A study of price elasticity: taxi fare (bonus, a tip for taking HK taxi)

Case study: Beijing

Wang Xiaofeng (aka "three watches/reps") discussed about the impact to recent price increase to the income of Beijing taxi drivers (linking to a newspaper analysis of Yenzhao Metro). The net result of a 12.5% price increase (from 1.6RMB/km to 2.0RMB/km) was a net drop in total earning of about RMB500, i.e. 25%.
  • The basic assumption of the authority is that price elasticity is negligible, so that volume remains virtually unchanged after the price hike, albeit there may be a short term dip in volume. The authority estimated the average price per trip (given the average length of the trip, I guess around 22.5RMB), to be RMB2.81 -- which I believe is pretty accurate -- so that the net income for the taxi drivers will increase by RMB580 per months
    • The assumption seems to imply about 206 trips/month, or around 8-10 trip per shift depending on the assumption of shift/day, seems to be too low. I thought a taxi driver would take at least 2-3 trips per hour and about 20 trips/shift.
    • It also implies the total revenue per month is about RMB4600, which also seeems to be small. In my past conversation with taxi drivers in Beijing the revenue per month is about twice that amount. The net income (see below) figures are consistent with the survey because the driver needs to pay for various fees
    • So perhaps the net increase in revenue is not wholly captured by the drivers or there is something more in these assumptions (I would welcome any new data to make sense of this -- though it is not essential for the conclusion in this post)
  • Unfortunately the naive assumption on price elasticity turned out to be totally wrong. It hurt both the passengers and the drivers. Now it has been more than 4 months after the price hike (June 1st), the data should not be affected by the initial (temporary) dip in volume. The recent survey revealed that the average income per driver decreased from RMB2210 to RMB1658, a 25% decrease (and about 10% drop in total revenue if the assumption above is correct -- i.e. 20% decrease in volume, 1.125x0.8=0.9)
    • I think this assumes the driver does not own his own car, but I am not sure if the fees the drivers paid have also increased a bit -- see above
  • I believe the study is quite accurate, because it also showed an interesting observation (and intuitive result) -- that the impact is most severe for old cars. Average income for new car drivers decreased by 20.27%, and that for old cars decreased by 38.22% -- this indicates that because of the price hike, passengers have more choice about which car to take on spot (due to over-capacity), and some may even decide to skip taxi if the car is old (feeling that old cars do not justify the price -- this should be temporary phenomenon though)
My hypothesis
  • The short trips should not be affected much by a price hike, since we are talking about only 1-5RMB more. It is the long trips that are affected most, since it usually means 5-15RMB more for the passengers. So even though the number of trips/shift may only decrease by one or two, the lsot businesses are also the most profitable trips. (As mentioned in the report, the price elasticity impact is strongest in the sprawling city of Beijing, since most trips are fairly long)
  • If we understand the economics of taxi drivers, we would know that the "cost" of finding a passenger (in between trips) is pretty high. To learn more about the taxi driver economics please refer to the MBA case study translated by ESWN. So the price hike is taking away the most profitable customers from the drivers.
  • My prediction: given the mass wisdom of Chinese capitalists and entrepreneurs, very soon we will see in Beijing the "Discount Party (clan)" like those in HK.

The Hong Kong case (update: a mistake in taxi rental/shift is fixed)

The case of HK is very similar. Taxi in HK is very affordable (compared with other cities in the developed world such as Tokyo, New York, Boston, London, with similar income level), at HKD15 first 2 km, and HKD1.4/0.2km or /minute-wait; i.e. HKD7/km)
  • Bonus finding: a tip to all residents/visitors in HK. It is cheaper to take 2 different taxis than asking a driver to wait for you in the middle of your trip (e.g. dropping off someone or picking up something), if both segments of your trip are over 1.5-2 km long (traffic jam means that you would reach HKD15 in less than 2km). This is because, compared with the incremental rate of HKD7/km (14/2km), you only pay HKD1 more if you break your trip into 2 taxis. Whereas if you ask the driver to wait, one minute wait will already cost you $1.4 !
I learned that revenue/shift (6am-6pm) a taxi driver in HK is aournd HKD1100-1400 (average HKD1250) in weekend and a bit higher in weekdays (maybe 1400). He pays about HKD300-350/shift for rent/gas to the taxi leasing companies (lower for long term leasing driver and those who own the taxi -- because the taxi leasing companies would pay around HK$500/day(2 shifts) to a taxi owner, taking HKD200 for various fees (license/insurance/discount party fee), management and its profit). These numbers may not be precise, but should be in range.

