Monday 28 February 2011

As always, a question of elasticities

Keith Ng makes his case against petrol price gouging. To summarize: petrol demand is almost perfectly inelastic in a crisis because it represents demand for security, not just petrol; price gouging consequently would not induce the appropriate intertemporal substitution. Instead, it would piss people off and help erode the fragile bonds of community spirit that are critical in times of crisis.

So we have two elasticity estimates floating around. First, the elasticity of petrol demand with respect to price during a crisis. Second, the elasticity of public good provision [people voluntarily doing things to help neighbours and community] with respect to temporary price hikes that would likely be misunderstood and resented by customers.

For starters, petrol demand is and always has been relatively inelastic in the short term: around -0.3: a 10% increase in price results in a 3% reduction in quantity demanded. But those estimates will be calibrated around relatively small and expectationally permanent increases in the price of gasoline; we have good reason to expect a short duration, sharper price spike would induce a greater behavioural response.

We know that demand for security in general is fairly elastic. Why else would we see such price dispersion in the various grades of, for example, kid car seats? Some folks put a lot of value on it, others don't. It costs less to have a monitored security system in your house than a Sky TV subscription. I've not looked at the numbers, but I'm willing to give 3:1 odds that more homes in Christchurch have Sky TV than have a working monitored security alarm. Folks are willing to pay a premium for security, but not an infinite premium. Further evidence, more earthquake related? In the last earthquake, bottled water was security. This time around, Council was very quick to get tanker water out to Brighton. But not so last time. After the September earthquake, everybody was out of the bulk cheap water, but you could still sometimes find the fancy water at its usual crazy high price. Water was security. But not at any price.

But let's grant Keith's assumption for now: folks have inelastic demand for security. Whatever prior estimates we might have on demand for security get thrown out the window because security has understandably become rather more salient. But how much petrol constitutes security? It's not an infinite amount - folks aren't filling up a pile of jerry cans along with their regular gas tank. Is a full tank security? Or is a tank big enough to get you to Rakaia enough? A full tank in one or two of the family vehicles, for those with more than one car? I felt pretty insecure in South Brighton with a quarter tank in the car that wasn't abandoned on the other side of the bridge because I knew traffic getting out of Brighton could take hours; it also seemed impossible to tell which stations would have petrol once we got through the traffic bottleneck at Travis Road. Pretty high risk we'd wind up stranded if we went for groceries or tried getting to the airport. I'd have been happy enough with a half tank, damned nervous about trying to get anywhere on a quarter tank. So if a tanker truck had shown up in Brighton on Wednesday selling petrol at normal prices, I'd have been tempted to fill to the top absent quantity restrictions. At double prices, I'd not have filled beyond the half tank. From a check of StatsNZ data, we're in the upper ranges of the South Brighton income distribution. But I'm horribly cheap - at $5 per litre, I'd only have filled up with enough to get me through to prices dropping. Would everyone else be substantially less price responsive than me? Am I really that cheap?

Even if demand for security is very inelastic, if "security" can vary across individuals and can be anywhere from a half tank in one car, a full tank in one car, or a full tank in two cars, it's still very plausible that a temporary doubling of petrol prices would have reduced queuing and ensured that adequate supplies were available for folks who really needed them.

As for social solidarity - I totally agree with Keith that neighbourhoods coming together voluntarily to help each other out has been totally laudable. I can't imagine anybody who'd think otherwise. But would that spirit of community have been broken if, on Wednesday following the quake, the following message had gone out?
Our critical transportation infrastructure has been badly damaged by Tuesday's earthquake. We've strongly encouraged people to stay off the roads except in case of emergency. Unfortunately, many of our major roads remain completely congested, sometimes preventing emergency crews from getting through to where they're needed. At the same time, the temporary closure of the Port of Lyttelton's petrol terminal has resulted in a short term gap in petrol supplies. This will be solved in two days when the petrol tankers bound for Lyttelton have been diverted to Timaru and tankers have made it up from there. But we need people to show restraint during that gap. Despite our having urged such restraint, queues at those stations that have not yet run out of petrol prevail. We consequently have asked the major petrol retailers to impose a $2 per litre surcharge on petrol, with the surcharge earnings to be contributed to the earthquake relief fund. This measure will help to ensure that those who absolutely need petrol will be able to find it in a crisis. Only buy what you need to get you through the next two days. After that, the surcharge will be lifted. Know that your contributions are going to help your neighbours in Christchurch.
And so on, but with more PR. I just can't see that temporary charge ruining social solidarity. Especially in the case where folks can see that the extra charge is going to the earthquake relief fund.

