I'm thinking of countries with economic and social policies like Germany. We can easily observe that in most developed countries, the birth rates are dipping (surprisingly). To my understanding, it is the young who are working (and hence highly taxed) keeping the system afloat.
Suppose there is some point in the future where the age pyramid flips, that is old people become a majority; then, what type of policies and checks do countries and states such as these have to deal with such scenarios?
Lots of countries are facing the challenge of an aging population. Basically the whole northern hemisphere does (with some exceptions, the most notable one being India). The only regions of the world where the population is still growing are sub-Saharan Africa and the middle east.
Possible measures to mitigate the problem are:
Most countries which face this problem use a mix of these techniques.
Change the tax system from labor to production
Along with an aging population, productivity is rising in many sectors, and the productivity increase is often outstripping the wage (and hence income tax) increases. Many proposals for a robot tax aim at preserving human employment, but they might just as well fund the welfare and retirement system. The German term is Wertschöpfungsabgabe, or value creation tax, a term very similar to VAT.
Thinking about this problem in terms of taxation and welfare is something of a red herring; the problems occur regardless of the fiscal structure. Retirement is not about redistributing money but about redistributing production. Or, as user3067860 pointed out in the comments, sometimes output of production.
For everything a retired (or a working) person buys, somebody has to put in a corresponding number of hours of work, to produce it, distribute it, etc. When you have fewer working and more retired people, you have fewer hours of work available. Worse, you need most of those hours of work at nearly the same time the demand is there (you can't bake bread 20 years in advance!)
Importantly, this is true regardless of how the retirees pay for goods or services.
The underlying mechanism how this comes about varies. If you are using a US/German-style Social Security system, you simply have too few people paying in to pay out benefits.
If you rely on stock investments, you have too few working people buying stocks and too many retired people selling stocks, leading to a drop in stock values at the exact time the stocks are needed.
If you rely on plain savings, the same problem would come about through inflation.
Thus, the demographics problem cannot be addressed by shifting how people provide for their retirements.
There are several approaches to solving this issue, but each one of them tends to have problems of its own. That's why the demographic pyramid leads to such passionate political debates.
This can be done through increasing the birth rate, or through immigration. Increasing the birth rate is notoriously difficult, has a 20-year lag time, and many people feel that it has undesirable environmental consequences. Immigration tends to be politically problematic, and can negatively affect the source countries (brain drain).
This is something most of the affected countries are doing on a large scale right now, but it only works due to huge wealth disparities between countries.
This would usually mean, more automation. Aside from the increased energy use this would usually entail, this is probably the most long-term sustainable approach.
This is of course not a real solution. It means returning to a society with widespread poverty in old age.
Another approach we are currently taking. It reduces the productivity of young family members dramatically, and really shifts the burden from all young people to a relatively few of them.
Update: one important approach I forgot:
Welfare is a rather broad term, as it includes income redistribution between high and low earners, helpt to handicapped, families with many children, etc.
Retirement benefits in many western countries are indeed based on the assumption of growing population (or at least non-decreasing population). A retired person of 60+ years old has their child (40+) and their grand child (20+) working and paying for their retirement, so that the income of two people is divided among three to guarantee everyone same level of life by giving away a third of their salary. If the population were doubling with every generation, we would have 6 earners (2 children and 4 grandchildren) working to support 7 people, that is the burden of the system would be much lower. (It is for this reason that some of the critics of retirement benefits refer to it as a Ponzi scheme - it depends on constant recruitment of new contributors. While there is some logic to this, the term is obviously charged.)
This system is already under strain in the last couple of decades, as the birth rates have been decreasing ever since the baby boom, and the baby boomers generation is retiring.
There are some possible adjustments (as briefly mentioned in the answer by @Philipp), the principled of which are:
Raising the retirement age
A glaring fact is that when the system was put in palce in many western countries, the retirement age was about the same as life expectancy. You may see that I cheated in the calculation given in the beginning, as I implicitly assumed that the retired person would live at least 20 years, till their children retire and take their place. In fact, if the retirement lasts less then a whole generation, the younger people needs to contribute even less than my simplistic calculation suggested. Thus, increasing life span in the western world puts as much strain on the system as the decreasing birth rates. E.g., the retirement age in France is 62, given the current life expectancy of 80+ - that is retirement does last a generation.
