth Carbon Budget  p 170
  10. Climate Change Committee (2020)  The Sixth Carbon Budget Methodology Report  pp 223-6
  11. Climate Change Committee, as (3) above  p 19
  12. DEFRA  UK’s Carbon Footprint 1997-2018  p 3
  13. Climate Change Committee, as (3) above  pp 16-17
  14. NIWA  What are ‘Global Warming Potentials’ and ‘CO2 Equivalent Emissions’?
  15. Sun T et al (2021)  Path to net zero is critical to climate outcome  Nature Article No. 22173 (2021)  p 2
  16. Sun T et al, as (15) above.  See Chart A p 4
  17. IPCC (2013)  Climate Change 2013: The Physical Science Basis  Ch 8 Anthropogenic and Natural Radiative Forcing  Table 8.A.1 pp 731ff
  18. EU Regulation No. 517/2014 specifies GWP100 in Article 2 Definition 6  Since Brexit the equivalent rules apply in the UK via Regulation SI 2021/543
  19. BBC (2/11’2021)  COP26: US and EU announce global pledge to slash methane
  20. Climate Change Committee, as (3) above  pp 21 & 26
  21. Gates B (2021)  How to Avoid a Climate Disaster  Allen Lane  p 200
  22. Science Direct – Technology Readiness Level
  23. H M Government (2020)  The Ten Point Plan for a Green Industrial Revolution  p 3
  24. Sun T et al, as (15) above  p 1
  25. Climate Change Committee (2021)  Progress in Reducing Emissions: 2021 Report to Parliament  pp 96-105
  26. Climate Change Committee, as (24) above  p 104
  27. Gates B, as (21) above  p 59
  28. Gates B, as (21) above  p 107
  29. Climate Change Committee, as (9) above  Read from Fig 5.6 p 261
  30. To convert Gates’ figures to abatement costs per tonne of CO2 we need the following data: UK cement production in 2019 was 9.1 M tonnes (31) and generated 4.4 M tonnes CO2 emissions (32), implying that emissions from producing 1 tonne of cement were c 0.5 tonnes.  The cost of producing 1 tonne of cement was c £100 (33), so with the green premium would have been in the range £75 to £140 per tonne of cement, or £150 to £280 per tonne CO2.
  31. Statista – Cement production in Great Britain from 2001 to 2019,million%20metric%20tons%20of%20cement.
  32. DBEIS – 2019 UK greenhouse gas emissions: final figures – data tables (Excel)  Table 1.2 row 78 col AF
  33. Construction Enquirer
Posted in Climate change | Tagged , , , , , , , | Leave a comment

UK Climate Change Policy – An Outline

Anyone who has followed the news in the UK over the last year will have heard plenty about COP26 and Extinction Rebellion, and about extreme heat, forest fires and melting ice in various parts of the world.  UK policy on climate change, despite its implications for everyone’s lives in the decades ahead, has received rather less attention.  Here I present, in Q & A form, an outline of the legal framework, current policy, progress to date, and ideas which seem likely to influence future policy.

What is the UK’s long-term target for reducing its greenhouse gas emissions as a contribution to mitigating global climate change?

The government has adopted a target of reducing net emissions to zero by 2050.

Which gases count towards this target?

All significant greenhouse gases, including carbon dioxide, methane and others.

Which emissions are considered to be the UK’s emissions?

Its territorial emissions consisting, broadly, of those emissions generated within the UK.  These exclude emissions from production overseas of goods imported to the UK, sometimes termed “consumption emissions”.  Emissions from international shipping and aviation were initially excluded, but more recently the UK’s share of such emissions has been considered part of its territorial emissions.

What is the significance of “net” emissions?

Deductions against total emissions are allowed for removals of greenhouse gases from the atmosphere and funding emissions-reducing projects abroad.

Wasn’t there a target of reducing emissions by 80%?

That was the target set in the Climate Change Act 2008.  It was changed to 100% (ie reduction to zero) in 2019 (1).

What else did the Climate Change Act do?

