The dynamics of inequalities and unequal exchange of labor in intertemporal linear economies

Introducing a concept of fairness of economic allocations, namely exploitation as the unequal exchange of labor (henceforth, UE exploitation) by generalizing Roemer’s (1981, 1982a) seminal models, this paper aims to answer the following two questions in the context of an intertemporal economy with linear technology: How is income and wealth inequality related (or unrelated) to the existence and persistence of UE exploitation? What are the mechanisms driving the persistent existence of UE exploitation in growing economies? Agents are UE exploited (resp. exploiters) if the amount of labor that they contribute to the economy is bigger (resp. smaller) than the amount of labor ‘received’ by them via their income. It is proved, first, that UE exploitation is monotonically correlated to functional income inequality. Second, it is shown that, unless agents discount the future, asset inequalities are necessary, but not sufficient for the persistence of UE exploitation, and capital accumulation leading to the disappearance of UE exploitation cannot be ruled out in equilibrium. Third, it is shown that, regardless of whether agents discount the future, labor-saving technical progress may yield sustained growth with persistent UE exploitation by keeping labor abundant relative to capital, which restrains wages from rising. Unlike in models with differentiable production functions, this mechanism does not rely on changes in the marginal productivity of inputs and it is entirely driven by the interaction between innovation and labor markets.