This isn't a "screw the poor" thing. Is a poor person worse off having to spend $40 than $20 to get enough gas to get through a two day period, or worse off having to spend a whole lot of time in a queue for potentially no petrol at all? Recall that poor households are more likely to be single parent. Who's looking after the kids while Mom's queuing for petrol? Further, count the costs of uncertainty. Lots of folks had to be making lots of plans after the earthquake, many of which would be contingent on knowing whether fuel would be available and at what prices. Everybody who happened to have a quarter tank or less at the time of the quake had to bear a whole lot of uncertainty costs. Rationing by queuing effectively locked a whole pile of folks in a part of town with no services and no food because they couldn't know whether they'd be able to find fuel to get home should they have left. Is that better?

Neither is this some crazy Eric libertarian thing: it's technocratic. I'm positing a market failure - that it would have been socially efficient for the Christchurch petrol stations to have raised prices in concert, but that none would do it on their own because of hugely negative reputational effects because of public irrationality about the working of the price mechanism. Consequently, I proposed a policy solution that removes that reputation cost: government coordinating a temporary price hike with the collected excess revenues going to earthquake relief. I hate the idea of "targeted tax increase dedicated to some social project". All manner of ridiculous redistribution schemes can gain support that way. But government coordination in this case could have helped; toss me out of the libertarian club if you like. It's odd how the party lines have broken on this one. The libertarians have generally supported my proposed government intervention; the folks on the left who generally favour technocratic dirigiste solutions haven't liked it.

I think social cohesion is far more robust to a petrol price increase than Keith does, and especially in the case that I proposed: a temporary hike where the raised funds go to earthquake relief. Would you suddenly stop helping your neighbours because you thought the gas station down the road cheated you?

It's a bit of a shame that Keith's initial good points - the elasticity questions - get lost a bit at the end. The footnoted tirade against homo oeconomicus and the Austrian school, and the threatening to bash anybody who believes in a strawman form of the argument I'd put up, don't help his argument. Homo economicus maximizes a utility function that can and does include loving their families and helping their neighbours. And Austrians support anything that's voluntary; I'd expect a proper Austrian would oppose my proposal that government try to coordinate a temporary price hike.

But we economists are wary of relying solely on altruism to get the job done - and the job here is a big one. There's only so much altruism to go around. We have some evidence that folks behaving altruistically on one margin then feel that they've done enough and so can afford to be less altruistic on other margins. We strain altruism if we ask it to do too much. And it denigrates the altruism folks have shown and continue to show to argue that it would have disappeared had gas prices had gone up for two days last week.

I'd argued last time round in favour of gouging more generally. I stand by it. The dairy owner who's massively short on supplies shouldn't be excoriated for keeping enough on the shelf for emergency need by raising prices. But I also cheer those who, seeing that folks on the other side of town are having to pay multiples of normal prices, load up trucks with the items in obvious short supply and bring them over to give away. It never occurred to me that folks could interpret this as "he likes one, he must hate the other". I'd think rather that evidence of the former helps to encourage the latter.

Update: Rauparaha at TVHE seems to agree.


  1. I keep coming back to the time I filled up those years ago in Kaikura. The price was so high, I put in just enough to be sure to get to Wellington.

    Had it been more reasonable, I'd have filled right to the top. I needed petrol, but I could get by with less that a full tank.

    And I've never purchased fuel at Kaikura again.

  2. I found this amusing:
    "I will fisticuffs anyone who reckons that this – people helping each other because they goddamn wanted to – was not an efficient outcome."

    Isn't this what a market is at it's most basic level, people entering into transactions voluntarily?

    It shouldn't matter if the financial cost to one party is $0.

    The whole point is that it is voluntary. I guess you are right that having the government act to put an additional temporary levy on petrol is not particularly libertarian.
    However it is better than in the event of fuel shortage a government official coming around to siphon fuel from your car.

  3. First off, I apologise for the parts where I got carried away with the trash-talk. I get a bit overexcited sometimes. I'm sorry.

    Let's start with the elasticity of security. I was in your shoes, I'd happily pay an extra $50 to fill my tank. And the fact that many people are prepared to queue for hours for it says that they are not put off by what we both agree is a pretty substantial cost.

    But let's work the problem from the other direction. You haven't mentioned income elasticity of demand at all. Given the normal income disparity, what sort of assumption do you need to make about price and income elasticity of security to get a scenario where you can price out rich hoarders without pricing out poor non-hoarders? If paying an extra $20 is really inconsequential for a poor person, is it reasonable to believe that the same $20 is enough to make a rich person forgo security?