It required the government to set “carbon budgets” for the UK covering all the main greenhouse gases  for 5 year periods starting from 2008-12, and to ensure that these budgets are not exceeded.  Budgets from 2023-27 were to be set at least 12 years in advance.  It also required the government to make 5-yearly assessments of the risks to the UK from climate change and to prepare adaptation policies to address those risks.  It established a Committee on Climate Change to advise the government on climate change matters including the setting of carbon budgets.

Where are we now in terms of the 5 year carbon budgets?

The first and second 5 year periods have been completed and we are now in the third (2018-22).  Carbon budgets for the fourth and fifth periods (2023-32) were set some years ago.  The carbon budget for the sixth period (2033-37) has a particular importance as it was the first to be set after the 2050 target had been amended to net zero. 

Are the UK’s carbon budgets consistent with international agreements on climate change?

The UK has generally set its carbon budgets to go beyond its commitments under international agreements:

  • For the Kyoto Protocol’s second commitment period (2013-20), the UK’s target reduction was 20% (all reductions quoted are relative to a 1990 baseline) (2).  Its carbon budget for 2018-22 is a reduction of 34% (3,4).
  • Following the Paris Conference (2015), countries were required by 2020 to submit their plans, known as nationally-determined contributions, for reaching the goal of limiting global warming to below 2 and preferably to 1.5 degrees Celsius above pre-industrial levels.  The UK’s submission committed it to a reduction in emissions of at least 68% by 2030 (5).  This did mean that its emissions would need to fall by more than the 57% that had previously been budgeted for the UK’s fifth period (2028-32), but for the sixth period (2033-37) its budgeted reduction was set at a much more challenging 78% (6,7) 

So the UK has been a good citizen internationally in respect of climate change?

That’s debatable. On the one hand:

  • The UK can reasonably claim to have exercised international leadership in its early adoption of a legally binding target via the Climate Change Act.

On the other hand:

  • In focusing on carbon budgets which exclude consumption emissions, the UK is arguably measuring its performance against inappropriate benchmarks.
  • Some argue for even faster emissions reductions by developed countries including the UK because of the risks climate change poses to life in the tropics and in low-lying islands.  They also point to the responsibility of developed countries, via their historic emissions, for the vast majority of climate change to date.
  • The Copenhagen agreement (2009) included a pledge by developed countries to transfer US$ 100 billion annually to poor countries by 2020 to help fund mitigation of and adaptation to climate change (8). The UK pledged to transfer £5.8 billion over the 5 years beginning April 2016 (9), equivalent to about US$ 1.5 billion annually, a very small contribution towards the US$ 100 billion target, although the contributions of other developed countries have also fallen well short. 

How have the UK’s actual emissions compared with its carbon budgets?

The budgets for the first two periods were comfortably met, that is, actual emissions were below the budgeted levels (10).  Results for the third period should be available in 2023.

So the UK has made a good start on the road to net zero emissions?

Again, that’s debatable.  Those budgets were set before the net zero target had been adopted.  The post-2008 recession helped to reduce emissions simply by reducing economic activity.  More fundamentally, it is much easier to reduce emissions from some sources than from others.  Much of the reduction was achieved by switching from coal to natural gas to generate electricity, but burning natural gas still produces about half the emissions of coal.  A net zero economy will need to generate very large quantities of zero-carbon electricity.

Where is it likely to be especially difficult to reduce emissions to zero?

Difficult sectors include:

  • Agriculture, especially livestock production (a major source of methane).
  • Shipping and aviation (unlike road and rail transport, these cannot be electrified to take advantage of electricity from renewable sources).
  • Cement production, for use in concrete (this currently involves burning limestone, a process which produces carbon dioxide even if the fuel source is zero-carbon).

What measures does the Climate Change Committee propose to reduce emissions by 78% as required by the sixth carbon budget (2033-37)?

The Committee proposes (11):

  • Conversion to low-carbon technologies in industry, transport and the home, to be achieved mainly by electrification or use of hydrogen fuel.
  • Expansion of low-carbon electricity from 50% now to 100% by 2035 using various renewable sources, the largest contribution coming from offshore wind.
  • Reduction of demand for carbon-intensive goods and services.
  • Changes in land use, with more woodland and biofuel crops, and restoration of peatlands.

