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Tuesday, May 31, 2005

Analysis of the bus and train fare hikes

The big news today is not that a Straits Times reporter was arrested in China, but that bus and train fares are going up:
  • one to two cents for bus fares with EZ-Link card
  • one to three cents for train fares with EZ-Link card
  • ten cents for cash-paying commuters on buses and trains
(The above applies only for adult commuters. Children and national servicemen enjoy prevailing rates.)

According to published reports, fares would be allowed to go up only by 2.4%. So let's do some math.

Firstly, some stats from today's Today article:
  1. There is an average of 3.4 million commuter trips daily.
  2. 200,000 trips (5.89%) are cash-paying --> 3.2 million trips (94.1%) are EZ-Link card-based.
  3. The average fare is 80 cents (from the older Today article).
(Dear Tor Ching Li: 200,000 of 3.4 million is around 6%, not 5%. Any primary school kid can tell you that 5.89 rounded to the nearest whole number is 6.)

Supposing the average increase for EZ-Link cardholders is two cents (based on the increases stated above), then their average increase is 2 / 80 * 100% = 2.5%. For cash-paying commuters, their increase is 10 / 80 * 100% = 12.5%.

Therefore, the average fare increase across the board is 0.0589 * 12.5% + 0.941 * 2.5% = 3.09%, or 0.69% more than the allowed increase of 2.4%.

In other words, commuters are screwed.

But children and NS men don't pay the increase. So let's suppose that there are 500,000 of them, or 14.7% of all commuters, and all of them use EZ-Link cards. Correspondingly, the number of EZ-Link cardholders who will have to bear the increase is 2.9 million, or 85.3% of all commuters. The average fare increase then is 0.0589 * 12.5% + 0.853 * 2.5% = 2.87%, or 0.47% above the 2.4% limit.

Screwed again.

The only way that the average increase can fall to 2.4% is if the number of EZ-Link cardholders who pay the increase is about (2.4% - 0.0589 * 12.5%)/2.5% = 0.6655 (66.55%) of all commuters, or about 2.26 million, which means there would be 937,300 children and national servicemen. Is this reasonable?

(Someone please correct me if my maths is wrong. If proven so, I'll pull this portion of my entry.)

So that's the financial side of the fare increase. To quote Jedi Master Yoda, more to say I have. But I'm going to hold my tongue because I don't want to live in fear of being sued. I'll just leave the above facts and figures for you to contemplate.

To round up, here are two classic quotes from today's Today article:
  • Nameless SMRT spokesman: "These (10-cent) increases will cushion the impact on Singaporeans who are frequent users and EZ-Link cardholders."
  • As written by Tor Ching Li: "While the public has expressed its disapproval at the fare hike application this year despite both public transport operators posting healthy profits this year,..."

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Mastermind said...

There is something wrong with your calculation and I need to point out an important fact that you missed out.

If the average fare now is 80 cents, after the increase, the average fare should be about 81.92 cents or about 82 cents. The way you calculate is assuming that the fare is 80 cents for all trips including students, children etc.

Bare in mind that among the 3.4 million trips many of them are more than 80 cents and for student/elderly rates, the fare is much less than 80 cents. So if you want to calculate you will need to know how many trips are 60cents, 80 cents, 1 dollar for example to calculated the average increase.

In other words, we do not have the information to calculate the actual average increase in fare as we do not have the breakdown of the information.

Yuhui said...

I am assuming from the older Today article that all of the different fares that you mentioned have already been worked out to give the average of 80 cents. If this assumption is wrong, then either Today is vague in their wording or did not do their calculations correctly.

Mastermind said...

Obviously you can't assume that. If you assume the Today article did their calculations, then average fare increase of 1.92 cents (or rounded off to 2 cents) is also calculated as the average increase, including the 10 cents increase for cash paying passengers. (With the suggested method below)

So if you factor it in your own calculation you are doing it twice already.

That's why all the calculations you did is unnecessary I'm afraid.

The problem does not lie with Today but with your calculations. To elaborate further. Let say I take a bus ride that costs S$1.48. After fare increase it's S$1.50 so the increase is 1.35%. If my ride is $0.63 to $0.64 then increase is 1.59%. Only when my ride is $0.78 to $0.80 then I'm screwed as the increase will be 2.56%. So if you look at the EZ-Link paying passengers the increase is definitely below the 2.5% you calculated from the simple average.

The best you can do is to choose a more scientific approach by assuming that the fare paid per trip could follow a certain distribution (say Gaussian) and work out the probability that an EZ-Link card holder pay a certain fare and find the average increase for that. Similarly apply it to cash paying customer.

But the problem is more complicated if you throw in the 25 cents discount for transfer as you need to assume a certain percentage of transfer also.

Sometimes things are not as simple as the newspaper put it. I doubt Today did their calculation nor you did yours correctly too.

Yuhui said...

Actually the two-cent average increase for EZ-Link cardholers that I mentioned is my own figure based on the stated fare increases (1-2 or 3 cents). Today did not mention (nor do I recall it mentioning) such an average increase.

Therefore, my average two-cent increase does not include the 10-cent increase for cash-paying commuters.

Also, in the real world, you can't pay with less than a cent, i.e. there are no fractions of a cent that you can use physically to pay for goods or services, which is why I rounded the number up to two cents. If the transport companies round the number down, i.e. to one cent, then I will have to do some recalculations.

Mastermind said...

Okay.. I got all the info from the links you provided.. so perhaps either I saw more into the articles than you did or I misread it myself.

All in all, your 2 cents average is way out. I kinda read some of your posts from technorati at times but this time your analysis and replies were a bit of a disappointment.

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