Therefore, on average a taxi driver (who does not own his own taxi) generates about 1300x22shifts=28600 in revenue, taking away about 350x22=7700 as leasing cost (average of long term lease from taxi companies), and about 4000-5000 for gas/etc, he makes about 16400 per month.

As people in HK would know, there are "discount clans" in HK catering for longer trips, especially in the evenings. In the past it was 20% discount standard. Recently I learned that 30% is common for late night lifts, and 40% for airport transfer. (i.e. applicable to only taxi fare, no discount for tunnel/bridge fees). Note that the drivers need to also absorb the cost of additional fuel to come to your doorstep and time wait for you for a few minutes, that means there is comfortable margin for such price. This also means that there is serious problem in the pricing structure of long trips. (Not just in HK, I believe this is applicable to almost everywhere else -- as you can sense the preference of long trips by almost every driver everywhere)

There have been a lot of debates in HK. Many argues that the price is too high while some argues that the discount clans should be persecuted an punished. In my view, HK is a very entrepreneurial and capitalistic society, and that the discount parties are merely reacting to the market appropriately. It is true that the taxi price is reasonable (and even cheap) for short trips; it is also very true the price for longer trips are too high.
  • Consider the cost of about HKD350/shift, i.e. HKD30/hour. Reasonable profit (income for drivers) implies revenue of at least HKD80-100/hour.
  • If all trips are at HKD15-20 then one needs to take about 6 trips per hour, which means improbably full capacity
  • OTOH, a HKD200 trip usually takes about 25-30 minutes to complete, which is 4 times more profitable than the very short trips
  • If one assumes that the average price/trip is around HKD40 or 10-20min in length, then about half of the times for each taxi is empty. the key is how to minimize the idle time.
  • Note also that gas is only a small portion of the cost. e.g. at USD5.62/gallon (HKD11/litre) and 18miles/gallon it means HKD1.5/km, i.e. about 15-20% revenue.
The only solution to this problem is to rationalize the pricing structure, i.e., sacrificing simplicity (if the HK government is willing to introduce the immensely complex GST, I do not see why there is any problem in adding a little complexity in taxi pricing, especially because the computer technology today allows the taxi meters to do a lot more complicated calculations than those in the past)

The objective is to realize the following characteristic in the cost structure of taxi drivers
  • opportunity cost in between trips (i.e. when a driver is searching for passenger)
  • capacity utilization
Let's assume that price elasticity in HK is similar to that of Beijing (in reality, there is difference, but the difference should not be too big). Then the volume (on average, though mainly contributed by the long distance trips) increases by 25% (from 80% to 100%) by a price decrease of 12% (1/1.125).

Therefore, given such price reduction, the revenue per shift of HK driver will increase from 1350 to 1350x1.25x0.88=1485, an increase of 10% (with negligible change in gas cost). The profit per shift now is 1485-350-25 (incremental gas cost is about 15-20% of incremental revenue, say, HKD25/day) x 22 -4500=1110x22-4500=19920. The average income per driver (assume 22 shifts) is now 20% increase from the old number, even if the incremental gasoline cost is higher as a percentage.

The optimal structure for such price decrease is to not change the price for the first 2-5km, and decrease the price for longer trips -- so that the price reflect the cost structure more accurately. One example is to decrease the price/km for each incremental km, e.g. by HKD0.1 per additional km, as shown in the tble below
  • under this example, discount for long trip of 30km (kowloon to airport) will be about 20%, for 40km (HK island to airport) about 30%
  • incremental price change per km will not drop below HKD3/km, or about twice (or 2.5x) the cost/km of gasoline, so that there is still small incremental profit for the driver
  • average discount is about 12% -- assuming certain distance profile centered at around 5-6 km trips (or lesser distance with some waiting)
  • decreasing price this way will boost driver income by about 15% if Beijing price elasticity is applicable -- since our scheme does not really discount the short trip prices, it is more likely that the income increase will be much larger
distCurrent pxPx/km
New pxPx/km

8.0 8.00 0%
15.0 7.00 0%
21.9 6.90 0%
28.7 6.80 1%
35.4 6.70 2%
42.0 6.60 2%
48.5 6.50 3%
54.9 6.40 4%
61.2 6.30 4%
91.2 5.80 8%
118.7 5.30 11%
166.2 4.30 19%
206.9 3.20 26%
210.0 3.10 27%
213.0 3.00 28%

Avg Px




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