Of these four areas, the first is projected to have the largest effect, but all are needed to achieve the budgeted 78% reduction.

Is it true that the UK already gets 50% of its electricity from low-carbon sources?

Yes, approximately.  Almost 50% of electricity in 2020 was from low-carbon sources, comprising wind (25%), nuclear (15%), solar (4%) and hydro (3%) (12).  But the low-carbon share of total energy, including not only electricity but also gas for home heating and oil for transport, is still much less than 50%.

Has the government accepted the Committee’s proposals on mitigation?

Yes, broadly.  Over the last two years the government has published a number of detailed documents setting out strategies and specific policies to reduce emissions:

There are also various policies which have been in place for some years which will continue with at most minor changes.  These strategies and policies to a large degree reflect the Committee’s proposals.  Most of them apply to the whole of the UK, although as the last two documents illustrate there are some exceptions in respect of matters devolved to Scotland, Wales and Northern Ireland.

What kinds of policy tools is the government using to reduce emissions?

A combination of project funding, taxes, regulation, and what might loosely be described as other financial incentives.

What funding is the government providing?

Funding commitments include (in rounded £ Million):

  • £2,500M over 2020-25 to help public sector bodies fund heat decarbonisation and energy efficiency measures.
  • £1,750M to fund energy efficiency upgrades in social housing and low-income households.
  • £2,000M over 5 years for schemes to facilitate cycling and walking (and so reduce car use).
  • £1,300M to accelerate the roll-out of electric vehicle charging infrastructure.
  • £1,000M to build an electric vehicle supply chain.
  • £600M to provide grants to help buy electric vehicles.
  • £300M to try to make electric vehicle batteries 95% recyclable by 2035.
  • £600M over 2020-22 for zero-emission buses (mainly electric but some powered by hydrogen).
  • £1,000M by 2025 for investment in carbon capture, utilization and storage (CCUS), a technology offering the promise of emissions-free use of fossil fuels and biofuels in electricity generation and industry.
  • £1,000M for the Net Zero Innovation Portfolio providing funding for low-carbon technologies and systems.
  • £450M over 3 years for the Boiler Upgrade Scheme to provide grants to help replace boilers by electric heat pumps (replacing the former Renewable Heat Incentive Scheme).
  • £240m to support hydrogen production projects.
  • £500M to increase planting of new woodland to over 100 square miles annually (13).
  • Numerous smaller sums, including funding for various competitions designed to stimulate innovation in low-carbon energy and emissions reduction.

What about taxes?

The government’s approach has been to use taxes to change business behaviour while avoiding climate-related taxes directly on households. Businesses can however pass on to households the costs of these taxes.  The main taxes are:

  • The Climate Change Levy, paid by electricity generators on their fossil fuel inputs and by other businesses on their electricity and fossil fuels, albeit with reduced rates for certain energy-intensive businesses (to mitigate loss of international competitiveness).
  • The Green Gas Levy, a tax on natural gas suppliers.  The money raised is used to fund the Green Gas Support Scheme providing incentives for the production of biomethane for injection into the gas grid.
  • The Landfill Tax, designed to discourage disposal of waste by landfill.  Introduced in 1996, this tax has contributed to an 80% reduction in landfill emissions (14).

There are also some tax breaks designed to encourage emissions reduction:

  • Exemption from vehicle excise duty (car tax) for electric cars and vans.
  • Electric vehicles are also exempt from fuel duty, a tax on petrol and other liquid fuels used in trasnport.
  • Enhanced capital allowances for businesses on the purchase of certain new energy-efficient or low-carbon equipment.

What regulation is in place or planned?

Regulations in place include:

  • The Renewable Transport Fuel Obligation requiring fuel suppliers to supply a certain percentage of renewable biofuels, currently 9.6% and planned to be increased to 14.6% by 2032. 