    The more reasonable scenario is that a price hike will result in some hoarders being priced out of the market, along with some non-hoarders. Specifically, some rich hoarders will *not* be priced out, while some poor non-hoarders *will* be priced out. I like what Lew Stoddart said:

    "it draws a distinction between those below and above the newly-established price margin which dispels the illusion of shared experience"

    The resentment isn't just towards the ones who do the price gouging/rationing, but it's also towards the people who emerge as winners. If we're talking about broader price rationing (as I was, with groceries), it's an inherently divisive process that draws a very clear line between the have's and have-not's. I guess we're getting into The Spirit Level territory here.


    Your appeal message was interesting. Your original argument is that a price hike will induce intertemporal subsitution because people will rationally choose to defer consumption because they can do it for a much lower price. Yet, your appeal message painstakingly avoids making people think about the reduction in costs from delaying consumption. You did exactly what the authorities have done: Reassure the public that supply will resume, appeal to their sense of civic duty.

    The price rise is completely superfluous to your message. You can remove it whole and the message is intact.

    I don't want to put words in your mouth, but I posit that you frame that message in that way because you felt - like the rest of us - that you can't motivate people with a straight-up appeal to monetary benefit. And that's my point.

  4. "Isn't this what a market is at it's most basic level, people entering into transactions voluntarily?"

    The key point is that people are not responding to price signals (e.g. Taking as much food and water as they can because it's free), therefore the entire invisible hand goes out the window.

    Defining this as a free market is broad to the point of being meaningless. You're just saying that people should have rights to property and their own labour that they can transfer to others.

    Under this definition, Soviet Russia was a free market.

  5. Actually, I retract that last part. 8-)

    But still, if we called markets without price signals "free markets", then people who advocate for an economy determined by the invisible hand would have nothing to call themselves.

  6. "The price rise is completely superfluous to your message. You can remove it whole and the message is intact.

    I don't want to put words in your mouth, but I posit that you frame that message in that way because you felt - like the rest of us - that you can't motivate people with a straight-up appeal to monetary benefit. And that's my point."

    The price rise is only superfluous in the sense that without, the message is completely worthless. The message may make sense, but no one seems to be acting on that (ie, forgoing current consumption for later consumption). Prices will make them act. The message is the PR spin on the price rise.

    "you can't motivate people with a straight-up appeal to monetary benefit. And that's my point"

    You've already admitted that some people will buy less petrol, although you think the distributional effects are worse. So you already agree that the appeal to monetary benefit (the raised price) motivates people...

  7. That sentence actually read "you felt you can't..". I meant that as in it wasn't appropriate, not that it was not possible.

    I was certainly not implying that price will have no effect. I said very explicitly that price will push the wrong people out of the market and have a negative impact on goodwill.

  8. I'm sorry. Who cant afford petrol at $5 per litre for two days? Who is the price increase pushing out of the market? Were those people even in the queue?

    If it is important enough, even the poorest people (who own cars) could find the money to get the fuel, or rely on the charity of others for the same.

    And who would be buying petrol at $5 per litre who wouldnt already be queuing for it at normal prices?

  9. Interesting that Eric's proposal requires government intervention on pricing and collusion of the fuel companies so we can get markets working to allocate fuel.

  10. @Keith,

    Sure, people aren't taking as much as they can just because it's free, but there are many examples (not in a crisis) where goods/services are provided free to consumers where demand isn't infinite.

    I'm also not convinced we really have a market without price signals. At some point in the chain there is still a price signal. We can donate things we don't produce for free for a certain period - for as long as our financial circumstances allow or as long as producers themselves are able to pass along goods at zero cost. However I would posit that this period isn't infinite, and would be related to inherent wealth, capacity to produce in the future etc.

    Isn't part of the reason we are able to be so generous at times of crisis in particular is because we are a relatively wealthy nation (despite complaints to the contrary). Consider how much ability the average Kiwi has to donate capital versus the average Haitian.

    Yeah, Soviet Russia was a really bad call!

  11. @scrubone: Kaikoura ought be considered an emergency fuel stop for most purposes. It's expensive to get fuel to there; higher prices give folks incentive to fuel up where it's cheaper. Prices are a bloody miracle.

    @Keith (1): I'd expect a paranoid rich guy would still fill up his tank and that poor folks / less paranoid rich folks would buy enough to get through the two days. The appeal is meant to help folks understand the point of the temporary price hike and is exactly in keeping with the initial proposal: two day price hike, extra money to earthquake relief. Folks can reckon their private interest quickly enough on seeing the price increase.

