Quantifying the benefits of HS2
The creation of a high-speed rail line from London to the north of England will produce quantifiable benefits to society, the government believes.
It has put this figure at £48.2bn for the whole project - significantly higher than its estimate of the cost, which is £25.7bn.
But critics have questioned the assumptions underlying the estimate of likely benefits.
So how did the government arrive at this sum?
Business travellers' time
The government assumes that business travellers do not work on trains.
It also believes that they will spend every minute trimmed off journey times working productively once they have reached their final destination.
The additional minutes business travellers spend at their desks have a value: this is deemed to be equivalent to the money they earn in this period.
To find out what the average business traveller earns in a minute, the government carried out a survey - between 1999 and 2001. This figure has been increased in line with GDP growth over the intervening period.
Estimating the benefit of all these extra minutes saved is then a simple matter of tallying them up, according to how many business travellers are expected to use the service, and multiplying this total by average earnings.
But campaign group HS2 Action Alliance thinks that the government is significantly overestimating the average earnings figure.
The business travellers surveyed in 1999-2001 would have been an elite bunch, it argues, and average earnings among today's business travellers - being more diverse, the campaigners contend - would be one third lower.
It also rejects the assumption that business travellers will not be at all productive while on board the train, accusing the government of ignoring research suggesting that at least half of the trip would be spent working.
The government is aware of concerns about its modelling, but fears there is currently "insufficient robust evidence to adopt a more sophisticated approach".
A Department for Transport (DfT) spokesman said the government was working on a more accurate model, which might prove that the benefits are in fact being understated, rather than exaggerated, by the current simplifying assumptions.
Leisure travellers' time
How much would a quicker journey be worth to those not travelling on business? The government tried to find out.
It carried out more surveys, asking whether people would be prepared to pay, for example, £20 more to cut a long train journey by one hour. It also examined data on the actual popularity of different train fares when faster and slower trains were available between the same destinations.
Alighting on a value of £5.77 an hour for leisure travellers (in 2009 prices), it was then a short hop to calculate the total benefit to them of switching to high-speed rail travel.
But HS2 Action Alliance notes that this figure has been reached by updating data from 2003.
Since leisure travellers now have faster internet connections on their mobile devices, the campaigners argue, leisure travellers enjoy their time on board trains more and might not be prepared to pay as much to cut journey times.
Similar surveys have helped the government to establish how much passengers would cough up to travel on less crowded trains. This too has been totted up and added to the projected benefits of HS2.
The campaigners argue that the government is drawing too stark a contrast: the models suggest that either HS2 is introduced, or very little investment in transport will take place.
They would rather explore cheaper ways to cut crowding, such as lengthening current trains.
But the government believes that they have significantly underestimated future demand for rail travel; HS2 is necessary to protect not only economy growth but also quality of life, the DfT spokesman said.
"While upgrading existing lines would provide a short-term fix, it does not provide the long-term capacity we so vitally need," he added.
The government predicts that HS2 trains will stick more reliably to their timetables than the average train.
This matters because passengers value being on time very highly - every minute they are delayed wipes out the value of three minutes' journey time, according to more surveys.
There is evidence to back the predictions, the DfT spokesman said, highlighting the reliability of HS1 - the high-speed link between London and the Channel Tunnel.
But HS2 Action Alliance argues that reliability will not be as good as predicted, again diminishing the projected benefits.