It is surprisingly easy to get the sign wrong when reasoning about quantities. Consider this old riddle:
Three ladies go to a restaurant for a meal. They receive a bill for $30. They each put $10 on the table, which the waiter collects and takes to the till. The cashier informs the waiter that the bill should only have been for $25 and returns $5 to the waiter in $1 coins. On the way back to the table the waiter realizes that he cannot divide the coins equally between the ladies. As they didn’t know the total of the revised bill, he decides to put $2 in his own pocket and give each of the ladies $1.
Now that each lady has been given a dollar back, each of the ladies has paid $9. Three times 9 is 27. The waiter has $2 in his pocket. Two plus 27 is $29. The ladies originally handed over $30. Where is the missing dollar?
To get the missing $1 in the question we have done this arithmetic: 10 + 10 + 10 – 1 – 1 – 1 + 2 – 30 = -1
The correct arithmetic is: 10 + 10 + 10 – 1 – 1 – 1 – 2 – 25 = 0
Positive numbers represent payments from the ladies to the restaurant, and negative numbers represent money received by the restaurant. The result should obviously always come out to zero. That +2 should be a -2. Okay, there is a 30 where there should be a 25 as well, but only because the +2 yielded an intermediate result of 29 which is close enough to 30 to cause confusion.
This getting the sign wrong is the same mistake that means Tim Worstall has to point out that jobs are a cost. The new widget factory will create 1000 jobs, we are told. If it produces 1000 widgets per year, that means we get one widget per man-year of time. The man-year of time is a cost. If we could somehow arrange for the widget factory to create only 100 jobs for the same output, we would have just as many widgets and 900 man-years left to spend on some other useful thing. We would be richer.
This mistake crops up in trivial ways all the time. My friend recently gave up full-time work to look after the children for various financial and logistical reasons. Think how the economy is losing out, she mused. Not only am I not producing widgets, I am not paying the nursery workers or buying train tickets for my commute. Well it is true that the widgets my friend used to make are no longer made, but the nursery workers do not count: the same amount of childcare is being done as was being done before. It is not correct to add the childcare previously done by the nursery worker to the childcare now done by my friend. At worst there is now an unemployed nursery worker who will go and do something else instead, but that is just a market optimising everyone’s activities to match the level of demand. The train tickets were just part of the cost of getting the widgets made.
Ah, train tickets. We are going to get a new high speed rail link between London and Birmingham. The government is going to ‘invest’ £32.7bn in order to reap up to £46.9bn of ‘economic benefits’. I wonder how many of these benefits have the wrong sign. Counted among the benefits are “hundreds of jobs”, but these are already included in the cost figure.
Also counted are ticket sales. Which makes sense if the ‘investment’ was really an investment. But invest here really means to steal from the British public £32.7bn so that they can then pay, say, £40bn for train tickets in exchange for £40bn worth of train travel. I make that -32.7 – 40 + 40 = -32.7. Where is the missing £32.7bn?
What the f**k are they f*****g thinking? Public finances are in a horrifying mess already. Even without considering the costs, the benefits of building this are negligible. £9bn was already been spend in the decade to upgrade the existing West Coast Main Line, and the present train service takes about an hour and 20 minutes London-Birmingham and 2 hours London-Manchester or London-Liverpool.
The pattern with other high speed lines suggests that most high value business travel will use the train for journey times of up to two hours, the percentage that does drops off for journey times between two and three hours, and for journeys over three hours most will make other arrangements. So reducing these journey times by 20 minutes just isn’t going to change travel patterns much. It’s also going to be *really* expensive. 300km/h railways are *much* more expensive than 200km/h railways.
If there were some other destinations that might have travel times reduced from (say) three hours to two, that might make a difference in travel patterns but this, not much at all. Glasgow and Edinburgh are so far away from London that it is always going to be easier and cheaper to simply use Easyjet.
The thing that bothers me most about HS2, is that it’s a great big Government assertion that telecommuting doesn’t work.
Unfortunately I forget where I read this many years ago, but I’ve seen a well-argued assertion that rail travel isn’t economically sound for the UK, as the landmass just isn’t large enough. Easyjet would suggest otherwise, although I still don’t see how they do it for the money.
After a short break from my (free) champagne. You are right, we’re being fucked. Again…
Well, in theory…
Because of the improvements to plant, the £40bn paid for HS rail fares will buy more service than £40bn spent on non-HS rail.
Dave Walker: I’ve seen a well-argued assertion that rail travel isn’t economically sound for the UK, as the landmass just isn’t large enough.
Huh! The big knock on rail travel in the U.S. is that the landmass is too large. Except in the Boston-Washington corridor, American cities are too far apart for convenient rail travel.
If Britain is too small, what about continental Europe?
Remember “business” (i.e. those executive creeps that are put on radio and television shows) support all this – and most of them are NOT just hopeing for construction contracts. Or ever utter morons who believe that as (because of Enron style accounting tricks) the money spent on the project will not appear in the government deficit figures it will “not add to the national debt” (“if we do not write the number in the ledger the spending has not happened” – much like bankers who believe that if they write numbers in ledgers they have lots of money to lend EVEN IF THERE IS NO ACTUAL MONEY, NO NOTES OR COINS, IN THEIR VAULTS – the numbers written in ledgers trump material reality you see, writing numbers on a computer screen is a sort of magic spell).
