Everyone is agreed on that. What is not clear is how these areas – particularly Glasgow and Edinburgh – are going to pull it off. They certainly can't do it on their own.
All recent studies argue that Edinburgh is better placed to take the lead. A strong private sector, high levels of entrepreneurship and a well-educated workforce are the factors that give cause for optimism that our capital city can quickly rebound from the disasters inflicted by the collapse of its banks.
Glasgow will have to struggle harder. The whole thrust of policy in the city is to create magnets for private-sector investment by sustaining expenditure on infrastructure. Significant sums have been spent on improving transport links, on building business parks, on cleaning up the sites contaminated by the wealth creation of the industrial revolution.
And the effort has paid off. The most recent example is Cambuslang Business Park, now supporting private-sector jobs on the site of Colville's steelworks. Thus, while cities such as Bristol have been losing private-sector jobs, over the past ten years Glasgow has gained 35,000 and increased private-sector employment by nearly 9 per cent – well above the UK average of 5 per cent.
Glasgow has not yet run out of steam. The M74 extension will further enhance transport links. Efforts are being made by Clyde Gateway in the east end of the city to ensure that the Commonwealth Games in 2014 will create the venues necessary for a spectacular sporting fortnight.
The same financial and intellectual investment will also ensure the completion of the facilities necessary for the enduring economic and social revival of this neglected part of Glasgow.
Speak to the city council and they will tell you this strategy is still working. They see a continuing strong demand for both office and industrial development, even at this stage of the economic cycle. There is no shortage of interested joint-venture partners.
The logic of this is that the first step to ensuring our cities can recover is to postpone cuts in public expenditure. But that's not how the parties' election programmes are shaping up.
So, if cuts inevitably follow the general election, then the buck passes to Holyrood. It is going to require a cold-blooded assessment of priorities if the correct decisions are to be made over how to allocate a smaller budget.
Growth has to be number one target, because it is out of growth that we fund all the other desirable objects of public expenditure. So the Scottish Executive should be looking to ring-fence local government investment expenditure.
This will call for exceptional bravery, as it will threaten the sacred cows of health and social services. But it is the only way of securing economic recovery and continued long-term funding for them.
The SNP's decision to drop plans for a rail link to Glasgow airport suggests they are not really thinking of cities in this way. But are they prepared to follow the logic of that decision and commit to making Edinburgh the airport for the Central Belt?
There doesn't seem to be a compelling reason – apart from local rivalry – to try to run the two in competition if the necessary connections are not there. As the market appears to be favouring Edinburgh, why not make the efficient choice and throw all the public effort behind it?
Policy-makers now recognise the concept of city regions as engines of economic growth. But this conversion has been too late for us to have a local government structure that reflects it.
The economic statistics for Glasgow quoted earlier include those for East Renfrewshire and East and West Dunbartonshire, clearly part of the Glasgow economy yet, administratively, lying outside the city. It does not make for joined-up thinking.
If cities are the answer, then the UK is fortunate to have one internationally powerful city, London. It is not a rival. Rather, Glasgow and Edinburgh should be gearing up to capitalise on London's growth. That means both excellent transport and communication links and strong political connections.
But as we are forced by the logic of city growth to argue for the public expenditure that will create the correct environment, we run up against the unanimity of all political parties vying with each other to list their manifestos of austerity. The policy conflict is obvious.
Certainly, under a Tory government the prospects for Glasgow are bleak. The Tories like cuts. The conventional wisdom that early and sustained reductions in public spending and debt are necessary chime precisely with their gut feeling that, whatever size it currently is, the public sector should be smaller. Doesn't mean they are bad people, just that they are bad people to be running the economy. But, to compete in these "responsibility" stakes, Labour and the Liberal Democrats have been seduced into staggering down the same path. They should turn for home. Because, if our cities are to avoid stagnation, the counter-arguments to the decimation of the public sector must be put.
They are sound and easy to make. Currently, the UK's ratio of debt to GNP is 81.7 per cent. Sounds high. But it is lower than Germany's 84.5, France's 85.4 and the United States' 93.6. As recently as last November, the IMF predicted that the UK's ratio of net interest payments to GNP for 2014 would be 1.6 per cent, while France's would be 3.2 and the US's 4.5.
Internationally, the UK is not out of line. Yet there is near panic among politicians over debt levels, an obsession that has led to the UK being the only G20 nation, apart from Argentina, to be fiscally tightening its belt this year.
Edinburgh and Glasgow and our other cities will contribute to, rather than hinder, the recovery only insofar as they can attract inward investment. Some must come from other parts of the UK and from Europe. Further afield, China must be a serious target.
Developing infrastructure, increasing skill levels and producing graduates in the relevant disciplines are essential as we compete in international markets. We must make our cities fit for this purpose by continued public expenditure. Room must be found in the public finances. It had better be. There is no Plan B.