Is Marx considered an important classical economist? In a post on the politics stack exchange, I came across the following description of how Marxism fits into the history of economic thought:


  Most professional economists consider Marx' work on economic theory to be a substantial part of economic theory. Marx and Engels are included in the list of great classical economists, along with Adam Smith, Jeremy Bentham, David Ricardo, and Thomas Malthus. Marx pointed out that the long-term equilibrium for the "standard of living" is what a class insists upon before having, raising, and equipping enough children to replace itself. Several key concepts of economics (including "Cobb-Douglas production functions" and "value added") are designed to explain Marx' observations about the fraction of a factory's revenue that is not paid out for materials or proletarian labor.


The idea that "the long-term equilibrium for the 'standard of living' is what a class insists upon before having, raising, and equipping enough children to replace itself." seems foreign to me as an idea in economics and I am curious about the accuracy of the claims about Cobb Douglass and Value added, since they were not supported with references.

Is Marx commonly considered to be an influential classical economist, and if so, what is an example of an idea he added to economics as a discipline?
Among economic historians, Marx is often considered the most important economist of the 19th century.  His attempts to provide a systematic explanation of the functioning of capitalism  was on a far grander scale than anyone who preceded him, and in that sense, he reset the bar very high for what would henceforth be considered comprehensive economic theory, even if parts of it were fundamentally flawed. Refer to Mark Blaug's classic text Economic Theory in Retrospect (Chapter 7) for a nice attempt to parse out Marx's economic theory from the rest of his ideas.  This is a standard and authoritative text in the history of economic theory. 

Blaug says of Marx "Marx the economist is alive and relevant today in a way none of the writers we have thus far considered." Those considered were Smith, Malthus, Say, Ricardo, &amp; Mill.  

In terms of his understanding of the dynamic long run evolution of economic systems, the nature of technical change, business cycles, and volume of employment, his insights were often brilliant, transformative and unparalleled in any writers that preceded him, and remain deeply influential.  (I'm paraphrasing Blaug here)

[It's worth mentioning that Blaug did his Ph.D at Columbian under George Stigler, who was a key leader in the Chicago School. So Blaug was hardly a lightweight, nor a "pinko" ;) ]