Final answer:
The economic system based on the ideas of Marx and Engels in 'Das Kapital' is communism, which advocates for a classless society with public ownership of production.
Step-by-step explanation:
The economic system that followed the ideas of Marx and Engels as written in Das Kapital is communism. Marx and Engels' writings, including The Communist Manifesto, argue for a society where the working class, not the bourgeoisie, controls the government and the economy. They believed that society would undergo a transition from capitalism to socialism, and eventually to a classless society, which is the core of communist ideology. This transition would feature the public owning the means of production, rather than private companies or individuals. Marxism anticipated that capitalism's inherent inequalities would become so severe that a worker revolution would ensue, leading to its collapse and the establishment of a communist system.
Long after Marx's death, his ideas continued to inspire revolutions and influence societies. Prominent revolutions, such as those in Russia and China, were influenced by Marxist thought, although they did not fully realize the economic or political equality Marx had envisioned.
In summary, when referring to the ideas of Marx and Engels in their writings in Das Kapital, the correct answer to the question is: a) Communism.