Hamish McRae: Twilight is falling on the Treasury, and Brown's successor may have that morning-after feeling

So welcome, Mr Straw (or Mr Clarke or maybe Ms Hewitt), to your new job. Gordon will be a hard act to follow, for he is on the face of it the most successful Chancellor ever. He has, after all, presided over the longest-ever period of uninterrupted growth in the British economy, as he irritatingly reminds people from time to time. But then he did inherit Europe's fastest-growing large economy, already in 1997 four years into its long boom. Your own legacy is not quite so glittering - better than that of most chancellors for the past half-century but with some disturbing features you will now have to tackle.

So welcome, Mr Straw (or Mr Clarke or maybe Ms Hewitt), to your new job. Gordon will be a hard act to follow, for he is on the face of it the most successful Chancellor ever. He has, after all, presided over the longest-ever period of uninterrupted growth in the British economy, as he irritatingly reminds people from time to time. But then he did inherit Europe's fastest-growing large economy, already in 1997 four years into its long boom. Your own legacy is not quite so glittering - better than that of most chancellors for the past half-century but with some disturbing features you will now have to tackle.

None of us know when the hand-over of economic stewardship will take place, or the circumstances under which it will happen, and still less who will move into the post. It is conceivable that it will be the Opposition's Oliver Letwin, rather than any of the above, who will take over the job, although that scenario feels to me to be three to five years away rather than one. But whether or not Tony Blair goes before the election, we are into the twilight of Gordon Brown's chancellorship. He may produce one more Budget but that is it. It is time to look forward. What will be the five biggest issues on the new chancellor's agenda?

The first is the most obvious: what to do about the public sector deficit. The deficit in 2004-05 is projected to come back down under 3 per cent of GDP and stay there, but that is on the assumption that the tax take will be very strong right through to 2009. As you can see from the first graph above, the Treasury expects taxes to rise as a proportion of GDP to the highest level for 20 years. Yet the experience of the past three years is that taxes come in well below estimates. Of course, the new chancellor can always butt up tax rates, but there are two economic objections to that - aside from the obvious political ones.

One is that a sharp rise in tax rates would clobber growth. The other is that increases in rates might bring in less tax, not more. Neither is easy to test in advance. It would be nice to be able to pop the figures into an econometric model and see what will happen. Such models do exist. The trouble is they give the wrong answers. There are long time lapses between changes in taxation and economic performance: the growth burst of the late 1990s may have had its genesis in the tax changes of the 1980s. And if the Treasury cannot predict revenues a year in advance on the basis of virtually no tax changes, it is hard to have any confidence in the estimates of revenue from big ones.

Part of Labour's problem has been the tough business conditions since 2000. These have cut company tax revenues, while the fall in share prices has cut capital gains tax receipts. Will share prices rise under another Labour government? Not if you look at the record. A slightly naughty pamphlet has just come out from the Centre for Policy Studies. It argues that Labour policies are bad for markets (see the right-hand graph). The next chancellor should at least ponder this one.

Issue number two is the efficiency of the public sector. On paper there has been a collapse in public sector productivity under this Government. Roughly 80 per cent of the additional funds put into public services has been absorbed in higher costs and only 20 per cent has gone into improving services. The figures may exaggerate the problem, but the Government is sufficiently disturbed to be putting a lot of effort into finding out what has gone wrong. Independent studies of public sector efficiency rate Britain below many other developed countries: we are not at the bottom but we are well below the US, Japan and several EU members too.

The new chancellor will have to tackle this; the success or failure of the next government may well turn on whether it can lift the performance of the public sector. There will not be much additional money, even if there are tax increases, so getting more output from the same input will be the game. This is not an easy task.

Issue number three will be the world economic background. The global economic recovery seems secure but it relies on demand from two countries, the US and China, to keep going. So if anything goes wrong in either country, there will be trouble. None of us is clever enough to predict when the next global downturn will occur. What the new chancellor will need to do is put UK public finances on a sound basis so that the country is in a stronger position to offset any global shortfall in demand.

That in turn leads to issue four: relations with continental Europe. The UK was very successful in managing its way though the last downturn, thanks to having started with a sound fiscal position and, in particular, to having control of its own interest rates. We were able to boost domestic demand by cutting rates and then start to raise them before either the US or the eurozone. After that early decision by Mr Brown, rates are set by the Bank of England, so are no longer a matter for the Treasury. But they are set in the UK, for the UK. Were Britain to adopt the euro, that would not be the case.

At the moment it seems inconceivable that Britain could enter the euro in the life of the next parliament. In economic terms, staying out for now must be the right decision. But it would be unwise for a new chancellor to take an anti-European stance. The EU remains a large market and the new members who joined this weekend will give it a vitality that has been lacking in the past few years. So the next chancellor needs to continue his predecessor's balancing act. Trouble is, that may be more difficult in the future if European economic performance continues to disappoint.

Finally, there is another issue Mr Brown has sought to tackle that will demand the attention of his successor. Nationally there has been some modest progress in cutting inequality, or at least, measured in financial terms, in lifting the position of some of the most disadvantaged. But inequality is not just a problem of different levels of income, which can be tackled by redistribution to some extent. It is also a question of different levels of opportunity: why does such a range of income exist in the first place?

The response of the present Chancellor has been to have lots of little initiatives. But this has hugely complicated the tax and benefits system and may now be self-defeating. So a final plea: whatever else he or she does, please keep it simple.

Endangered museums deserve a bigger bite of public funds

May is Museum Month. The idea is to have a series of special events and activities, some of which will carry on into the half-term week at the beginning of June. The main point of the campaign is that the museums feel they have been treated as the poor relations of the arts world in terms of funding, and want to highlight what they are doing for education and culture.

The museums make a powerful case. An interesting report, Valuing Museums, by Tony Travers of the London School of Economics and Stephen Glaister of Imperial College London, puts some numbers on the business and its contribution to the economy. Turnover at the main museums is £715m, but the overall economic impact is around £2bn. Invisible exports are £320m a year - six out of the top 10 visitor attractions in Britain are museums. And 8.6 million people took part in some kind of learning activity run by the museums in 2002.

Yet public money is tight, with grants rising only in line with the retail price index, unlike average earnings and public spending. Over the next two years the museums will get just 5.2 per cent of public funding, while government spending as a whole is scheduled to rise by nearly 14 per cent.

A lot of us have some reservations about the wisdom with which public funds in general are spent, as noted above. Further, as the universities have discovered, putting pressure on organisations' finances does force them both to increase their productivity and to be innovative in finding new sources of revenue. But like the universities, much of the costs are in salaries and these inevitably rise faster than inflation. And again like the universities, if the museums are squeezed too hard for too long, they have to trim their service. If their contribution to education does not convince the Treasury of the case for more generous funding, maybe the invisible earnings will. At any rate I shall pop something more into the box next time I visit a museum.