The two relevant points (leaving aside moral ones) are that:

the UK's population is rising fast, whereas Germany's is falling fast;

the dependency ratio (the proportion of expensive older people in the population relative to able-bodied, tax-generating workers) is rising much quicker in Germany than in the UK.

So to put it another way, it is arguably particularly useful to Germany to have an influx of young grateful families from Syria or elsewhere, who may well be keen to toil and strive to rebuild their lives and prove to their hosts that they are not a burden - in the way that successive immigrant waves have done all over the world (including Jews like my family in London's East End).

Here are the European Commission's projections from its Ageing Report that was published earlier this year.

It projects that Germany's population will shrink from 81.3 million in 2013 to 70.8 million in 2060, whereas the UK's will rise from 64.1 million to 80.1 million.

As you can see, what is striking is that the UK is set to become the EU's most populous country, ahead of Germany and France, as a result of a relatively high fertility rate and greater projected rates of net migration.

It is probably relevant that the Commission forecasts that the proportion of the German population in 2060 represented by migrants arriving after 2013 would be 9%, compared with 14% in the UK. So Germany would be a lot less multicultural than the UK.

As for the dependency ratio, the percentage of those 65 and over compared with those aged between 15 and 64, that is forecast to rise from 32% to a very high 59% in Germany by 2060.

Or to put it another way, by 2060 there will be fewer than two Germans under 65 to work and generate taxes to support each German over 65.

Because people are living longer more or less everywhere, the dependency ratio is also set to increase in the UK, but by less - from 27% to 43%. Which still represents a massive increase in the burden on the younger generation of supporting the old, but not as great as in Germany.

One way of seeing the impact of ageing is in differences in the relative burdens on the public finances of support required by older people.So in Germany, age-related spending on pensions, health and long-term care is expected to rise by a hefty five percentage points of GDP or national income by 2060, more than double the projected 2.3% increase anticipated for the UK.

Here is the thing. Wherever you stand in the debate on whether immigration is a good or bad thing - and most economists would argue that immigration promotes growth - right now immigration looks much more economically useful to Germany than to the UK.

That is perhaps one of the unspoken reasons why Germany is being much more welcoming to asylum seekers from Syria and elsewhere right now.

That said, some business leaders and a couple of Tory ministers gave me what can only be described as an off-message critique of David Cameron's approach to the migrant crisis over the weekend.

They said that Angela Merkel is creaming off the most economically useful of the asylum seekers, by taking those that have shown the gumption and initiative to risk life and limb by fleeing to Europe.

Precedent suggests they will be the ones that find work fastest and impose the least economic burden on Germany or any other host country.

By contrast, David Cameron appears to be doing what many would see as the more morally admirable thing - which is to go to the Syrian camps and invite children and the most vulnerable of refugees to Britain.

But this version of living up to what the prime minister calls our moral responsibilities is undeniably more expensive in the short term than giving a welcome to the able-bodied refugees already in Hungary, Greece or Italy, and desperate to come here.

(BBC)