    @Keith(2): I count it as a free market whenever there is a voluntary transaction between two parties. I have no clue how you'd consider Soviet Russia to be anywhere near that. The Kulaks didn't liquidate themselves voluntarily.

    @Luis: That's why it blows my head off that folks have been all "Oh, there goes that crazy libertarian Eric again." It's pure technocratic basic price theory market failure economics.

  12. I have to say I think Keith's logic is pretty tortured. There are two ways to help people for whom $4/litre petrol really does present a problem because of a cash constraint. One is through underpricing. But the elephant in the room is the other solution, which is through public and charitable emergency assistance. I recall my early econ 101 class: if you decide the poor need assistance, do it via income transfers and leave prices untouched for the sake of letting scarce resources find their highest value use (which, by the way, most certainly includes providing resources to the poor).

    Now one may argue government and charity is a pretty imperfect way to find and help those in genuine need, and you'd be right, but its costs are but a tiny fraction of the losses associated with mispricing that causes an entire population to do things like queue for hours and then horde perhaps the single most important resource in a crisis without being able to understand the consequences for other people, which are serious. I would bet good money that when the fuel runs out in a shortage a study would show it is the poor who are most disadvantaged by it, and vastly moreso than from a temporary spike in price.

    It would be helpful for Keith to explain why he thinks emergency income transfers/higher prices is not a better solution to the underpricing/hording/shortage outcome.

    There is also an obvious unresolved tension in rejecting temporary price increases out of concern for the poor and yet accepting them permanently (via tax hikes) for other political causes.

  13. @ben: Keith's best reply would be that you can't operationalize the second welfare theorem at an hour's notice. The best reply to that would be helicopter money - perhaps literally - over affected suburbs. I just can't see this being an issue though for a two day doubling of petrol prices. Everybody seems to be assuming that if you go to fill your tank, you have to fill it to the top. Lots of folks in the poorer parts of town put in $20 or $40 as they have it - enough to get through the next few days. That wouldn't change.

  14. @ben Subsidizing consumption would defeat the whole purpose of the suggested price increase.

    @Eric "It's pure technocratic basic price theory market failure economics" I'm still trying to parse that sentence without a smile. By the way, I'd never use "crazy libertarian" to describe you; I disagree with some of your ideas but I think you're right many (most?) times.

  15. @Eric, you still haven't dealt with this:

    "If paying an extra $20 is really inconsequential for a poor person, is it reasonable to believe that the same $20 is enough to make a rich person forgo security?"

  16. Luis

    @ben Subsidizing consumption would defeat the whole purpose of the suggested price increase.

    Lump sum transfers have quite different efficiency properties to price changes, and these differences are the reason economists argue for transfers over price manipulation. Transfers will certainly increase consumption but by preserving price signals, petrol is able to find its highest value use; without price signals it cannot.

    Eric, I have sympathy with your take on Keith's take - but not much. Emergency assistance in all its forms - government, charity, neighbours helping each other out - would have to be pretty darned slow and inept to justify misallocating petrol across the entire city in crisis (Keith appears to disagree such misallocation is even occurring, which amounts to a claim that the petrol going into a guy's fifth jerry can produces higher surplus than if it were to go to the guy at the back of the queue who need 10 litres to to get home to his family before the station runs dry).

  17. I have a response to Keith's question

    "Given the normal income disparity, what sort of assumption do you need to make about price and income elasticity of security to get a scenario where you can price out rich hoarders without pricing out poor non-hoarders? If paying an extra $20 is really inconsequential for a poor person, is it reasonable to believe that the same $20 is enough to make a rich person forgo security?"

    The question depends on a misunderstanding of why hording occurs. Hording occurs because the market is not being allowed to clear; people anticipate a depletion of inventory, and, sure as night follows day, price rationing is replaced by non price rationing: queuing. Hording occurs because it is made essentially costless by eliminating a reward for delay in the form of a future price reduction (requiring a temporary price spike now).

    It is not a question of pricing out rich horders, because hording is not related to either ability or willingness to pay. The issue is allowing a price to emerge that people can see will prevent a shortage, and rewarding a delay in consumption why supply is constrained.

    Keith's question, in others words, has a false premise.

  18. @keith I'm 'rich'. And I'd have only bought a half tank at double prices.

  19. @eric, you can't point to your own hypothetical preferences as a definitive measure - especially in the face of people queuing for hours (which, we both agree, is a huge cost) to hoard petrol.

    Your case hinges on petrol-hoarding being much more price elastic than petrol-using, *AND* petrol-hoarding being income inelastic. I don't think you've made the case for either, but then again, I'm not sure if it's something we can deduce.

