I recently traveled to Exeter by train. There were 3 basically empty first class carriages and 3 standard carriages full with people. Why dont they cut the empty first class carriages and save money?
First class carriages do carry passengers at times. Clearly, in this case not so, but probably someone figures that there is money to be made out of having those seats and selling them some of the time, sufficient to cover the marginal cost of pulling along a few extra carriages.
My guess is that you saw a train at non-peak and that the same train, at peak, would have its first class carriages filled to at least a sufficient degree to cover their cost.
Some train operating companies (Chiltern, recently, IIRC) have decided that first-class sections aren’t the most profitable way to use the carriage space, and have done away with them entirely. It’s a tricky balancing act - one first-class open return can easily cost ten times an off-peak standard day ticket. So many empty first-class seats can still be profitable. However, the companies are also aware of the bad impression it gives to the majority of the public, to see all this empty space set by for a small elite.
The UK train service is pretty crap at the best of times. The cost of a standard ticket is extortionate - why pay the thieving fkers even more?
I would think most of the people in 1st class are on business expenses.
However, i dont travel by train that often. It is alwasy cheeper to drive ( unless you book weeks in advance ). Good system eh?
Sin
Business expenses are still income for the TOCs. And if first class isn’t available, some of them will choose to travel a different way - not because of the absent luxury, but because many of them want to have a table to work at during the journey, which is far less likely in standard class.
Do the sums properly (ie don’t just look at the cost of the petrol), and this is rarely the case.
Now try buying the cheapest ticket you can find that will allow you to travel between point A and B at the time you want to without visiting C,D,E and the remote parts of F. It will keep you delighted and entertained for days.
As someone who gets on trains a lot, I’m becoming an expert at this game. 
Ah, the old Routeing Guide!
Another answer, and one that still amazes me. We British seem to like being treated like cattle. Me? If I can’t find a seat in standard and the first class is empty then I push through the corridors jammed with bodies and cases, sit down and brazen it out with the ticket inspectors. Without fail they back down.
Back to the OP. Perhaps the simplest answer is that the first class carriages weren’t needed on that particular run but somewhere and somewhen else. You have to move them around somehow, and the easiest way is probably just to hook them up to an already scheduled train.
I know that empty freight cars are transported for this reason and empty trucks do the same thing. It’s called “deadheading.”
That used to be the case - but nearly every train in Britain now is in a semi-permanent coupled configuration. And in many cases, the first-class section is only half a carriage. It’s the opposite of the first-class seats actively being moved to a new location - there’s no way to not bring them along!
(Slight hijack - now that Virgin CrossCountry has got its new stock, are there any traditional loco-hauled passenger configurations remaining in regular use anywhere in the country?)
(Wait - make that except for the sleeper services, which still are)
Wow, when I’ve been in Britain and Europe, I’ve been unfailingly impressed with the amazing train systems - you get where you want to go for cheap and on time! How wonderful! You guys are so spoiled.
Except that one time when it was all of, what, 86 F? And you all thought the blistering heat was going to warp the rails? WTF? 86 is a lovely spring day here. What exactly are you making your rails out of? We were an hour late coming into London because the train started going real slow, just in case. :rolleyes:
Then I don’t understand the OP’s question at all. It was clear that six carriages were involved, three first class, three standard. No halfsies.
If there’s no way not to bring them along, how can there be a question of why they are there? 
Even if it’s three-and-three, they’re still a single six-car unit - there’s no way of driving them except at one end. More like American subway trains than mainline ones. The question was asking why they designate so much of a fixed-length train as first-class, when it seems that there’s insufficient capacity for standard-class.
Trouble was, over the past couple of decades, they made all the knowledgeable seasoned rail-workers redundant, and replaced them with accountants. So nobody working on the railways knew how different sections of track would behave in unusually warm weather (which is what it was, for Britain). Plus that they’re erring on the side of over-cautious, given the recent history of bad safety and maintanence errors.
OK, I plead to being American. 
But can’t I at least gripe about the use of the “cut” instead of “convert” in the OP? :mad:
Kind of…it could imply convert 
I have been informed that if you hold a normal ticket, you can sit in first class if there are no other seats available - but you have to move if the conductor finds you a seat (perhaps later, when the train has emptied somewhat).
That might be a policy of individual TOCs, to accomodate the Conditions of Carriage:
(My bolding) - you don’t have an automatic right to settle down in First Class.
I agree. The trains in the UK are much cleaner, more comfortable, faster, and more frequent than they are in Australia. They cost a bit more (but not that much more) but I think you are really lucky in the UK.