A new report from the Centre for Social Justice, Maxed Out, reveals that UK household debt is now almost as big as GDP. The right-of-centre think tank (founded by the well-known social scientist, Ian Duncan Smith), wrings its hands over the disproportionate impact on the poor, but has few suggestions beyond "access to affordable credit", "responsible lenders" and greater "financial literacy" (the poor must be taught better habits). I was particularly struck by this nugget (pg 40): "The rapid growth of mortgages over the past two decades has contributed the largest total amount to Britain’s personal debt. However it is not as concerning as the rise in consumer debt over that same period. Unlike mortgage debts, which are tied to the value of a house, unsecured consumer borrowing is at higher interest rates and is more likely to spiral out of control, driving people into problem debt". In other words, despite the evidence of your own eyes, mortgages are not a problem. No, sireee.
Mortgage debts are not really tied to the value of a house, contrary to appearances. Though we think of a mortgage as a loan for which the property acts as collateral, in reality the loan is securitised against future income. As such, a mortgage is a form of "fictitious capital", like stocks and shares. It's a claim on the future. A subprime mortgage is risky not because of the quality of the property, but because of the quality of the borrower's future income stream. Property does not have an intrinsic value beyond that of the land it stands on (the productive value) and its utility as shelter. This is not trivial, but it is clearly much less than the market value. This Christmas there will no doubt be a new must-have toy, and with demand temporarily greater than supply, these will change hands on eBay and in pubs at a markup to the retail price, but that markup won't be £1 million, because the market-clearing valuation of buyers isn't that high, even on Christmas Eve. So what determines the persistent high price of housing?
I'm going to approach the answer via Paul Gilroy's preview of Steve McQueen's new film, 12 Years a Slave, in which he notes that "slaves are capital incarnate. They are living debts and impersonal obligations as well as human beings fighting off the sub-humanity imposed upon them by their status as commercial objects". Our key image of the antebellum South is of plantations and pathological gentility. In fact, most whites in the South were self-sufficient small farmers of modest means, i.e. "rednecks". This in turn meant low levels of urbanisation and industry, compared to the North, and consequently low levels of credit and a shortage of ready money. After slave imports were banned in 1808 (following the British abolition of the slave trade in 1807), domestic reproduction became the main means of growing the plantation workforce. The number of slaves grew from 750 thousand in 1800 to 4 million by 1860. The growth in the slave "crop" fuelled the expansion of cotton and other cash-crop production into the new territories west of the Mississippi, which was a primary source of the friction that led to the Civil War.
The recycling of export revenues into expansion, combined with limited money, meant that slaves became the dominant form of capital in the South and a de facto medium of exchange, used to settle debts and act as collateral for loans. The market value of a slave represented their future production. During the eighteenth century, slaves were seen as disposable commodities, often being worked to death within a few years of purchase. This partly reflected their economic equivalence with white indentured labour on fixed-term contracts (i.e. one died after an average 7 years, the other was freed), and partly the relatively low cost of adult replacements via the trade from Africa. Over the course of the century, rising prices for imported slaves and the growth of cash-crop demand (notably cotton for the Lancashire mills), led to an increasing reliance on slave reproduction, which is why the end of imports after 1808 did not lead to crisis. This in turn made it economically attractive to maximise the slaves' working lives, which led to the ideological reframing of them from the subhuman commodity of earlier years to the "children" in need of benevolent discipline familiar from Southern rhetoric.
The capital value of the slave was a claim on the future, i.e. the potential production of their remaining working lifetime, rather than the embodiment of past production. In the Northern states of the US, capital and labour were separate, even though all capital (e.g. plant and machinery) was ultimately the transformed surplus value of past labour. Future labour was "free", in the sense of uncommitted, although in reality the sharp tooth of necessity (and the flow of immigrants) meant the factory owners could rely upon its ready availability. So long as labour was plentiful, capital did not need to make any claim on the future beyond the investment in health and education required to improve the quality of the workforce in aggregate. The increase in demand for labour after WW2 allowed workers to negotiate improved wages, i.e. current income, but it also drove their demand for shorter hours and earlier retirement on decent pensions, i.e. a larger share of future time was to be enjoyed by the worker rather than transformed into capital.