Among planned regulations are some which will have very direct effects on households and individuals:

  • The sale of new petrol and diesel cars and vans will be banned from 2030.  Sale of hybrid vehicles will be allowed until 2035, from which date all new cars and vans will have to be zero-emission.
  • All new heating systems will have to be net zero compatible by 2035, implying that the installation of new natural gas boilers will be banned.  In the meantime, policy will aim to ensure that electric heat pumps become an attractive and cost-effective alternative.
  • The sale of peat for garden use is likely to be banned, to help preserve peatlands.

What are the “other financial incentives”?

There are three large and complex schemes:

  • The UK Emissions Trading Scheme is a “cap and trade” scheme which replaced, following Brexit, the UK’s participation in the EU Emissions Trading Scheme. It applies to electricity generation, energy-intensive industries including steel and cement production, and aviation on some routes.  The government sets a cap on the total emissions allowed by businesses within the scheme, and issues emissions allowances to businesses to the amount of the cap. These allowances can be traded which encourages businesses to reduce emissions where this can be done at least cost. The cap will be gradually reduced as the UK moves towards net zero. For electricity generation only, the Scheme applies in conjunction with a Carbon Price Floor ensuring that the effective cost of emissions reaches a cerain rate, currently £18 per tonne of carbon dioxide. For other sectors the cost per tonne has at times been much lower.
  • The Contracts for Difference Scheme is designed to support low-carbon electricity generation from sources which, at a certain stage of development, are too expensive to compete with electricity from conventional sources.  Generators submitting successful bids for new low-carbon capacity are paid over a 15 year period at a rate calculated to reflect their extra cost over the average UK price of electricity. 
  • The Renewables Obligation closed to new renewable generating capacity in 2017, but continues to require electricity suppliers either to obtain a certain proportion of their electricity from certain renewable sources accredited prior to closure, or else suffer a financial penalty. 

What is the long-term vision for energy supply?

It is envisaged that the UK will need much more electricity than now, partly because of normal growth in demand, but also to meet new demands for electricity including heat pumps, electric vehicles and hydrogen production.  The  majority of electricity will be from renewables, mainly onshore and offshore wind and solar, also biomass, with energy storage in the form of hydrogen to overcome the intermittency problem of wind and solar.  There will also be significant contributions from nuclear, and from gas with carbon capture and storage.  Transport will be powered mainly by electricity or hydrogen, with some use of biofuels especially for shipping and aviation.

Is carbon capture and storage a proven and cost-effective technology?

Around the world, there are currently some 40 carbon capture facilities in operation (15).  However, some of these use the carbon (eg for enhanced oil recovery) rather than storing it. The effectiveness of storage – whether there is a long-term risk of leakage to the atmosphere – is hard to prove and may depend on the storage site.  It is probably fair to say that capture has been proven to be feasible, but that whether capture and effective long-term storage can be delivered at a cost comparable with other low-carbon technologies remains to be demonstrated.  It may be however that, as with wind and solar over the last decade, costs will fall as experience is gained.

How much will it cost to get to net zero?

The Climate Change Committee estimates that the annual investment needed to deliver its proposals will rise to about £50 billion by 2030 and remain fairly stable thereafter (16).  That’s a 12% increase on current total annual investment of about £400 billion.  The required investment can be delivered largely by the private sector provided that the government creates a stable long-term policy framework. The Committee also estimates that there will be a net decrease in annual running costs, largely due to fuel cost savings in industry, and that these savings will steadily rise, so that by around 2040 they will more than offset the required annual investment cost.

Households are being faced with large increases in energy costs right now.  How far is that due to climate change policies?

It is true that household energy costs are higher than they would be without policies to reduce emissions.  Several of these policies increase costs to energy suppliers, and some at least of these extra costs are passed on to households.  However, policies such as the Renewables Obligation and the Climate Change Levy have been in place for some years, and have not changed dramatically over the last year.  The main reason for the sudden increase in energy costs is the combination of:

  • The UK’s heavy reliance on gas which heats 85% of homes and is the source of 35% of its electricity.
  • An increase over the last year in world demand for gas.

