If the age of irresponsibility is yielding to the age of austerity, it is not clear that the political class has understood yet. Gordon Brown and David Cameron both made a claim to providence and prudence in their conference speeches.

The rhetoric would have been more persuasive had they not both followed up with further spending commitments. Mr Brown offered free nursery places for two-year-olds and free health checks for everyone over 40. Mr Cameron is now a hostage to health service inflation and strong claims on the Armed Forces. The political class needs to accept that these are promises that will not be redeemed. The state of the public finances will not allow it. For all the serious tone of the conference season, the politics has not caught up yet with the economics.

There is no definitive answer to how much public spending is affordable. But as Chancellor, Mr Brown was wont to argue that reducing public sector debt translated to lower long-term interest rates and faster growth. His fiscal rules were a commendable attempt to codify this principle. As things now stand, the growth of public borrowing puts economic stability at risk.

Economic growth is already sluggish. This is taking its toll of VAT and corporation tax receipts. Housing transactions have all but frozen. Prices are falling dramatically, depleting stamp duty receipts. Unemployment is rising, further depleting revenues and increasing the benefits bill. At the same time, general government spending over the first five months of 2008-09 was 6.4 per cent higher than in the same period a year earlier, against a Budget forecast of 5.3 per cent.

The Chancellor appears sanguine, without justification, about the need to borrow more. It is obvious that, short of alchemy, the golden rule is defunct. Now that the Northern Rock debt is included in public sector, net debt has reached 43.3 per cent of GDP. It will get higher yet.

Each 1 per cent shortfall in the economy below the official forecast reduces tax revenues by about 0.7 per cent of gross domestic product. On GDP of £1,500 billion, borrowing rises by about £10 billion for every 1 per cent of lost output.

Economists are arguing over the size of the debt figure. There is, as ever, a dispute about how bad it might be, but the consensus is that it will be very bad indeed. The risk is that the shortfall in tax receipts will be wider than forecast, as corporate profitability is being squeezed. The banking sector, most obviously, is set for significant losses. Moreover, there is persistent upward pressure on public spending. The rise in unemployment is only the most visible sign of expanding state benefits. Added to that, public debt will be aggravated by rising inflation. Benefits are pegged to the retail price index each September: the August inflation figure was an annual rate of 4.8 per cent, well above the Government's target.

Furthermore, there are the financial consequences of the Government's own mistargeted interventions to consider: compensating those who were disadvantaged by abolition of the 10p tax rate, and paying for the suspension of stamp duty. The cost of rectifying the 10p tax fiasco is estimated officially at £2.7 billion, while the stamp duty measure will cost £600 million.

The Institute for Fiscal Studies says borrowing in 2010-11 will be £60 billion, at least. The Centre for Economics and Business Research has forecast £90 billion for 2009-10. Citibank is offering £95 billion in 2010-11 and Capital Economics suggests the deficit will reach £100 billion. Only the Treasury stands apart. Its forecast is £32 billion.

The Government faces an uncomfortable but brutal fact. Either tax rates will have to rise or else public spending will have to be reined back. The Chancellor may decide to borrow the dilemma away - which is where the problem started.