The counter-measure to this claim on future time by workers was the growth of the property mortgage, which is a claim on future labour. The need for housing is constant and the rate of turnover is low, but these characteristics actually make it particularly elastic in price for two reasons. The first concerns disposable income. In a society where most people rent, average rents will settle at a level representing an affordable percentage of average disposable income. This level will in turn reflect the cost of other necessities, such as food and fuel, required for labour to reproduce itself and thus keep earning. This is a basic economic equilibrium. The price of a necessity cannot go so high that it crowds out the purchase of other necessities without social breakdown (hence why the price of bread is still regulated in some countries).
The cost of housing therefore relates to the value of current labour time - i.e. what you can earn this week or this month - and the percentage of income left after non-housing necessities are paid for. This serves to put a upper limit on the current cost of housing (i.e. rents and equivalent mortgage repayments), even where the rental sector is relatively small. The 80s and 90s were an era of falling real prices for food and clothing and flat prices for domestic fuel, which meant that the share of disposable income available for housing grew. From the mid-00s, the real cost of these other necessities started to increase above inflation, so constraining income for housing. Schemes like Help to Buy are therefore a reflection of increasing utility bills and more expensive shopping baskets as much as limited mortgage availability arising from the credit crunch.
The second reason is that the cost of housing also reflects longevity. In a society where most people buy a house, the utility of the property will typically be a factor of the future years of the buyer - i.e. how long you expect to be able to enjoy living in it. Assuming you have the funds, you will pay more, relative to current income, if you expect 100 years of utility rather than 50. The assumption is that a longer life means a longer income stream, which essentially means a longer working life. Mortgage terms are typically based on a peak earning period of 25 years, with a buffer of a decade or so either side - e.g. start work at 21, buy a house at 31, pay off the mortgage at 56, and retire at 66. If longevity were 100, and the retirement age were 80, we would have mortgage terms nearer 40 years. But that would not mean correspondingly lower repayments (the monthly outgoings would be the same because that would reflect the "rent" level), rather purchase prices would be higher.
The combination of these two factors - current relative affordability and the duration of a working lifetime - is what determines the long-run cost of housing. Though property prices in the UK, and particularly in London, are heavily influenced by induced scarcity, this localised "froth" serves to mask the strength of these underlying forces.
Between the mid-70s and mid-00s, house purchase prices relative to average earnings roughly doubled, from 2.5 to 5 times, facilitated by easier mortgage credit. However, this did not cause a "crisis of affordability" for three reasons. First, more properties are now bought by dual-income couples. The increase in working women has two effects: it increases the income stream for some buyers, but it also lowers the average of earnings (because of the gender pay gap). Second, the average ratio is affected by increasing inequality - i.e. if the prices paid by the top 10% grow faster than those paid by the remaining 90%, the average cost of housing will be dragged up. Third, the average age of a first-time buyer has increased from mid-20s to mid-30s since the 1970s. This means that their income will tend to be higher, relative to the average of the population as a whole, because most people hit their earnings peak around 40.
Seen in this light, historic house price inflation reflects three secular trends: increased longevity; the absorption of women into the workforce; and increasing income inequality. This is not to say that the share of income going to housing hasn't increased - it has and the UK is particularly expensive - but that the increase in housing costs is driven by more than just demand outstripping supply. Even without induced scarcity over the last 40 years, we'd probably have seen the cost of housing go up. The point is not that "houses are more expensive", but that the amount of future income (and thus labour time) you have to promise in return has grown. The consequence of this will be an increase in average mortgage terms to keep pace with an increasing retirement age.
A paradox of modern society is that while technological advance should allow a reduction in working time, we are taking on more debt and thus pushing back the point at which we can begin to reduce hours. Some of this debt can be considered as investment finance, i.e. where we expect increased future income as a result, such as student loans, but the bulk of it is mortgage debt, which is unproductive at a macroeconomic level beyond the consumption sugar-rush of equity release. We kid ourselves that this is an investment too, but the capital appreciation on property, which reflects the future income of potential buyers, is only possible in a society committing an ever-larger amount of future labour time. While some individuals can buck this trend, either through luck or calculation (some will always buy low and sell high), society in aggregate must make a bigger contribution with every passing year, which for most people means working longer.
