Short answers, pulled from the story.
Marxian economics is a heterodox school of political economic thought rooted in Karl Marx's critique of political economy. In academic settings it is distinguished from Marxism as a political ideology and from the normative aspects of Marxist thought, treating Marx's analytical approach to economic development as intellectually independent from his advocacy of revolutionary socialism.
The labour theory of value holds that the value of a commodity equals the average socially necessary labour time required to produce it. Marx adopted and extended this theory from classical economists Adam Smith and David Ricardo, restricting its validity to useful commodities and specifying that value is determined by the labor of a worker of average energy and ability using prevailing techniques.
Surplus value is the difference between the value workers produce and the wage they receive. Workers are paid only for necessary labor, the time required to cover their subsistence, while the remaining surplus labor generates value that the capitalist appropriates as profit. Marx described this gap as a form of unpaid labor.
The first volume of Das Kapital was published in 1867, the only volume Marx completed in his lifetime. Friedrich Engels edited the second and third volumes from Marx's notes after Marx's death, and Karl Kautsky later edited Marx's Theories of Surplus Value.
Writing in 1988, Stigler and Solow argued that Marxist economics had virtually no impact on English-speaking economics, represented only a small minority of modern economists, and amounted to an irrelevant dead end.
Neo-Marxian economics emerged as a distinct tradition in the 1970s and 1980s, extending classical Marxian thought by incorporating dependency theory, world systems theory, and neoclassical techniques including game theory and mathematical modeling. Key figures include Paul A. Baran, Paul Sweezy, Michal Kalecki, Rosa Luxemburg, John Roemer, and Samuel Bowles.