Marxian economics refers to a body of economic thought stemming from the work of Karl Marx.
Marxian versus Marxist
The adherents of Marxian economics, particularly in academia, distinguish it from Marxism as a political ideology, arguing that Marx's approach to understanding the economy is an intellectually valuable one, independent of Marx's advocacy for revolutionary socialism or the inevitability of proletarian revolution. It does not lean entirely upon the work of Marx and other widely known Marxists (Lenin, Trotsky, etc.), but may draw from a range of Marxist and non-Marxist sources. His work is seen as the basis for a viable analytic framework and an alternative to more conventional neo-classical economics. For others, the distinction between "Marxist" and "Marxian" is totally academic.
Marx and classical economics
Marx built on, and critiqued, the best-known economists of his day, the British classical economists. These were the same "bourgeois economists" that modern pro-capitalist economists credit as the founding fathers of their discipline, such as Adam Smith and David Ricardo. In particular, Marx based much of his work on the labor theory of value, then a bedrock of economic thought, whereas modern pro-capitalist economists theorize that value is generated from other sources than labor.
The labor theory of value holds that the value of an exchangeable good or service lies in the amount of labor required to produce it; the source of profits under capitalism, then, is value added by workers not paid out in wages. He developed this theory of exploitation of the proletariat with an exposition of the labor theory of value in the first volume of Capital, while remaining aware that the labor theory of value was not a valid theory of relative prices. He critiqued Smith and Ricardo, on the other hand, for not realizing their economic concepts reflected capitalist institutions, not innate natural properties of mankind. Thus, such theories did not necessarily apply to societies with different modes of production. Marx's theories of business cycles; of economic growth and development (especially in two sector models) and of the declining rate of profit, are other important elements of Marxian economics.
Marx's economic theories
Marx's master work on political economy was Capital: A Critique of Political Economy (better known by the German title Das Kapital), a three-volume work, of which only the first volume was published in his lifetime (the others were produced by Engels from Marx's notes). Marx wrote other treatises on economics: Critique of Political Economy, one of his early works, was mostly incorporated into Capital, especially the beginning of Volume I. Marx's notes made in preparing to write Capital were published years later under the title Grundisse.
Marx begins his analysis of capitalism with an analysis of the commodity, which he says is an object that is unique to capitalism. The first sentence of Capital, Volume I states: "The wealth of those societies in which the capitalist mode of production prevails, presents itself as 'an immense accumulation of commodities,' its unit being a single commodity."
Under the labor theory of value, the direct value of a commodity stems solely from the socially necessary labor time invested in it. But commodities also have a use value (that is, the direct utility gained from an item) and an exchange value (roughly equivalent to its market price, though Marxian economics would measure it in labor time). For example, the use value of a carrot lies in eating it and no longer being hungry, while its exchange value might be found in the quantity of gold (whose true value also lies in the labor which extracted it) which it could be sold for.
However, capitalists do not pay workers the full value of the commodities they produce. The gap between the value a worker produces and his or her wages are a form of unpaid labor, known as surplus value. To Marx, this is wage slavery, a central feature of capitalism as a mode of production.
To understand surplus value, consider a widget that sells for $1,000 that takes a single worker, paid $10 per hour, ten hours to produce. The worker is being paid only $100 to produce the widget, so the remaining $900 is surplus value which is being appropriated by his or her employer. He is thus said to be working for himself for only one of every ten hours.
Moreover, Marx notes that markets tend to obscure the social relationships and processes of production, a phenomenon he termed commodity fetishism. Consumers see a commodity only in market terms. In looking to obtain something as private property, they consider only its exchange value, rather than its true value -- the labor used to produce it.
The Austrian School was the first group of liberal economists to systematically challenge Marxian economics. This was partly a reaction to the Methodenstreit, an attack on the Hegelian doctrines of the Historical School. Though many Marxist authors have attempted to portray the Austrian school as a bourgeois reaction to Marx, such an interpretation is untenable: Carl Menger wrote his Principles of Economics at almost the same time as Marx was completing Das Kapital. The Austrian economists were, however, the first to clash directly with Marxism, since both dealt with such subjects as money, capital, business cycles, and economic processes. Eugen von Boehm-Bawerk wrote extensive critiques of Marx in the 1880s and 1890s, and several prominent Marxists--including Rudolf Hilferding--attended Boehm-Bawerk's seminar in 1905-06.
In contrast, the classical economists had shown little interest in such topics, and many of them did not even gain familiarity with Marx's ideas until well into the twentieth century.
Current theorizing in Marxian economics
Marxian economics has been built upon by many others, beginning almost at the moment of Marx's death. The final three volumes of Das Kapital were written by his close associate Friedrich Engels, based on Marx's notes. More recent economists who have made significant contributions in the Marxist vein include Paul Sweezy, Harry Magdoff, Joan Robinson, Richard Wolff, and Stephen Resnick
Though Marxian economists today are far outnumbered by their neo-classical counterparts, many continue to teach and to publish, particularly in Europe. To some, Marxian economics may be viewed not as an all-encompassing approach, but as one important element in an analytical toolset--perhaps part of a broader category of heterodox economics or radical political economy.
In the United States, the leading academic department for Marxian economics (and heterodox economics more generally) is at the University of Massachusetts Amherst.
English-language journals include the Monthly Review, Rethinking Marxism, and Capital & Class.