One result of this is that average working hours have increased in a bid to maximise future income, which means that the housing market works against productivity growth - i.e. we are driven towards increasing the quantity of time, not its quality, as a quicker way of increasing income. Job security has evolved from a dull constraint in the 60s, through a refuge from turbulence in the 80s, to an elite aspiration now. Ultimately, this constrains innovation and risk-taking (outside of financial services). It is a commonplace that high property prices distort the economy because more and more capital is tied up unproductively, but what isn't so readily recognised is that the embodiment of labour in mortgages also acts as a psychological drag: "The delirious rise in property prices over the last twenty years is probably the single most important cause of cultural conservatism in the UK and the US".
The "capital incarnate" of slavery undermined the economy of the South (1). When the Civil War broke out, the Confederacy had only 10% of manufactured goods in the US and only 3% of the firearms. Though it had been responsible for 70% of US exports by value before the war (mainly "King Cotton"), most of the receipts had been recycled into slaves or used to buy goods from the North. The failure to grow industries outside of the plantation system meant it had a population of only 9 million compared to 22 million on the Union side, and 4 million of that figure were slaves who could not be trusted with a weapon. The duration of the war was largely a result of the South having a third of the soldiery and (initially) the better generals, but unable to buy sufficient materiel, and unable to liquidate their slave capital or use it as collateral for foreign loans, the outcome was never in doubt.
I was always bemused by the claim made in the 1970s and 80s that the "right-to-buy" was a good thing because it meant council tenants would take better care of their properties. It was obvious on the ground that the tenant's pride reflected the quality of the housing, not the nature of tenure, and it was a myth that councils wouldn't let you paint your doors a different colour. It is only with time that I have come to appreciate the ideological foundation of that claim, and to see the parallel with the claims made by Southern planters in the US that their slaves, as valued property, were better cared for than free Northerners thrown out of work during industrial slumps.
1. The total capital value of slaves in 1860 was $3 billion. The total cost of fighting the Civil War was roughly $3.3bn for each side, though this was a much larger per capita burden for the South. In other words, fighting the war cost the Union roughly the same as it would have done to buy-out the slave-owners (cf. the £20 million spent by the British government compensating West Indies slave owners in the 1830s). As such a prohibitively expensive scheme would have been politically impossible, while war against an aggressively secessionist South would have patriotic backing irrespective of the casus belli, an armed conflict was probably the only way of reforming and integrating the US economy as it expanded westwards.
David,
ReplyDeleteI don't want to be picky, but there are a few things I'd have to take issue with.
1) “...the loan is securitised against future income.” That used to be the case until 20-30 years ago. But, in fact one reason that there has been a bubble is precisely because the loans were secured against the idea that the value of the property would always rise, facilitating further borrowing. That's why not only were income multiples expanded, but banks and building societies effectively abandoned any verification of whether lenders income was capable of covering repayments.
2) Land has no value, because it is not produced by labour. It has a price equal to capitalised rent, and rent only arises because land is monopolised. But the house that stands on the land does have value, because it is the product of labour. In fact, as with every other commodity, that value should be declining, because increases in productivity mean that less labour-time is required for that production.
3) You could make the same argument about say cars. But, the value of commodities be they cars or houses is not determined by the subjective utility of consumers for them. It is determined objectively by the labour-time required for production. On top of the transformation of such values into prices of production based on cost price plus average profit, market prices also reflect conditions of monopoly giving rise to rent, as well as conditions of demand and supply. That is particularly significant where such commodities are prone to speculation as houses have become.
4) If you look at the price of houses in the UK from 1900 onwards, you will see that they remained flat in real terms until around 1960, despite the fact that wages, and disposable income varied considerably over that period. Even after 1960, the increase in price was modest compared to the rise that occurred in the 1980's, and the rise after 1997, which has taken prices almost parabolic, which is a sure sign of a bubble.
5) “current relative affordability”, if property really was relatively affordable, property ownership would be rising, but, in fact it is falling, and a majority of people who do not currently own a home, believe they will never be able to.
6) “First, more properties are now bought by dual-income couples.” But, they aren't! The opposite is true in a big way. In 1971, 80% of houses were multi-occupancy (70% couples), and only 21% single occupancy. Today only 59% are multi-occupancy (52% married or co-habiting couple), whilst 41% are single occupancy.
7) The above is one reason that although today there is 50% more houses per head of population compared to 1970, we continually hear stories about housing shortages.
