Viability of an economy with constrained inequality

Governments want to prevent high inequality while maintaining economic effi ciency. This paper investigates how an economy can satisfy both these constraints. We use the relative factor share as a proxy for inequality and so can use a representative agent model to understand how inequality evolves. Our representative agent model includes capital, consumption and debt which, like the relative factor share, are influenced by tax rates. Whether the model's evolutions can be constrained is understood as a problem of viability theory, and so we compute the viability kernels corresponding to our constraints. These kernels explain both how policy makers should act and why they act as they currently do. For example, we show that substantial government debt will require policy makers to reduce inequality. More importantly, we demonstrate that viability theory is a meaningful, interesting approach to understanding the tradeoff between inequality and efficiency