Of these factors, the second is largely outside the UK’s control, but the first is partly due to UK policies over the past decades (although alternatives such as a slower removal of coal from the energy mix or greater investment in nuclear would also have had disadvantages).  In the long run, further expansion of wind and solar should make UK energy costs less dependent on world markets.

What is the UK’s long-term target for adaptation to climate change?

There is no clear target. Climate change presents many different risks, and the extent of future warming and other changes in climate is far from certain.  Unlike mitigation, adaptation is not usefully framed as working towards a single numerical target.  

What are the main conclusions of the Climate Change Committee’s latest assessment of the risks from climate change?

Its Independent Assessment of UK Climate Risk, published in 2021, states starkly that “adaptation action has failed to keep pace with the worsening reality of climate risk” (p 11) and that the government “has not heeded our past advice” on setting and adequately resourcing “a framework of targets, incentives and reporting” (p 23).  It identifies eight risk areas judged to require urgent action:

  • Risks to natural ecosystems from increased temperatures and extreme events such as droughts and wildfire.
  • Risks to soil health from increased flooding and drought.
  • Risks to natural carbon stores such as soil, trees, saltmarsh and underwater kelp forests.
  • Risks to crops, livestock and commercial trees from multiple hazards including heat stress, drought, flooding, fire, pests, diseases and invasive non-native species.
  • Risks to the supply of food, goods and vital services due to climate related impacts on supply chains and distribution networks.
  • Risks to electricity supply from climate-related hazards including flooding, water shortages, increased tenperatures and wildfire, sea level rise and storms.
  • Risks to human health, well-being and productivity from increased exposure to heat in homes and other buildings.
  • Multiple risks from climate change effects overseas which could lead to cascading impacts across sectors and countries.

What specifically does the Committee recommend?

Its most prominent recommendations take the form of principles for good adaptation. It asks the government to:

  • Set out a vision of a well-adapted UK.
  • Integrate adaptation to climate change into policies on a wide range of matters (rather than treating it as a self-contained topic).
  • Take early action where necessary, eg to prevent irreversible changes to ecosystems or avoid the need for expensive retrofitting of buildings.
  • Prepare for extreme weather events and not just for average temperature rises.
  • Assess interdependencies such as the human and economic effects of climate-related failure of electricity supply.
  • Address climate-related inequalities, eg low-income households being more exposed to flood risk.

What does the government see as its role in respect of adaptation?

The second National Adaptation Programme was published in 2018 (the government has not yet published a third programme responding to the Climate Change Committee’s latest assessment).  The Programme includes a very long list of actions, but it also includes passages which suggest that the government sees for itself a limited role. It states for example that infrastructure operators are private businesses responsible for their own business continuity measures, and that the government’s responsibility is to ensure that no policy or regulatory barriers prevent them from managing their climate risks (p 31).  Of the actions in the Programme, many refer vaguely to, for example, “supporting” or “encouraging” initiatives, “working with” partners, and “monitoring” progress. The only major  funding commitment highlighted in the Programme is £2,600 million over 6 years to reduce flood and coastal erosion risk. 

So the government is not actually doing all that much about adaptation?

That’s debatable.  There are a number of areas in which climate change adaptation has been integrated into broader policies.  To give a couple of examples:

  • Farmers and others can obtain funds via the Countryside Stewardship Scheme and similar schemes for projects to improve the rural environment.  Guidance includes climate change adaptation among the outcomes supported (p 7). 
  • The National Planning Policy Framework sets out law and guidance to be followed by local planning authorities in England in determining planning applications for new housing and other developments.  It states that plans should take a proactive approach to adaptation to climate change, “taking into account the long-term implications for flood risk, coastal change, water supply, biodiversity and landscapes, and the risk of overheating from rising temperatures” (p 45).

However, it is easy for the government to add wording about climate change adaptation into policy documents.  The Climate Change Committee clearly considers that there is much more to be done in terms of funding and delivery. 

This post is intended to be largely factual.  I plan in due course to post a critical analysis of UK climate change policy.

