Understanding the New Left
You are very incorrect in your political philosophy. The range from left to right of the political spectrum goes like this: [Left] Communism, Socialism, Market Economy, Fascist Economy [Right]. Communism involves the whole populace being part of the government. No money is available. Socialism is Communist-lite, with government doing most things and allowing private businesses to operate with money. Those two are the left side of the political/economic spectrum. What we call the political spectrum has to do with economy rather than political governing or rulership. There's no left/right to do with monarchy, republic, empire, shogunate, or what have you.
On the right, there is market economy, with very little interference from government in private economic affairs. Libertarians are on the right (Conservative), meaning rulership doing little on their own besides the private sector. Quality and value is very high in a market economy.
Fascist economy is further right, needing only a head of economy to provide order. The benefit of fascist economy is equal to that of market economy, the difference being market economies can trade with each other [while fascist economies can provide for themselves internally everything they would need to import otherwise]. Nazi Germany was fascist (called National Socialism by Germans in those days), the United States were fascist under Franklin Delano Roosevelt, the Holy Roman Empire was fascist under High King Charlemagne, and the Incan Empire in South America was fascist under their emperors.