Still back to the mainstream “business” people and so on.
They have all been taught (in school and university – and in the financial press every day) that government spending “stimulates” the economy via the “multiplyer effect” (they can do a lot of mathematics to “prove” this).
And they have ALSO been taught that government “infrastructure” spending is especially good – it is “investment” you see.
The Daily Telegraph (the leading “conservative” newspaper) has joined hands with the vile creatures of the Financial Times and (I am expecting) the Economist magazine. And why not? After all the writers for all these publications were taught the same things.
And if it is “like the Victorians” – accept that “business” in those days actually paid for the railways (and so on) privately, by people risking their own money (and sometimes losing it – there were many railway related bankruptcies). That will not do now – not for modern “institutional investor” owned business.
So everyone (the media, the unions, the academics [including most of the mathematical economists], the leading politicians of all parties, and “buiness”) is happy and in agreement.
And the plan will utterly and completely fail – it will be a financial blackhole and the railway (if it is ever finished) will be of no use what-so-ever. Bastiat (of whom most of these people have never heard) will be vidicated yet again – and the leading people STILL will not understand (and we will head further towards utter destruction).
This is not the failure of a few politicians and civil servants getting their sums wrong – this is a CIVILIZATIONAL failure. The people in the leading institutions of our society (education, media, “business” and so on) believe things that are JUST NOT TRUE.
And these are fundemental things – not just a matter of one railway project.
“to steal from the British public £32.7bn so that they can then pay, say, £40bn for train tickets in exchange for £40bn worth of train travel”
Hmm.
I bet it will be more like stealing from the British public £90bn so that they can pay about £10Bn for about £8Bn worth of train travel (add one or more noughts depending on how much “Quantitative Easing” takes place over the next decade or so).
Oh, and all that several years after they’re predicting at present.
And….by using public funds to keep the cost of commuting lower to the consumer, than the actual costs of providing the service warrants, this reduces the incentive to look for more efficient alternatives…such as telecommuting.
Landmass is irrelevant. Population density is what matters (well, clearly there is also a minimum absolute population that is required for, say, an underground line to be viable).
I was disappointed by this announcement. I had hoped that the government might see sense in the face of such strong opposition, with it being generally (I think..I try not to discuss these things with my lefty friends as I get too annoyed) accepted that the cost-benefit was only marginally in favour at best. But I guess this is how it goes when Cameron’s haircut is making policy.
On the issue of jobs being a minus…
If value is subjective and I, as someone who needs a job in order to have the money to live and am currently working a poorly paid job see that a project will come with 1000 nice gleaming jobs which are, compared to the one I currently have, comfortable and easy. Wouldn’t I value this new job as a positive thing?
That said, if the mad house who are proposing this railway really want to go down the “jobs are a good thing” line, it would be far more effective to point out how much each new job costs.
Jamess: yes, indeed. No voluntary transaction ever occurs without it being beneficial to both parties. So from the point of view of someone taking the job, the money is worth more than the time, and from the point of view of the employer, hiring that employee makes you richer than not hiring him.
The problem is with declaring to third parties that the jobs are a benefit in their own right, and adding that to the other benefits of doing the project.
You can’t sum these two things because from that point of view the jobs are a cost.
The other assumption inherent in saying “look at these new jobs” is that these people would otherwise be idle. It’s more likely that they would be doing something else.
And in the case where we have non-voluntary transactions like with government projects, that something else is almost by definition going to be more useful because if something is the most useful thing to do you don’t generally need force to get it done.
In re HS2, it’s the same old confusion – the wrong sign if you like – justified by cod-keynesians and loved by politicians and bureaucarts that ‘economies grow because people spend’, whereas we all know that it is the exact opposite – ‘People spend because economies grow’.
It’s the Socialist Right what do you expect?
Btw i don’t think that riddle isn’t well explained from language point of view.
I doubt a single member of this government or indeed the business class that Paul Marks rightly attacks has ever read Frederic Bastiat or Henry Hazlitt, two men who brilliantly framed the point about how politicians and other such folk can only see the visible benefits of, say, a high speed rail link or whatnot, and not see the costs. They don’t see that this vast amount of money could have been invested in something else. The entrepreneurs who would have invested in new firms will now not do so, but no one sees that.
But I also agree with Paul that we are reaping decades of mal-education in our schools and universities. We are talking about people who are thick. Indeed, it is the people who paid attention in their economics classes who believe all this rubbish about “multipliers” and whatnot.
Hadn’t seen that riddle in decades. It’s one of my favourites. Like the various “proofs” that 1=2, it titillates the numerate but is completely uninteresting to the innumerate — a joke they can’t “get.”
On this I was wrong about the Economist magazine.
Their article on this matter was actually quite good.
I apologize.