In this bold experiment, the stick is as important as the carrot

Will more money fix things? And can he afford it anyway?

These two huge questions overshadow the Chancellor's spending plans. Gordon Brown is well aware of the dangers of not getting value for money, hence the emphasis on reviews and audits, the replacement of failing public service managers and local authorities – the general bossiness of tone. He seemed less aware of the way in which a slowing world economy is likely to cut back his revenues, and the danger that these plans might either have to be scaled back or lead to substantial increases in tax rates.

Take the "can he afford it?" first, for it was, after all, the day on which the FTSE 100 share index fell below 4,000, a 14 per cent decline in just six days. The markets are running scared. They are scared more by a possible deteriorating world financial outlook than anything to do with Mr Brown, but they are scared none the less.

Some numbers. Government spending is planned to rise in real terms by 3.25 per cent a year through to the end of these plans. There is no way our economy will grow that fast, for trend growth at best is 2.75 per cent. In the Budget the central point of the growth forecast for this year was 2.25 per cent and next year 3.25 per cent. The consensus of economic forecasters is 1.8 per cent and 3.0 per cent. So if you believe the Treasury, spending will grow a bit faster than output; if you believe the consensus it will grow much faster than output.

It is worse than that. Both the spending and the tax side of the budget are geared to the economy. Spending rises faster in periods of slow growth because, amongst other things, of higher unemployment. Taxation rises more slowly, as company profits fall and there are lower receipts from things like capital gains tax and stamp duty. Suddenly, the wonderful virtuous circle of the strong economy flips into the vicious spiral of a weaker one.

Gordon Brown knows nothing of this, for he has only been a Chancellor in good times. He used the boom to strengthen public finances and deserves a cheer for that. Lower interest charges and relatively low national debt are a great help. But he inherited a competitive economy in a world boom. We still have a competitive economy, but whatever the warnings the markets are trying to signal we are unlikely to have much of a boom over the next four years.

He may just get away with it, but the balance of probability is not. When, faced with the choice of higher borrowing, higher taxes or cuts in public spending, which will he choose? One of Mr Brown's two big tests – or that of his successor – comes then.

The other test is whether these plans will deliver value for money. In a way, given political realities, he had no alternative but to give public services a sharp increase in funding. We all want better services. Squeeze the public sector and it has an excuse for poor performance, for it is very difficult to improve services if resources are being cut back. Give it the money and you take away the excuse. I understand that the Chancellor has considerable doubts about the ability of some parts of the government machine to reform, which is why there was all that emphasis on performance targets and independent auditing. If UK Government Ltd is being given a carrot, it is also being threatened with a stick.

These spending plans are often characterised as "Gordon's big gamble". There is an element of a gamble, to be sure, for it will be very hard to sustain increased spending on this scale in a difficult world economic environment. But more than a gamble, it is an experiment. It is an experiment in public-sector management: whether, given adequate funding and the right auditing controls, the UK public sector can manage to lift its game enough to make Britons feel we are getting good value for our taxes.

It is an experiment as radical, in its way, as the Thatcher experiment of cutting taxation to encourage entrepreneurs, and pushing responsibility away from the state to the family.

Our problems with public services are far from unique. Everywhere state services are under pressure and most of Continental Europe is now cutting back the role of the state. The question for us is: Can our 1950s model, substantially updated, still be made to work? If, in three or four years' time, education standards have improved further, health care is significantly better and police reforms have helped cut crime, then Gordon Brown will have won.

If not, then other governments, perhaps here but more likely in other developed countries, will have to figure out other ways of ensuring that all citizens have access to good services – and rethink the state's role in making sure that that happens.