Use values and exchange values in Marx's extended reproduction schemes

Marx-Engels’ numerical illustrations of the extended reproduction suggest that a two-sector economy reaches a balanced growth path, from the second period onwards. We explain this surprising result and show that, for technical reasons, disproportions between sectors can prevent the system from reproducing itself. But, in Marx’s reproduction schemes, such a crisis is not only due to purely technical factors and one must wonder what role is played by the relative price in the reproduction of the system. The answer is given by comparing two models having a similar structure but quite different rules for the determination of the relative price. In Marx’s model, the price is given by the labour values and thus it is exogenously fixed. We contrast Marx’s analysis with an endogenous price model in which the price depends on the conditions of the accumulation of capital. The Appendices point out the complete accordance of Engels’ corrections with Marx’s model and Marx’s unfruitful quest for a balanced growth path as a tool for the analysis of crises