This is a scholarly article written by a free market economist, a "classical liberal:"
My purpose today is to make just two main points: (1) To show why Nazi Germany was a socialist state, not a capitalist one. And (2) to show why socialism, understood as an economic system based on government ownership of the means of production, positively requires a totalitarian dictatorship.
The article makes these points, among others:
1. Capitalists under the Nazis were capitalists in name only, stripped of the power to control what was supposedly their own property. Their actual status under the Nazis was one of sharecroppers or of government pensioners.
2. De facto socialism in Nazi Germany was established with the establishment of wage and price controls, which cemented central control of the economy. The effects of wage and price controls, which lead to shortages and other problems, produced a series of events whereby the Nazis ended up with control of all aspects of the economy, i.e., prices, wages, production, capitalization, etc.
3. Establishment of de facto socialism leads inevitably to totalitarianism.
In sum, therefore, the requirements merely of enforcing price-control regulations is the adoption of essential features of a totalitarian state, namely, the establishment of the category of "economic crimes," in which the peaceful pursuit of material self-interest is treated as a criminal offense, and the establishment of a totalitarian police apparatus replete with spies and informers and the power of arbitrary arrest and imprisonment.
Once the elites decide that they know better than the free market how to run the economy and know better than the people how to run the government one is put on a path that invariably ends up at the same place, i.e., totalitarianism. Whether you call that path Nazism, communism, socialism, or fascism makes little difference.
Left leaning historians have two lines of argument that supposedly distinguishes Nazism from socialism. The first is the issue of motivations. For example, the Nazis were nationalists, meaning they were mainly motivated by an interest in bettering the lot of the German people and cared nothing or less than nothing for anyone else while the Communists and Socialists were motivated by a concern for all people, were internationalist and somewhat more pluralistic. However the central definition of the term "socialist" says nothing about nationalism vs internationalism.
Second is the way in which German capitalists and conservatives worked in favor of the Nazis, an association that scholars would like to say brands Nazis as capitalists and right wingers. However, faced with the rise of Communism in Germany, clearly the more powerful of the contending political ideologies in Germany at the time, which would have thrown capitalists and other property owners out on the street or would have them lined up and shot, and the Nazis, who were willing to leave the middle class alone or even help them out even while taking control of the economy and providing the common German people with welfare, employment, and benefits, who does one suppose that capitalists and other property owners were going to favor? That association says nothing about what the Nazis actually were, only about what was perhaps the dilemma of the propertied classes of Germany at the time.