8) Another point I'd add is that the mortgage debt is different to credit card debt. Many people are shown as having large amounts of the latter, but in fact its always paid off at the end of the month. Moreover, few people take on credit card debt of £150,000 as they do for a mortgage. The bigger problem is actually the people who have dropped off the end of credit card debt into the need to borrow from pay day lenders.
9) “councils wouldn't let you paint your doors a different colour”, but if you did you had to take responsibility for future maintenance too, and many people did find dealing with local state bureaucrats oppressive.
Boffy,
ReplyDeleteBe as picky as you like. In answer to your points ...
1) The belief that mortgages could be secured against rising house prices was a delusion. My point is that the underlying security for a mortgage has always been the borrower's future income. The apparent evaporation of subprime risk through CDOs can now be seen for what it was: a pathological denial of reality that could only be sustained through a belief in ever-rising prices.
2,3) I'm using "value" here in the sense of what could be produced by the land if it weren't used for housing (e.g. a sheep or two), rather than the technical sense employed by Marx. As you rightly say, a house is a commodity, but the cost of its production (labour, bricks etc), even when added to the opportunity cost of the land is very low.
4) My suggestion is that a major driver for the increase in house prices since the 70s was capital's need to lock-in the future labour of skilled workers, at a time when productivity improvements (containerisation, automation and ICT) were in danger of leading to reduced working hours (and thus access by capital to surplus value). The "property-owning democracy" was part of an ideological campaign to get the workers of most value to capital to "sign up" for the duration. To prevent the mortgage being seen as a ball-and-chain, it had to be transformed into a desirable object, i.e. equity as a result of ever-rising prices.
5) I was using the term "current relative affordability" to describe all immediate housing costs, i.e. rent as well as mortgage repayments. My point is that there is a natural limit to this, which reflects current wages. If rents are affordable but mortgages are not, this should logically lead to a fall in house prices, but I suspect UK prices will be maintained in future by extending mortgage terms - i.e. making repayments more affordable.
6,7) I think you've misunderstood me to be suggesting that there are more couples than singles buying. I'm not. My point is that there are more "dual income" couples, because of women entering the labour market. You can have a growth in dual-income couples at the same time that the share of buyers who are couples declines. In fact, declining household density is partly a product of this. As more women have become financially independent, they have found it easier to separate. What I'm talking about is not household density at all, but the total income of the buyer(s) - i.e. more houses are bought on the basis of shared mortgages (two incomes) today than in the 60s/70s. It's the quantum of income, not occupants.
8) Credit card debt is another factor in the lock-in, to which we can now add student debt. Payday loans are just opportunistic extortion in a society with persistent unemployment and inadequate wages.
9) While local government has always had more than its fair share of jobsworths, the whole "council tyranny" schtick was overblown in the 70s (you can trace this Tory trope all the way back to Churchill's ill-judged "Gestapo" gaffe in the 1945 election). The irony is that the place where you would then (as now) face the greatest restriction on your right to paint your front door whatever colour you saw fit was in middle class conservation areas. Try putting up vulgar Xmas lights in Wimbledon Village or Chipping Norton and see what happens.
David,
DeleteLet me start by saying that I agree with your basic thrust, but disagree with your reasons for it.
1) The idea of issuing huge mortgages on the basis of rising prices was a delusion. That's true, but mostly because the idea of constantly rising prices was a delusion. The basis upon which loans were always made, was the ability to repay, but the underlying principle until the last 20 years, was that if repayment did not occur, the value of the underlying asset was at least equal to the loan. That is why until then, borrowers were expected to put down a minimal 20% to show that a) they could save, b) they had some commitment to buying a house rather than spending the money on other types of purchase, c) it meant that even if house prices fell slightly, the building society would always get its money back. Its only when house prices move and down by huge amounts that this breaks down.
2) I'd say the opportunity cost of land is negligible in relation to a house. In fact, we have lots of land in Britain that is lying doing nothing. Agricultural land values are a tiny fraction of building land values. The reason building land values are high, is, in fact because house prices are high, not vice versa. So long as house prices are high and rising, land owners have an incentive via their monopoly to hold back supply. A drastic fall in house prices would slash the price of building land, particularly if landowners thought the fall was going to be persistent. Much lower prices of building land would then reduce the cost of new build homes. The much lower cost of new build homes would mean that builders profits rose, for the reasons Marx sets out in Capital III, Chapter 6. That is they would be able to sell such houses at much lower prices. That would cause demand for these houses to rise. A much larger proportion of surplus value is then realised as profit.
