Question: Has there ever a period in history when people were nice to each other and not killing each other?

In other words, since humans arrived, have the inhabitants of this planet ever enjoyed ***world peace***?

To answer this, we first have to define *period*. Let's define *period* as a minimum of 50 years. If there are any periods of time without records, we will have to ignore those periods.

Now let's define *not killing each other*. By this, I mean no known battles, wars, or genocides on planet earth. I'm not referring to individual acts of violence.

*As a curious side note, with over 5,000 questions asked on this StackExchange site, this is the first question to ever implement the [peace](/questions/tagged/peace "show questions tagged 'peace'") tag. Well... almost... I just realized that I don't have enough rep to create a new tag, so perhaps a moderator will be kind enough to add it.*

Answer: 
I can't speak to the specifics of the Soviet Union, but I want to address the opening assumption of the question.

> 
> Generally, Communism believed in economic central planning, with each field being serviced by one "company" (to avoid waste).
> 
> 
> 

This is untrue of (or at least unnecessary for) both communism and [centrally planned economies](https://en.wikipedia.org/wiki/Centrally_planned_economy). A centrally planned economy is one where production, prices, and distribution are set by the government, not by market forces. No monopoly is necessary. [Communism](https://en.wikipedia.org/wiki/Communism) does not require a centrally planned economy, but rather is about the ownership of the means of production which covers a wide spectrum of social, political, and economic structures.

What you're asking about is [the Soviet model](https://en.wikipedia.org/wiki/Soviet-type_economic_planning). It's important to not use the Soviet model as a stand in for communism. Communism is a very broad set of social, political, and economic philosophies. The Soviet model is a specific, and rather broken, flavor featuring a centrally planned economy, single party control, and powerful committees. The Soviet model is more like an oligarchy masquerading as communism.

Two examples of centrally planned economies within the United States are large scale manufacturing for the military and, until very recently, space. The US government is the major buyer of things like aircraft carriers, tanks, nuclear submarines, and heavy launch vehicles. They effectively control what is produced, who it gets distributed to and, somewhat, the price.

The US government deliberately doles out contracts to multiple suppliers, even to the point of paying more money, in order to keep multiple suppliers around (also to get the votes of powerful senators by funneling money to their districts). This is to foster competition, prevent a single company from controlling the market, and also as a hedge in case one goes out of business.

For example, there were two builders of US Navy submarines, [Newport News Shipbuilding](https://en.wikipedia.org/wiki/Newport_News_Shipbuilding) and [General Dyanamics Electric Boat](https://en.wikipedia.org/wiki/General_Dynamics_Electric_Boat), but reductions in the US navy's submarine fleet means now there is only one, Electric Boat. Should something happen to General Dynamics this would be put the US's ability to build submarines, a highly specialized skill, in danger.
Ryszard Kapuscinski in "*Imperium*", makes the point that often the centrally-planned COMECON economies like the USSR had *more* competing companies, not *fewer*, as they company with the inferior products would not go bankrupt. 

The example he gave was televisions, at the time, a high-tech, prestige product. Directors of large industrial concerns would want to build them, even if it was not in the plan, and so would divert resources to make them. Therefore, there were very many substandard televisions on sale, built solely as vanity projects. 

In the case of aircraft, it would be hard to divert the required quantity of resources to their production, but the simple fact that it is more efficient to rationalise production is not a necessary reason for doing it, except in a market economy. 

It's also worth pointing out that the centrally-planned economies were not always exact copies of each other, all permitted various forms of market mechanisms, and that people did not always do what was in the plan. As others have pointed out, even in "market economies", government bodies often enforce rationalisation in industry.