What are the benefits and costs of a diverse population? How should a liberal democracy define the limits of multiculturalism? In answering these questions, the high-income countries will also define what kind of society they wish to be in the 21st century.

As the World Bank's latest Economic Prospects report makes clear, the pressure for migration from poor to rich countries is a permanent feature of our integrating world. The share of migrants in the populations of the high-income countries rose from 4.4 per cent in 1960 to 11.4 per cent in 2005. It seems certain to rise still further, given both demographic trends and the persistent gaps in incomes and wages between developing and high-income countries.

A vigorous and often ill-tempered debate has opened over the consequences of this movement of people. In a thought-provoking new book, Philippe Legrain, the British author of Open World, a splendid work on globalisation, takes a bold position: let them all in. More precisely he says: “It would be best if our borders were completely open. But if that is deemed impossible for now, let them at least be more open. And if even that is not acceptable, let them at least be better regulated.”

Mr Legrain performs an invaluable service: he makes a good case for the unpopular cause of free flows of people. The book is a superb combination of direct reportage with detailed analysis of the evidence.

What I find missing, however, is analysis of what might happen if no restrictions were indeed placed on the movement of people. Basic theory suggests that the flow of migrants to a place where there is a chance of obtaining a far better income might continue until the wages to which the migrants aspire have fallen to the same level as at home (after adjustment for the costs both of moving and of living). Alternatively, it would continue until the condition of many of them has become even worse than at home. We would then see in the developed world what we see in developing countries: vast slums.

No high-income country is going to allow this to happen. For this reason some controls will remain in place. Moreover, such controls are effective, even if porous. The gaps in wages across the globe to which Mr Legrain points in arguing the economic benefits of free flows also demonstrate the efficacy of controls. Making migration both costly and unpleasant works. But those costs are indeed enormous, as is always the case when market forces are driven underground.