The reverse of that applies currently. Because house prices are high, demand for new build houses is constrained. Builders are reluctant to build because demand is constrained, and profits are thereby constrained other than on the most expensive houses – one reason builders object to having to build “cheap” , “affordable” housing. Because, that constrained new build supply, prices are pushed up, as new supply then relies on existing owners putting their houses on the market.
3) I agree with the general thrust of your point 4, but the trouble is that the real increase in home ownership came after WWII, and into the 1960's, though it started in the late 1930's, as workers in the Midlands and South-East began to be employed in relatively high paying jobs in car production, and consumer electronics, and as new building techniques reduced the price of new homes. The workers who bought these houses were precisely your high value added, skilled workers. Many of these, as a result of the inflation of the 1970's and early 80's, actually did very well, and were able to obtain some degree of freedom from capital as a result, because the capital value of their mortgages was inflated away. In fact, the expansion of credit, which resulted in the inflation of house prices was a by-product of the attempt by Thatcher and Reagan to create low-wage/high debt economies, and of the global falls in interest rates caused by rising rates of profit.
Cont'd
Cont'd
Delete4) I think you have your point 5 back to front. Ultimately, wages as the phenomenal form of the value of labour-power are determined by the costs workers face, not the costs workers can pay being determined by their wages! It is precisely because of their goal of building a low-wage/high debt economy, that Thatcher and her successors were led to blow up the value of Housing Benefit to ridiculous proportions to cover the astronomical rise in housing costs without, wages rising to cover it, for the worst paid workers. The effect of removing Housing benefit, and other such subsidies, would in fact be higher wages, and more small inefficient businesses going bust, not lower rents or house prices.
5) I think your point 6 is factually wrong. The big increase in dual income households arose in the 1950's and 60's. That was when capital was short of labour and encouraged housewives to go to work, as well as encouraging immigration. My Mother was very unusual in our village in not working during that period. I'd say 90% of housewives worked, and it was how families did move at that time to buying rather than renting, and how they began to buy cars and various consumer durables. By the 1970's that was well established, so that when I got married, it was normal for women to start work from school, and continue in work when they married, only taking a short time off when they were pregnant. The fall in multi-occupancy households from 1970, was accompanied by a fall in the number of multi-incoem households too. Its why, banks and building societies had to continually expand income multiples for mortgages.
6) As someone who has both worked in Local Government, and been a Local Councillor, I'd say your impression of the local capitalist state suffers from rose tinted glasses. As even a Councillor, I found it infuriating simply trying to get the simplest thing done, and as a Local Government worker, I found the attitude of management and other staff both to the Public they were supposed to serve, and to local Councillors appalling. In fact, several times, people I worked with had to check themselves in what they were saying, when they remembered that I too was a Councillor! In the 1970's Marxists repeatedly analysed the bureaucratic and oppressive nature of the local state. Its why some of us at the time attempted to build local organisations of tenants and residents against it. I think that the experience of the last 30 years, has simply caused some on the left to mistakenly look back to that period as some kind of “golden age”, as an alternative. Ken Loach's “Spirit of '45” is an example of that, but if you watch it critically, even with that you can see glimpses of the reality, such as the woman who relates about how one woman had secured a Council House, by going in to see the Housing Manager, closing the door, and spreading her legs for him!
a) "The big increase in dual income households arose in the 1950's and 60's".
ReplyDeleteI disagree. The percentage of women of working age in the labour force grew from 46% in 1955 (the low following postwar demobilisation and the baby boom) to 55% in 1975, but this rate of change then accelerated to reach 67% in 1995. The current figure is about 72%, which suggests a recent slowing-down as the percentage approaches the male norm of 80-85% (maternity presumably puts the "natural" cap nearer to 75%). The period of most rapid transition, which will have served to boost mortgage values, was therefore the 80s and 90s.
b) "The fall in multi-occupancy households from 1970, was accompanied by a fall in the number of multi-income households too".
My point was about the income stream (and thus occupancy) at the time of purchase, as this is what dictates mortgage affordability and thus house prices. You're absolutely right that household density has fallen (for a number of reasons), but this doesn't undermine my point.
