Costs have risen; the question is whether they would have risen anyway. I don't know how you could prove that they wouldn't, and therefore this is an assumption, and one that I don't necessarily fully agree with.
The majority of this was addressed in the McNulty report. Costs have risen for a number of reasons, from above inflation pay rises, to the Hatfield effect, the bankruptcy of Railtrack and the financing of NR, from fragmentation and over specification, to over regulation and inefficient supplies and labour markets.
http://assets.dft.gov.uk/publicatio...ealising-the-potential-of-gb-rail-summary.pdf
I feel pretty certain that both power and staff costs, at the least, would also have risen under BR.
Power costs make up a relatively small proportion of overall costs to the industry. As for labour costs, it is highly doubtful they would have risen so fast. The labour market is highly unionised and has fully exploited either skill shortages, or the fragmentation of the industry. It has been able to gain above inflation pay rises because it is a specialised market, with a highly restrictive input. None of this was properly anticipated for or evaluated during privatisation.
Also a doubling of passengers does not necessarily mean a lowering of unit cost. That's another assumption. There are plenty of examples where size has led to inefficiencies, or
diseconomies of scale.
No, but under normal circumstances increased ridership does lead to less call on the public purse. You only have to look at the late 1980s boom in passenger numbers under British Rail and the consequential falling subsidy.
I accept the privatised train companies could have chosen a form of operation that is not especially cost effective, it terms of service pattern, interfaces, or delivery, and this is somewhat addressed in the McNulty report too.
However, the wider question is why has private industry failed to deliver significant cost benefits over a supposedly inefficient nationalised model. I think there are a number of reasons for this, the most significant being public service obligations cannot be squared with the desire to make a profit, and consequently over regulation (demanded by the public and politicians) leads to further erosion of that position. The question of moral hazard within the industry, and lack of truly open supplies, labour and management markets is another problem.
It's not to say another model of privatisation could not have delivered more. Nevertheless, my point stands that in financial terms for the tax payer and fare payer, the current model to date has not been a good deal and a lot of money has been wasted. This is almost universally agreed by economists, transport commentators and academics.