The law of the value of commodities (German: Wertgesetz der Waren), known simply as the law of value, is a central concept in Karl Marx's critique of political economy first expounded in his polemic The Poverty of Philosophy (1847) against Pierre-Joseph Proudhon with reference to David Ricardo's economics. Most generally, it refers to a regulative principle of the economic exchange of the products of human work, namely that the relative exchange-values of those products in trade, usually expressed by money-prices, are proportional to the average amounts of human labor-time which are currently socially necessary to produce them within the capitalist mode of production.
Thus, the fluctuating exchange value of commodities (exchangeable products) is regulated by their value, where the magnitude of their value is determined by the average quantity of human labour which is currently socially necessary to produce them (see labor theory of value and value-form). In itself, this theorem is fairly simple to understand and intuitively it makes sense to many working people. However, theorizing its implications is a much more complex task as it kept Marx busy across more than two decades.
When Marx talked about "value relationships" or "value proportions" (German: Wertverhältnisse), he did not mean "the money" or "the price". Instead, he meant the ratio of value (or 'worth') that exist between products of human labour. These relationships can be expressed by the relative replacement costs of products as labour hours worked. The more labour it costs to make a product, the more it is worth and inversely the less labour it costs to make a product, the less it is worth. Money-prices are at best only an expression or reflection of Marx's value relationships—accurately or very inaccurately. Products can be traded above or below their value in market trade and some prices have nothing to do with product-values at all (in Marx's sense) because they refer to tradeable objects which are not regularly produced and reproduced by human labour, or because they refer only to claims on financial assets.
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Marxian economics, or the Marxian school of economics, is a heterodox school of political economic thought. Its foundations can be traced back to Karl Marx's critique of political economy. However, unlike critics of political economy, Marxian economists tend to accept the concept of the economy prima facie. Marxian economics comprises several different theories and includes multiple schools of thought, which are sometimes opposed to each other; in many cases Marxian analysis is used to complement, or to supplement, other economic approaches.
Simple commodity production (einfache Warenproduktion), also known as petty commodity production, is a term coined by Friedrich Engels to describe productive activities under the conditions of what Karl Marx had called the "simple exchange" of commodities, where independent producers trade their own products. The use of the word simple does not refer to the nature of the producers or of their production, but rather to the relatively simple and straightforward exchange processes involved.
In 20th-century discussions of Karl Marx's economics, the transformation problem is the problem of finding a general rule by which to transform the "values" of commodities (based on their socially necessary labour content, according to his labour theory of value) into the "competitive prices" of the marketplace. This problem was first introduced by Marx in chapter 9 of the draft of volume 3 of Capital, where he also sketched a solution.