Though women started to enter the workforce in much larger numbers in the 50s and 60s, this did not (easily) translate into financial independence until the 1969 Divorce Reform Act. The consequence of this was an increase in couples splitting, which is one of the factors that has led to falling household density from the 70s onward. However, at the time a mortgage is taken out, the couple is still a couple, so you can have both an increase in the number of dual-income mortgages (and thus an increase in average household income measured at the point of mortgage) and a decrease in occupancy more generally. The two are not in conflict.
David,
DeleteCould you provide the source data for the participation rate? I've been trawling ONS, OECD, World Bank etc. and can't find data prior to the 1970's, and some of the later data from Trading Economics, for instance, using WB data suggests that the current rate is only around 55%, which can't be right.
To be honest the figure of 46% for 1955, doesn't pass the sniff test. I grew up in a former mining village, therefore, a traditional working-class community, where studies have shown that female participation rates tended to be lower than in communities of the new working-class, and middle class. The part of the village where I lived was made up of a dozen terraced streets, about 1000 houses. Because of the nature of the community, everyone knew each other, home-owners had themselves been born and bred in the village, as kids we all went to the same school, we had competing groups based around the closest bit of derelict land for the purposes of bonfire night, but we all played football and cricket together etc. In short, from about the time you are aware of these things, in my case here from the start of the 60's at the latest, I was aware of how many kids mothers were working.
I can still now think back to who lived in what house, and what they did. I'd say that way more than 50% of the married women worked, let alone the women on the village in general. So, I'd say the idea that from the 1960's onwards, mortgages were based on the income of a single male breadwinner doesn't stand up. Building Societies certainly took female wages into consideration from that time, though only in part, to take account of women being out of the workforce to have children.
In fact, even on the basis of the above figures, however, the percentage growth between 1955 to 1975, and 1975 to 1995, is about the same - 19% and 21%.
The point about female financial independence is irrelevant. My argument is not that the proportion of single occupancy homes is due to single women buying homes. Its that single people in general have bought - and rented - homes whereas in the past they would either have been living at home, or else as with two of my uncles, living with brothers and sisters, or else would have been marrying, and buying homes on the basis of joint income. I don't think there is any evidence that in the 1980's and 90's people bought homes as couples, then split up and bought homes singly, as an explanation of the rise in single occupancy homes. In fact, the proportion of single parent households, which might be an indication of that remains small as a proportion - 2% in 1971, 8% in 2011..
Boffy,
ReplyDeleteI got the stats on female participation for the years between between 1955 and 1995 from here:
http://www.ehs.org.uk/dotAsset/4e68f7d2-4ddb-4d34-889d-30c831beb6b1.pdf (table 1, page 2)
These apparently originate in the OECD Labour Forces Statistics.
The "current" figure comes from the 2011 census data, which is included in an ONS comparison of Census and ONS Labour Force Survey figures here:
http://www.ons.gov.uk/ons/rel/census/2011-census/key-statistics-for-local-authorities-in-england-and-wales/rpt-labour.html#tab----economic-activity-status
I suspect the World Bank data is for workers as a percentage of the total adult female population (i.e. including OAPs), rather than just working age (15-64 or 16-65, depending on source).
Just to re-emphasise the point about single occupancy homes v couples. By 1981, the percentage of homes occupied by couples had fallen to 63%, a 10% fall. The percentage of single person households had risen to 23%, a 25% increase. By 1991, the former had fallen to just 55%, a 21% fall from 1975, whilst the latter had risen to 27%, a 42% increase from 1971.
DeleteSo clearly, in the period you were describing of the 1980's and 90's, already a rapidly increasing proportion of property was being bought by single people. I'd suggest that there are several reasons for that, which I have set out elsewhere. Amongst them are the large rise in the number of people going to University, who moved away from home at an early age.
But, another reason was that as prices rose rapidly during the 1980's - and as I am demonstrating in a post shortly the biggest rise in asset prices arose during the 1980's and 90's, with more recent money printing only being able to keep those bubbles inflated - and as Thatcherism created a cult of money grabbing and individualism, so many people were encouraged to see buying a house as a means of getting rich quick, or at least of not being left behind as prices rose. In other words, the classic conditions for creating a speculative boom of the type we have seen repeated be it for tulips, railway shares, technology shares and so on, and which all necessarily burst.