What is the definition of capitalism? Is it compatible with people owning the things they produce?

I know I am doing your homework here

The reason I am posting this anyway is that I hope you'll learn something from it. Please read it and try to understand it.

The first thing to say here is that capitalism/communism is not a binary thing at all, even though many people (especially from the US) seem to believe.

Instead, there is a whole spectrum between pure capitalism and pure communism. In fact, there has never been any large-scale real-world implementation of either pure capitalism or pure communism.

But let's start with definitions.

Pure capitalism

In a pure capitalistic system, the state basically doesn't exist. This is often called anarchocapitalism, because for pure capitalism to exist, you also need an absence of government => anarchism.

In such a system there is no regulation, no taxes, none of the basic services are provided by a government. Instead, money is king. In pure capitalism money doesn't equal power, it is the only power. There is only a completely free market as the only mechanism that is supposed to balance anything out.

Pure communism

In a pure communist system, there is no private sector and even no private property. The whole power lies solely with the state, money has no meaning. For the state to be able to really govern everything that a capitalist system does with money, it pretty much needs full control over everything.

Why can pure capitalism not work?

In a pure capitalist system, if you have more money, you have more power, which makes it easier to gain more money, and with more money comes more power and so on. Without any regulation the free market is unstable and tends towards monopolies. Basically, once you gain an advantage over your competitors, you can use your money to suppress or buy out your competitors until there are none left. If anyone tries to enter your market segment, you just buy them out or e.g. buy their suppliers. (Google Standard Oil for a good example.)

So for the free market to work, you need to have regulation.

The other side here is that in a completely free market, employers have ample options to exploit their employees. Until they band together, strike/revolt/start a revolution, and make sure that the free market isn't as free any more, meaning that they get treated fairly and get a bigger share.

Why does pure communism not work?

Well, even the Sowjet Union wasn't a pure communistic system. There is some level of personal property that people need to have as an incentive to work. If it doesn't matter what you do at work and you always get the same reward, no matter whether you even show up for work, then your system will also fall apart.

What exists between capitalism and communism?

There's a massive spectrum in between. There are countries that are quite capitalist, like the US. Here you have a mostly capitalist system, but basic services are still provided by the state.

There is social market economy, like many European countries are using. Here you have state-owned companies in all important sectors, that have to compete with private companies. More than just the basic needs are covered by the state.

And then you have something like the UDSSR, which is mostly communist, but you are still allowed to have some private property.

Back to your questions: Since your answer above likely included the word “capital”, what is capital?

Capital is any kind of property belonging to persons, that can be used to influence the behaviour of others by trading. Money, companies, stocks, real estate, basically anything that can be sold. Depending on the specific system, even humans.

How does capitalism empower people to own what they produce? Or, how does capitalism strip people of their control over what they produce?

The question really misses the point. If you have the capital, it the product will belong to you. If you don't, it won't.

Say you are an individual who sells something you create. Are you a capitalist?

Again, misses the point. If you are a slave who produces something and then has the task to sell it for your master, you definitely aren't a capitalist.

If you are the master, who doesn't produce and doesn't sell, but earn from the work of others, then you are a capitalist.

If you are the above person, can you exist in both capitalist society and one in which private property has been abolished?

False dichotomy. Neither a pure capitalst nor a pure communist society exists.

Say you create and sell some product regularly (as above), but have more orders than you can fulfill alone. Is there any way to expand your operation and meet demand without using capitalist methods (such as hiring wage workers or selling your recipes / process to local franchisees for a cut of their proceeds, etc)?

Again, false dichotomy. Cooperation also exists in a communist-oriented (or even a theoretical pure communist) system.

And actually, even in a capitalist-oriented system you don't have to use any of these methods. You can just cooperate with others on a same level. E.g. I build X to sell. I could ask someone to join and that person could run their own business side-by-side doing the same thing. We wouldn't need to have a business partnership at all. Both independently build and sell. Of course, that would mean that I'd have no control over the other guy and I don't earn money from their work. But there's no law telling me I have to.

Is the distinction between a worker cooperative and a more traditional business important? Why is the distinction important?

Yes, google it yourself.___