    I'd actually be really interested in seeing research on this (as in behaviour in Chch) once things settle down.

  20. I have no problem with introspection as evidence, especially when the question is "what would a hypothetical rich person do".

    You need something beyond income elasticity for what you are trying to argue, Keith. Income elasticity says how much more of something you buy as you get richer. What you really want is differential measures of price elasticity sorted by income. But those will fail for your purpose here as the main substitute for petrol, busses, were out of action.

    I never said anything about hoarding vs using; I'm not even sure that there is operational content to the difference. All I need is that people buy less when it is more expensive.

  21. I don't understand the hypothetical rich person argument. What use is a hypothetical argument.
    Christchurch is collapsing for God's sake.
    Stop the waffle.
    My brother is rich but he was called out to give medical help, and concentrating on this, he ran out of petrol, I'm poor and I had to pick him up.
    Bla Bla economic absurdities in the middle of a bloody crisis.

  22. "I have no problem with introspection as evidence, especially when the question is "what would a hypothetical rich person do"."

    Problem is that your introspection is not obvious or intuitive to me, and we have clear evidence that plenty of people disagree with you (see: queuing).

    "What you really want is differential measures of price elasticity sorted by income."

    Yes! Thank you. I've been struggling to find the right concept.

    "I never said anything about hoarding vs using; I'm not even sure that there is operational content to the difference."

    That is not true! In the original post, you talked about the vicious cycle of panic buying as the consequences of a bad equilibrium, and you proposed a price hike to break it. Am I mistaken in thinking that you - like me and everyone else - thought that panic buying was a bad thing and wanted to stop it? And is panic buying different from hoarding?

    And in this post, you make a very clear distinction between security and actual usage. Security is used in the sense that you might absolutely need it, and you are uncertain that supply will be accessible. Again, isn't this hoarding?

    "All I need is that people buy less when it is more expensive."

    This is why I have a serious beef with it. You are saying you don't care whether some people with immediate need are priced out while others can still afford to hoard, as long as demand is aligned with supply. Yes, I agree that this is the definition of efficient allocation, but surely, you can see how the people who miss out will get really pissed off - and not just at the situation, but at the system and at the people who could afford it.

    It's not nearly as grotesque and in-your-face as people who have swimming pools in drought-ridden countries, but it's the same concept. When people perceive resources being wasted (e.g. Petrol being hoarded) while they are going without, it's an incredibly divisive force.

  23. Queuing isn't evidence that people aren't responsive to price. There are two margins to think about. First: am I going to buy ANY fuel. Second: how much will I buy? Queuing suggests that lots of folks wanted to buy at least some fuel - the first margin. But there's lots of room for action on the second.

    You queue for 2 hours for fuel, are you going to go away with only a half-tank? Or are you going to be sure to fill the thing up? Being willing to queue is evidence that you need SOME fuel. But says nothing about how much you need in the tank for the next two days. If the price doubled, folks would have gone in for smaller amounts.

    I did talk about panic buying. But that was still rational behaviour on each party's part given their correct forecast of everyone else's behaviour. I wanted to fix the forecast of everyone else's behaviour, which would consequently have everyone buy only smaller amounts for the short term disruption. I wouldn't put hoarding in the pejorative in that case. But it's part of a bad equilibrium that could have been fixed. The optimal amount of fuel that each buyer would have wanted would have decreased, because the precautionary motive for fuel purchase would have been strongly attenuated.

    The poorest folks in Aranui take the bus rather than drive. The buses were stopped. But there'll be some folks in each neighborhood who have a car. They buy their gas $20 at a time as pay comes in. Drive till almost out of gas or pay comes in again, then repeat. I fuel up in those neighbourhoods fairly often. Tons of folks only ever buy $20 worth of gas.

    Before you go "Aha! They couldn't afford $40!", stop and think. All the gas stations that side of town were down. Nobody in Aranui had a clue where the nearest open petrol station would be. Neither did we over in Brighton. None of the grocery stores were open in either spot. But if you had a clue that it was better over on the west side of town, you could pool with neighbours, get cash together, and have SOMEBODY drive over to the west side to get groceries for everybody, fuel up, then drive all the groceries home. But they could not do that if all the damned gas stations had run dry because all the folks living on the west side of town decided to top up their tanks. Yes, the Aranui guys would still be pissed off at the high prices and there's no way they'd make the connection between that and their having been able to get gas. But they'd at least have been able to get a load of groceries and enough gas to get home. That would have been enough to really help in those two days.