Raising the retirement age is an obvious adjustment, as most people at 60-70 today are in rather good physical shape to work and contribute to the social welfare. But this solution is obviously unpopular with those approaching retirement, who are effectively told to work for 5-10 years more than they expected. Fixing retirement age to the life expectancy (just as the welfare benefits or poverty income are fixed to the spending basket) could be a more subtle way to do it... but it also appears to be too radical a change to be seriously contemplated.
Immigration
The population decrease actually happens only in developed western countries, whereas the world population continues growing very fast. Allowing more young immigrants may alleviate problem - both because they are gainfully employed (substituting for the non-existent children), but also because they come from different cultures, where the birth rates may be not as low. (Contrary to the claims that immigrants and their chidlren rely on welfare and thus expand the national resources.) This is arguably one of the main reasons why most developed countries do allow constant influx of immigrants, despite the unpopularity of this in some quarters.
Similar to how an individual can plan for retirement when one is young by saving up a portion of one's paycheck and investing it or saving it, a welfare state must save up a portion of everyone's paycheck starting at a young age, and the state can invest it.
All the money that is saved can be invested in ETFs, mutual funds, lent out with interest, or otherwise invested in something.
Imagine 20% of everyone's salary for decades has been put towards a savings fund for everyone's retirement. By the time the population has aged, there would be a cushion of saved wealth the aged population can rely on even though the country isn't generating new wealth.
Consider the following diagram that demonstrates the powerful effect of a single individual increasing savings by just 1% at a young age:
This is a short term issue, and would need a short term solution. For example: reducing retirement benefits, raising retirement age, etc.
As Philipp♦ mentioned, living a family lifestyle/pronatalism can help.
I'm surprised nobody has mentioned Hungary. They essentially encourage families to have more children by offering tax breaks.
I'm thinking of countries with economic and social policies like Germany.
Germany has been cutting back on welfare arrangements for decades now - like other EU kinda-social-democracies. But ok.
We can easily observe that in most developed countries, the birth rates are dipping (surprisingly).
Not surprising at all actually.
To my understanding, it is the young who are working (and hence highly taxed) keeping the system afloat.
While the young do more work than the older, people do many kinds of work, and important non-work activities, until a much later age than, say, the median.
But regardless of that - in most countries, wage distribution is skewed, so that the majority make (relatively) low wages and pay less tax, in both absolute and percentile terms, and an increasingly small minority pay increase larger amounts and fractions of tax, personally. This what it looks like in Germany (or looked like in 2008 anyway): the top 30% pay nearly 80% of all income tax.
In terms of age - young workers typically earn the lower wages and pay less tax per capita and per EUR earned than older workers.
No less important is the question of what gets taxed, which others have mentioned. Why should the majority of state income be tax on labor? Why not the tax on corporate profits? Or on existing capital/wealth? If the former is the case, that is because of the relative weakness of the working class vis-a-vis capital.
then, what type of policies and checks do countries and states such as these have to deal with such scenarios?
In itself, that's no trouble whatsoever. After all, productivity has increased tremendously over past years, and workers are made more redundant and obsolete with every passing day - with automation (e.g. think of driving, postal work, sales in shops and markets etc). So, instead of there being wider unemployment among the young, there will be more work, in relative terms, for them to take care of, with the elderly part of the population working less; plus care-giving. (Although TBH care-giving for the elderly is a real pain in the ass past the point of senility / inability to move; but never mind that.)
So, why is this a problem? Because of the problems with distribution of work, planning of production / services, and the distribution of products and services. To describe it vulgarly and simplistically: If the old rich people hog the power and resources, then the retirement benefits afforded to regular working people will be insufficient; there will not be enough demand for products and services to gainfully employ the young; and it will mostly be the needs of the rich minority which are met.
Naturally reality is somewhat more nuanced and there are a bunch of other factors. But still, this is only a problem to the extent capitalist societies - albeit with welfare state measures - like Germany, make it a problem.
The solutions have always been there:
E.g. the concept of extended family as robust business unit.
Extended family is a microcosm, where needs and burdens are traceable and so controllable and so can be optimized towards independence from public registers, which would be essentially relieved.
In macrocosm we have the concept of a thin state: less taxes, self-organization, private education, ...
Living example are the Amish: They are rich, they own land, they understand, that we live from the things that grow and cannot eat money. So they don't fear inflation and surprisingly they overcame recent epidemics.
Seems like centralized attempts for balancing material needs are more cause than solution of problems on political scale; the aspect demography appears more as indicator of man made problems than being a problem.
Conclusion: The welfare state as central facility won't survive inside a democratic foundation; all historic examples with central welfare facility since industrialization were socialist from the beginning or turned into such.
