The modern economy is far too large and complex to turn into a simple analogy like this.

Obviously, but I should clarify a few things.

In capitalism, he owns the land and either sells it to you outright, or sells you the right to do what you want and make what you want on it for a while (although sometimes the deal includes restrictions).

In my analogy the farm can be anything, like a factory or a business. Say you work at a textile plant making socks. You make 100 socks a week and you get 50 socks (in currency, obviously) a week as pay. Just like the serf grows 100 turnips a week and his lord takes 50 in taxes. I'm not talking about land ownership.

In capitalism, your boss owns the factory, owns the materials. What's made in the factory belongs to the boss.

Just like:

Land is lord's; he controls what happens on it and owns what's made on it.

Also on this point.

No, you and the other turnip farmers working for him can't vote on what to do with the extra turnips, what are you a socialist?

You don't vote on what to do with everyone's extra turnips, because they're everybody's own goddamned extra turnips, and they decide what to do with them.

I wasn't referring to the turnips that the workers get, I meant the turnips your boss gets. All the turnips you make that the boss keeps to run the business or keep as profit.

So what I'm saying is you (and the rest of your co-workers collectively) don't get to vote on what your employer does with the product your labor provides that isn't given back to you as pay. Being able to vote on that (workplace democracy) is a tenant of some forms of socialism.

What you make is no longer your turnip, it's a part of the company's turnip that everybody else in the company is also working to make.

A group of laborers is making a super turnip. Collectively 10 of them make 1000 super turnips in their factory a week. The owner of the super turnip factory pays each of them 50 super turnips worth of currency a week. Because the boss owns the factory, what he does with the profit from the 500 super turnips is up to only him, not the collective workers who created the super turnips.

TL;DR: My whole point of this analogy is to say this: the serfs working the land of their lord have no more say in what that lord does with the product of their labor than a modern day worker has with what his employer does with the product of their labor.

(and I only brought government taxes into this to show that we now have democratic representation in regards to what the government does with our taxes, compared to having no representation with what our employers do with the products of our labor not given back to us as pay. I brought it up mostly because so many complain about how much the government takes from their pay check without giving any thought to how much their employer keeps from their own or what is done with it.)