Orsdxy

We keep hearing a lot about economical growth in the media and this answer shows us why it is so important:

Therefore, we have three options:

• A constant increase in unemployment. (Generally feared and loathed.)


• Less time at work per person. (Sometimes impractical. Wastes
  educational resources as people would still have to study and train
  just as much only to produce less. Might reduce people's earnings,
  etc.)


• Constant economic growth to create new jobs and counteract the
  reduced need for manpower caused by technological advancement.

The third option is generally preferred by policymakers, academics, the

public, etc. for the reasons described above, as well as other
reasons.

However, constant economic growth within a planet having finite resources is not possible (it is not sustainable):

Capitalism requires a constantly expanding production and consumption
of goods, which can only be achieved through the increased
exploitation of the planet’s natural resources at an unsustainable
rate. Because of this reality, sustainable development cannot be
achieved without a dramatic reduction in the levels of production and
consumption, which directly contradicts the growth logic that drives
capitalism.

So, I am wondering if how capitalism can deal with this? What if we reach the limits of the environment and economic growth is no longer possible?

Not all parts of the economy consume finite resources equally. In fact, only a minor portion of it is related to the manufacturing of goods. Most of the economy is services by now and, even more related to your question, most of the growth is growth in services.

Manufacturing is on the decline while capitalism thrives.

Source

Growth is growth in services.

Source

In fact, there is plenty potential for services to grow even more. For example, if you live in a western country and you get older, you wish there were more service workers tending to elder people available.

And services are very friendly on the environment. Just an example: Being an Instagram influencer is a very eco-friendly job consuming comparably only few of the finite resources.

Also, some resources are renewable: food, energy, recycled materials (to some extent), wood, .... With regard to manufacturing and production there certainly is a desire to use existing resources as efficiently as possible with this kind of optimization still ongoing.

Yes, saving the planet mostly probably will mean not using more (rather less) of the resources, but that won't be the downfall of capitalism at all. If I would be worried about capitalism, I would worry about ongoing trends in artificial intelligence and automation.

Capitalism's answer is global crisis, which weakens world economic powers and redistributes resources consuming. Crisis may be either peaceful - like Great depression in the US, or non-peaceful - like WWI, for example - when growing economic powers - German block tried to overpower existing economic powers - western world mainly.
So, in fact, there is no such problem in capitalism - its decision is stored inside.

About "growth in services economics, which is unlimited".Let's consider, why it is naive.
The process itself is very good described in @Trillarion answer. Answer describes so-called "post-industrial" economics.

What's wrong with it?

At first, should notice, that graphics (services percent) are true, but for VERY special countries from western world, which have such huge services sector (US and UK are most known). You may look at the second graph. We now, that main part of UK GDP is formed by banking sector and services. From the first view, it sounds good - it is a pure service sector, we are just servicing our and foreign banks money, giving credits, so on.

BUT. of course, there is 'but'.) Financial sector cannot live in a vacuum. When it grows too much over REAL sector, we obtain a financial bubble. It may be a big amount of credits, an exchange bubble, or something else, but what we have? We have an economic sector which growth, in fact, is a fake.

Bright example - Brexit. You may, again, look at the second graph from @Trilarion answer. UK have a huge financial sector (result of M. Tatcher politics of 'de-industrializing'). What Brexit means? It means (and Deutsche Bank already have done it), that EU banks will stop to use UK bank services, because of UK is exiting, and retrieve their finances from UK back to homeland. How do you think, this will affect UK bank sector (and, as it is huge, huge part of economics)? It will collapse. You may say - but what's the difference between EU and UK, if both have a financial sector and banks? Yes, both have, but EU do have a big REAL sector (which can be an investment target to the banks, and supports it) and UK does not.

To conclude. That theory - about constant growth, provided with services constant growth - is applicable in a one-hegemony-world, which is globalised. While hegemonic growth its services, which is consumed by others, others, in return, provide something REAL. Bright example is 'late-Washington' world - before Russian comeback to global powers. But now, as world become multi-polar again, this is not more than a pure theory.