For those that don’t read Transportblog on a daily basis, this is the third part of a series I’m writing on the economics of public transport fare policies. Part 1 discussed a key rationale for public transport subsidies – lower fares keep people from clogging up already-congested roads. Part 2 considered the case for distance- or zone-based fares to ensure that people taking longer (and hence more expensive) trips pay more.

In the comments on those posts, several sharp readers asked about the relationship between fare levels and ridership, and whether there are any opportunities to improve outcomes by targeting lower fares to highly price-sensitive groups. These are excellent questions to ask!

In this post, I’ll take a look at the first question: In the aggregate, how does ridership respond to changes in fares? Hopefully, this will give us the theoretical tools to take a look at the second question in the next installment of the series.

In economic terms, we are asking about the “price elasticity of demand” for public transport. Fare elasticities measure how responsive people are to higher (or lower) prices. They’re usually estimated empirically by analysing data on changes in fares, patronage, and other control variables (e.g. per capita income or GDP) over time.

There are many studies on fare elasticities from around the world, some of which are summarised in the Australia BITRE elasticities database and this useful summary paper by Todd Litman. NZTA has also commissioned research into the structure of demand for public transport – see e.g. Wang (2011) and Allison, Lupton and Wallis (2013).

These studies don’t always arrive at precisely the same result, but they agree on one key thing: Demand for public transport is relatively “inelastic”. All else being equal, a 10% reduction in fares will increase ridership by less than 10% in the short and long run.

Some odd bloke demonstrating the concept of elasticity

The implication of this is that if a public transport agency reduces fares, it will tend to collect a smaller amount of money from users and hence require a larger subsidy. And, conversely, raising fares can increase overall revenue, albeit at the cost of unintended consequences for increased traffic congestion.

Here’s Litman’s best-guess estimates of elasticities for public transport. The key figures are in the first row – “transit ridership with respect to transit fares” for the overall market. Litman’s estimates a long-run fare elasticity between -0.6 and -0.9. This means that a 10% increase in fares would be expected to reduce ridership by 6-9% in the long run.

Notice that short-run elasticities tend to be smaller, indicating that people take a while to fully respond to changes in prices. For example, if someone’s fares for their bus to work went up significantly, they may tolerate it for a little while but choose to buy a car (or rent a parking space) six months down the line.

Litman (2014) recommended transit elasticities

Personally, I wonder if Litman’s estimates are a bit on the high side. Figures from Wang (2011) suggest that long-run fare elasticities (in the second row of the following table) are -0.46 in Wellington and -0.34 in Christchurch. This would indicate that a 10% increase in fares would reduce ridership by 3.4-4.6%.

Wang (2011) NZ bus demand elasticities

Both of these tables also contain information on how people’s demand for public transport changes in response to other price changes and service changes, which is another interesting topic. Without going into a great deal of depth, I’d note two things:

  • First, increasing petrol prices do tend to increase public transport demand, but this effect may be relatively modest. Car ownership, on the other hand, can have a big impact, as people who have already paid the fixed costs to own a car have strong incentives to get as much use out of it as possible.
  • Second, improved service quality – meaning better frequency and reliability of buses and trains – has a stronger impact on ridership than lower fares. This has important implications for transport agencies, who are often better off putting their marginal dollar towards upping frequencies.

Lastly, it’s worth considering how this might play out in practice. Let’s assume, for a moment, that fare elasticities of demand are at the low end of Litman’s range, i.e.:

  • Short-run fare elasticity = -0.2
  • Long-run fare elasticity = -0.6.

Now, let’s consider a hypothetical scenario in which public transport fares are $2 and there are 1,000 daily riders on a given bus route. The public transport agency collects $2,000 in fares every day ($2*1,000 riders).

Now let’s consider what would happen if the agency chose to reduce fares by 10%, from $2 to $1.80. This is obviously great for people who are already on the bus, as they can pay less to get the same service. Daily revenue collected from them drops to $1,800 ($1.80*1,000 riders).

However, the lower fares also attract new riders. In the short run (0-2 years), we predict that a 10% reduction in fares will lead to a 2% increase in ridership (-10%*-0.2). This means that an additional 20 people (1,000 riders*2%) will take the bus and pay a total of $36 in fares every day ($1.80*20).

So far, this is not looking great from a financial perspective. The transport agency has lost $200 in fare revenue from existing riders and gained only $36 from new riders.

Things aren’t much better in the long run, where a 10% reduction in fares is expected to lead to a 6% increase in ridership (-10%*-0.6). This means an added 60 riders who pay $108 in fares every day. Again, this is not enough to cover the loss in revenue from existing riders.

Does this mean that fare reductions are never worth it? Not necessarily – if the reductions in congestion from fewer people driving are sufficiently large, then we should be willing to pay a bit more in subsidies.

singer subsidy cartoon

A second factor is that different people and different types of journeys respond to higher prices in different ways. In principle, we may be able to increase patronage at a relatively low cost by targeting fare discounts to price-sensitive people. But that is a topic for next time!