Notes and References

  1. The Climate Change Act 2008 (2050 Target Amendment) Order 2019
  2. Wikipedia: Kyoto Protocol – Emissions Cuts
  3. Climate Change Committee (2008) Building a Low Carbon Economy  The 34% reduction in emissions in the 3rd carbon budget, implying a budget of 2,570 MtCO2e, is on p xix.
  4. The Carbon Budgets Order 2009  The Order shows that the 3rd budget was set at 2,544 MtCO2e, very close to the Committee’s recommendation.
  5. DBEIS The UK’s Nationally Determined Contribution under the Paris Agreement,2030%2C%20compared%20to%201990%20levels.
  6. Climate Change Committee (2020) The Sixth Carbon Budget  UK Carbon Budgets – Climate Change Committee ( The 78% reduction in emissions is on p 38, and can be seen from the chart on p 39 to imply a budget of c 1,000 MtCO2e.
  7. The Carbon Budget Order 2021 The Carbon Budget Order 2021 (  The Order shows that the 6th budget was set at 965 MtCO2e, very close to the Committee’s recommendation.
  8. House of Commons Library (2021): COP26: Delivering on $100 billion climate finance
  9. HM Government UK International Climate Finance  The £5.8 billion figure is on p 4.
  10. Cambridge Econometrics (2019) How the UK met its carbon budgets p 5
  11. Climate Change Committee, as 6 above, p 25
  12. These percentages are derived from the following figures in the Digest of UK Energy Statistics Table 5.6 Electricity fuel use, generation and supply  In row 504 (All generating companies, supplied gross) (in GWh) Wind 75,380, Nuclear 45,668, Solar 13,158, Hydro 6,636 + 1,397, All Sources 297,683.
  13. HM Government (2021) The England Trees Action Plan 2021-24  The figure given (p 3) is 30,000 hectares, equal to c 116 square miles (1 square mile = 259 hectares).
  14. DBEIS Final UK greenhouse gas emissions national statistics 1990 to 2019  Table 5.1 Estimated territorial greenhouse gas emissions by end user category, UK, 1990=2019, row 111 Landfill.
  15. IEA (2021) About CCUS
  16. Climate Change Committeem as 6 above, pp 20-1
Posted in Climate change | Tagged , , , , , , | Leave a comment

The Maximum Duration of Constant Consumption

At what rate should an essential non-renewable resource be depleted to sustain an economy for as long as possible? 

Suppose the inputs of a closed economy consist of produced capital, a non-renewable resource and labour .  Output is of a single good which can be either consumed or added to the stock of produced capital.  The quantity of output is determined by a constant-returns Cobb-Douglas function, implying in particular that if any of the inputs is nil then output is nil.  Technology is constant, as is labour input.  Produced capital depreciates at a constant positive rate .

Question:  Given that (as explained in my previous post) constant consumption cannot be sustained forever, for what length of time can it be sustained at a given rate, and at what rate should the resource be depleted to achieve that maximum time?

Suppose the production function is:

Y(t) = A(K(t))α(R(t))β      (A,α,β > 0; α + β < 1)


Y(t) = output at time t;

K(t) = stock of produced capital at time t;

R(t) = rate of use of a non-renewable resource at time t;

A, α, β are fixed parameters, the value of A reflecting the  technology and the labour input, both of which are assumed constant.  

The initial stocks of produced capital and the resource are K0 and S0, and depreciation of produced capital is at a rate δK(t) (0 < δ < 1). We wish to find the maximum duration T for which consumption can be sustained at a given rate C, and what the associated time path of use of the resource.

The charts below show the optimal time paths when A=1, α = 0.3, β = 0.2, δ = 0.1, C = 2 and K0 = 100, with several values of S0.  I start with S0 = 5, for which the maximum duration of consumption at the given rate is 22, the optimal time path of use of the resource being as shown in Chart 1 below.

Even in this simplest case, the optimal rate of use of the resource is not constant.  Use of the resource increases over time, being always just sufficient for output to equal the required rate of consumption.  There is no additional output to offset depreciation, so capital decreases, which is why use of the resource must increase to sustain output and consumption. 

