Existence of Equilibria in Economies with Bads

We consider an exchange economy in which there are infinitely many consumers and some commodities are bads, that is, cause disutility to consumers. We give an example of such an economy for which there is no competitive equilibrium or its variants (quasi‐ or pseudo‐equilibrium), and an example of the failure of the so‐called uniform integrability condition of equilibrium allocations of increasingly populous finite economies.