Price Singularities: Representation vs. Exclusion - (Now published as 'Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time', in Economic Theory, vol. 20 (2002), pp.503-537.)
Anthony Horsley and Andrew J Wrobel
Bewley's programme of excluding price singularities in equilibrium solutions for commodity spaces of bounded functions is reconsidered. From two recent examples in which singularities are indispensable, viz., marginal cost pricing in continuous time and an overlapping generations model, it is concluded that, although L?-model makes sense only when prices are represented by densities, price singularities can be incorporated by restricting the commodity space to be subspace of L?. Bewley's approach is rejiged for use in continuous time by weakening his Exclusion Assumption to obtain a price density result with extended applicability; also, the Mackey topology is replaced by the topology of convergence measure, which is simpler and more closely matches the economic properties modelled.