  The unit value of a commodity that Michio Morishima's method and its
variations enable to determine correctly, is the sum of the value of the
commodities it contains (inputs) and the quantity of labor required for its
production. However, goods are sold at their market production price only when
they meet a solvent social need that involves the entire economy with its
interconnections between the different industrial sectors. This condition gives
full meaning to Marx's fundamental equalities, which derive from the law of
value and constitute invariants that apply to the economy as a whole. These
equalities are necessary to determine market production prices. We demonstrate
that they also enable to solve the transformation problem for a simple
reproduction system without fixed capital by starting from Morishima's
formalism and returning to a formalism closer to that used by Marx.