What do you make of the data on fare elasticities of demand?

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  1. I would be extraordinarily careful when using elasticities and making predictions from them – have the predictions been validated? Are they network or city specific?

    A city based study would be best I would think. You can run trials to determine this by loading a card with credit.

    Many commuters in peak would be inelastic because they have to get to work. Also fare passes make an additional trip costless.

    Also it depends on the network quality. Clearly people are happy to pay more for quality and less for poor service.

  2. public transport fares have to be attractive to average “punter”. They have to look at the options and think “well if i add it up it makes sense to take the bus or train or ferry…”

  3. A few caveats to all of this:

    The problem is that elasticities are not static, they’re dynamic, and they increase when fares are perceived to be expensive. I would argue that for many transit products in NZ, that perception is held.

    (Yes, I know that total cost of ownership is usually higher, but for most NZrs these are sunk costs and thus discounted to near-zero.)

    Long run elasticity is also substantially different than short term elasticity. I would be very cautious about extrapolating strong conclusions from models or data that looks only at the short term.

    To quote Litman:

    Commonly used transit elasticity values primarily reflect short- and medium-run impacts
    and are based on studies performed 10-40 years ago, when real incomes where lower
    and a greater portion of the population was transit dependent.

  4. In Sao Paulo, buses have a sign on the side of them…it translates as “Transport: a citizen’s right, the state’s responsibility”. When the council attempted to raise public transport fares last year, there were huge protests, and they backed down. Public transport users in Auckland suffer unreliable services and continue to pay more and more, and we do so with grace and dignity. But in such do we not deserve the same respect in return? Traffic downtown last night was ridiculous. There is nothing elastic about single person vehicles blocking the link bus!

  5. I was reading this post on the train on the way to work and started thinking about how you would change the elasticity of consumers.

    What I came up with that it is more a societal issue about how PT is perceived, rather than being price dependent, although price elasticity is easier to measure.

    When I started working in Auckland 20ish years ago, I caught PT to work for 18 months and then got a car, which I continued to use through jobs in Auckland and Wellington, although at a second job in Wellington I walked to work most days. After living in London and using both PT and driving to work, I now chose to live close to work or close to PT that gets me to work easily.

    How changes in preference through generations shape investment and subsidies in the future will be interesting, especially if those who are currently labelled baby boomers turn out to be the blip and PT returns as the dominant form of transport for urban dwellers.

  6. The cartoon at the bottom seems to miss the two biggest subsidies:
    * Healthcare costs for obesity
    * Council / government owned land being gifted for roads when there are much better uses (e.g. Fanshawe Street, Quay Street)

  7. The big issue in NZ urban Transit is our very high peakiness. We are often at over or near capacity at the peaks but have plenty of capacity off peak at night and weekends. So it is a very good question to ask whether pricing has a role to play in capitalising on this spare capacity and relieving pressure at peak load times. This is also generally true of the road networks too.

    Differential time of day pricing is surely worth trying on both systems, but for now we only have the tools to do it on PT systems. Why not run at least a long term trial on what a radical drop in off peak fares could achieve? If it does stimulate both new ridership and time shifting it may prove fiscally neutral or positive by taking cost pressure off peak systems and adding zero marginal cost off peak riders? Good proof of concept for road pricing too.

    1. To satisfy those who want fares to rise (see above), you could increase peak fares by a small amount, while decreasing off-peak by the same or a similar amount.

      For example, a $3 fare between 4:30-7pm becomes $3.50, and an interpeak fare becomes $2.50. Easy to understand, easy to justify.

      1. I’d halve true off-peak, but apply no other discounts, student etc. Still reckon it probably won’t require rises at peak. Our fares are high by international standards, it’s just that our ridership is low, a problem that is being fixed with service improvement.

    2. I recently went to Sydney for the weekend and took advantage of an Opal card which caps Sunday PT travel at $2.50 as a ‘family day’.
      As a sweetner for the Auckland residents hit with ever increasing rates we should look at introducing something like this here – its not as if Sunday is really busy on PT,the trains and buses will still run whether empty or full.

  8. Economists love elasticities but they suffer some serious logical problems. The elasticity is different at different points on a demand curve – even if the demand is linear! So elasticity says more about where you are on the curve than anything about the market for the goods but that also implies elasticity is only good as an estimate of behaviour over a very small range of prices. If you move up the demand curve due to a price increase you will expect quantity to decrease but if you recalculate elasticity you will get a new value. Secondly because economists screwed up supply and demand graphs by using the wrong axis for each the elasticities for demand are all the wrong sign so a high value is actually smaller than a low value- crazy stuff that makes simple ideas harder to explain.

  9. I’d pay MORE for a PT system that gave me the same flexibility, reliability, and speed as private transport (driving) than I would pay for the car etc. as then I’d gain the leisure time from not driving (reading a book).

      1. It’s all part of the wonderfully diverse tapestry of human existence! People like different things, and it’s reasonable to expect that we have a transport system that enables them to choose different ways of getting around.