When the initial stock of the resource is larger, the possibility of setting use of the resource as always just sufficient for output to equal the required rate of consumption may not be optimal, but remains available.  Thus the time until the resource is exhausted when its use follows that path provides a lower bound on the maximum duration.  We can state:

Proposition 1: A lower bound on the maximum duration T is given by:

\qquad T\,\geq \, \dfrac{\beta}{\alpha \delta}\ln\Bigg(\dfrac{\alpha \delta S_0A^{1/\beta}K_0^{\alpha/\beta}+\beta C^{1/\beta}}{\beta C^{1/\beta}}\Bigg)

with strict equality if:

\qquad S_0\,\leq\,\dfrac{C^{(1-\beta)/\beta}}{\alpha A^{1/\beta}K_0^{(\alpha -\beta)/\beta}}

In the case shown in Chart 1 the strict equality condition is satisfied.  We now consider the case  S0 = 30, for which the condition is not satisfied.  In this case Proposition 1 implies that T is at least 33, but it is in fact 34, this slightly longer duration being obtained when the time path of R is as shown in Chart 2.

It can be seen that the time path of use of the resource is slightly kinked at around time t = 26.  After the kink, it follows the simple path described above.  Before the kink, use of the resource is somewhat more than sufficient for output to equal the required rate of consumption, so that there is a little extra output offsetting part of the depreciation.

The timing of the kink depends on the depletion of the resource.  When the initial stock of the resource is sufficiently large, it is worthwhile to use some of it to invest in produced capital, because a larger stock of produced capital enables output and consumption to be sustained with less use of the resource.  When the remaining stock of resource becomes sufficiently small, the maximum time over which the required rate of consumption can be sustained becomes so small that it is not worthwhile to use any of the resource to invest in produced capital.  How small is sufficient in any particular case depends on the values of the various parameters. 

Chart 3 shows the optimal time path when S0 = 500.  The maximum duration is 104, much more than the lower bound implied by Proposition 1, which is 52.  Here the kink, at t = 101, is much sharper and proportionately much closer to the maximum duration.

What is especially striking in Chart 3, as compared with Charts 1 and 2, is the concave shape of most of the optimal path.  It is also notable that use of the resource increases over the range 1-70, then decreases, then increases again after the kink.  To understand this apparently bizarre behaviour we will proceed directly to Chart 4, which shows the optimal path when S0 = 2000.

Here the optimal path is still concave over most of the time period, but almost constant over the range 80-240.  Capital is almost constant over the same period, during which output exceeds the required rate of consumption by almost exactly enough to offset depreciation.

There are many possible combinations of capital and use of the resource having the property of keeping capital constant.  Among these is one which minimizes the rate of use of the resource, and that minimum rate is approximately 7.59, which is the value to which in Chart 4 it approximates over the range 80-240.  Being the smallest such value it enables the required rate of consumption to be sustained for the longest time from a given quantity of resource.  Using a term common in the study of optimisation problems, we may describe the almost constant section of the time path as a turnpike

We can now see why the path in Chart 3 takes the shape it does.  It is trying, as it were, to reach the turnpike, but the stock of resource is not quite sufficient.  Nevertheless, getting close to the turnpike for at least a small part of the time path contributes to maximising the duration.

Returning to the case S0 = 2000 (Chart 4), the lower bound on the maximum duration implied by Proposition 1 is 61, a very poor approximation to its actual value, 302.  However, when the initial stock is sufficiently large that the turnpike occupies a high proportion of the optimal time path, we can obtain a much better approximation by dividing S0 by the value of R during the turnpike.  Hence we arrive at:

Proposition 2: If S0 is large then a reasonable approximation to the maximum duration T is given by:

T=S_0A^{1 /\beta}\Big(\dfrac{\alpha}{\delta}\Big)^{\alpha /\beta}\Big(\dfrac{1-\alpha}{C}\Big)^{(1-\alpha)/\beta}

For S0 = 2000 this yields a value of 264, reasonably close to 302. 

The mathematics underlying the above may be found in the following two downloads. (pdf and Excel 2019 format respectively) 

Posted in Macroeconomic Theory, Mathematical Techniques, Sustainability | Tagged , , , , | Leave a comment