This reply owes a lot to the work of Professor Anwar Shaikh of the New School, especially his 1978 essay “Marx’s Theory of Value and the Transformation Problem” and his 1982 article “Neo-Ricardian Economics: A Wealth of Algebra, A Poverty of Theory”
The transformation problem in classical political economy
The law of value as developed by classical political economy held that the value of a commodity is determined by the amount of labor that under the prevailing conditions of production is on average necessary to produce it.
According to the classical economists, the value of a commodity determines its natural price around which market prices fluctuate in response to changes in supply and demand. The fluctuations of market prices around values—or what comes to exactly the same thing, according to classical political economy, natural prices—regulate the distribution of capital among the various branches of production.
As far as the classics were concerned, natural price (to use Adam Smith’s terminology) or cost or price of production (to use Ricardo’s preferred terminology) was identical to the value of the commodity.