        1. I agree.

          Picking sides by commenting on the enlightenment of any of the various options or positions that people would chose is something I wanted to stay away from.

  10. “considered the case for distance- or zone-based fares to ensure that people taking longer (and hence more expensive) trips pay more”

    This isn’t quite true. The further you go on a train, the cheaper it becomes to transport you on a per-km basis. This is why fares and freight rates get lower and lower the greater the distance of the journey.

    Someone travelling Papakura-Britomart should be charged less on a per-km basis than someone travelling from Penrose to Britomart.

    There’s also a lot more value in moving someone long distance than a short distance in terms of roading, social and environmental benefits (as opposed to driving), and such travel should be incentivised through cheaper fare offerings for long distance travellers.

  11. I reckon travel modes are so inelastic because the cost of travel varies so widely between modes. The cost of taking public transport regularly is orders of magnitude higher than the cost of walking/cycling everywhere. And the cost of owning a car and driving everywhere is orders of magnitude higher than solely using public transport. A small shift of 10 or 20% in the price isn’t going to register that strongly in people’s decision-making about which mode they use.

    I would suggest there are other factors which feature much more strongly in most people’s decision-making than price, such as time, convenience, flexibility, comfort, privacy, safety, effort required…etc. Maybe small changes in these would result in greater changes to ridership than small changes in price do.

      1. That’s just from personal experience, so yea. I remember as a student I biked everywhere and used to dream of the day when I could afford to catch the bus everyday. Now I catch the bus everyday because I can afford it, but still can’t bring myself to go out and spend lots of money on a car.

  12. Only in the short term and mostly for regular users, is PT demand is likely to be inelastic. Regular users often allow various living patterns to form around being able to use a certain service in a certain way at a certain price, so they are to some degree ‘held captive’.

    But only to some degree. If the service changes or if fares go up, or other things happen, regular users might grumble and endure for a while, but eventually reach an accumulation point at which they decide, “Stuff it. I’ve had enough!”, and make a sudden change away from what they were doing.

    Too often transport policy-makers, analysts and commentators fall into the trap of categorising travellers as ‘motorists’, ‘rail-users’, ‘bus-users’, etc, as if these are immutable groupings like gender or ethnicity. This is nonsense. As has been stated many times before on this blog, people will generally use whichever option suits their needs best. And a whole bunch of factors (perceived or real) will be processed by an individual in making a choice. Fare levels are one factor. Each factor and its relative weighting will have a part to play in the outcome. So if people feel let down by over-priced PT, or swayed by car-encouraging policies, (or vice-versa), they will make or change their choice accordingly, sooner or later. I call this elasticity.

  13. Not sure where to put this comment, probably doesn’t belong here but what about the idea of a ‘tag off’ lottery?
    I’m thinking only RTN initially.

    Could you programme a reader to say at random offer a couple of free trips per 100 tag offs? Or say a few $10 credits for every 1000 tag offs? Maybe even a serious prize in cash or goods per 10,000 / 100,000 tag offs?
    Generated randomly but averaged out at the above rates so that no one knows when the winning tag off would occur.

    This might help incentivise behaviour if you had say a 2-4% chance of tagging off for free… and even if it didn’t incentivise fare evaders at least it would reward the users who do pay.

    So if say the Avg PT fare is c.$3 for every 100 ($300) you (AT) might write off $6-12 (2-4 trips), for every 1,000 fares ($3,000) you (AT) might credit $20-50 on HOP cards.

    1% of revenue for say 100,000 trips would be $3000. Maybe you could offer a cash / goods prize pool of $5,000 per 100,000 trips..?
    12 months to May (2015) there were c.16.5m trips on the RTN – c.$50m revenue, 1~2% would be 500k – $1m in prizes! (marketing and administration could be deducted from this pool.)
    With the current tag off data and a fixed pool of money based on RTN revenue, trips + avg fare, it would be easy to see the cost of the lottery and whether it is covering itself and increasing revenue from increased tag offs.
    If it is costing too much, scale it back. If it is largely ineffectual, discontinue it after say a full financial year.

    Things don’t have to be all stick, everyone loves a little carrot… and how easy to market / advertise / promote…
    “I tagged off on Monday morning and won an iPad / $1000 @ _____ station, thanks AT!”
    In the game with PT / How do you ride? / Are you high rolling? / ‘CASHtag’ $tag etc etc

    1. This is a really good idea – the more you tag-on and tag-off, the higher the value of a prize you get a chance at winning. You could dish out Hop credits at the lower levels (to help entice casual users) and then give people make a habit of it (3 – 5 times a week) a shot at winning something a bit pricier. Keeping it simple would probably be the most effective way of offering a prize, not sure about the milestone credits but the actual prizes are something AT should look into.

    2. ““I tagged off on Monday morning and won an iPad / $1000 @ _____ station, thanks AT!”
      In the game with PT / How do you ride? / Are you high rolling? / ‘CASHtag’ $tag etc etc”

      My eyes bled reading that (CASHtag T_T), thank you.

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