# An Unexpected Economic Computation

Here’s a calculation that I found pretty surprising. Have a guess as to its meaning:

$\dfrac{\left( \dfrac{60}{(24-15)} \times 2.40 \right)}{1 - (0.4 + 0.02)} \approx 27.59$

If you guessed something relating to savings, you’d be on the right track; the denominator would probably have clued you in to something along those lines, since the $0.4 + 0.02$ is the marginal tax that higher rate earners in the UK would face (as of the 2016/17 tax year). You might have figured out then, that the fraction on top probably refers to some form of a time savings expressed in minutes. The $2.40$ is probably a bit more puzzling especially if you’re not from London; from the previous observations it’s the cost of taking some convenience that saves nine minutes. That’s right; you might recognise that as the price of a single-trip Tube fare.

Putting that together, that computation is actually the effective hourly gross rate I’m being paid to walk to my office as opposed to taking the Tube. Specifically, I’m comparing (a) taking the Tube, which takes about 15 minutes plus a single trip fare of 2.40, and (b) walking, which takes 24 minutes. We’re thus looking at a net rate of 2.40/9 minutes. Of course, I pay for the Tube using post tax money, so we need to factor that in, and to get an hourly rate we scale that linearly.

Now of course this doesn’t mean I’ll never take the Tube to work again, or even that I’ll take it much less often – the 9 minute difference can be important (say there’s a high priority issue going on, or I’m about to be late for a meeting), and walking can be pretty unpleasant (if I’m very tired, it’s late, or it’s too cold; that said, I’ve done this in the current ~0 degree weather and found it fine, at least). Probably, doing this in the mornings would generally be more reasonable and sustainable as I’m pretty tired by the end of the day. Saving one trip even occasionally is enough of a win, I’d say, and getting some time to clear my head in the mornings is probably not too bad as well.

A question could be why I don’t use a Travelcard for the computations instead. The weekly one for zones 1-2 costs $33$ and since I largely stay within zone 1 and 2 we can assume that that’s all I’ll need (I’ll ignore the odd trip to Heathrow). I think $16$ or $17$ is probably about the number of rides I’d take in a week if I used it aggressively (two a day, maybe three or four on the weekends). We can re-run the numbers with $\frac{33}{16.5}$, which means a trip costs $2.00$. Our final answer is $22.99$ which is still pretty solid (if you work 42 hours a week that’s a gross annual income of just over $50,000$). Anyway, as it turns out because I use contactless, if I happen to have a week where I do travel a lot I’ll effectively be using one.

Now let’s have a look at the monthly or annual tickets. These cost $126.80$ for monthly, or $1,320$ for annual. Assuming that we make $2.357$ trips a day on average (taking the middle of the estimates above), and a month as $365.25/12$ days, with the monthly card the cost of a trip falls to $1.767$ and with the annual card it falls to $1.533$. The “gross wage” calculations become $20.31$ and $17.62$, which while not as high are still solid amounts. $17.62$ an hour corresponds to about just over $38,000$ in gross income assuming a 42 hour week, which would put you in about the 78th percentile of earners according to the ONS data for 2013-2014. I guess this will probably be a bit lower now, with inflation/wage growth, but still decent.

Assuming usage is high, it seems that the annual card might be the way to go. However, an issue is that I sometimes need to travel overseas for work potentially a fair chunk (let’s say personal plus work travel adds up to two months a year), so the annual one is quite definitely a non-starter. Multiply the price of a trip by $6/5$ to factor that in, and you end up with a per-trip figure that’s higher than the monthly card. I have been getting the monthly card in the past, especially when I was a student and it only cost $86.50$, partly because walking to Imperial was going to take a very long time (that route yields savings more on the order of $30$ minutes). Note that while losing a card is a legitimate concern, you can usually recover the travel passes using the TfL website.

(N.B. This idea was conceived independent of the currently ongoing Tube strike, though in a sense it’s a bit of a bonus that things aren’t affected.)