  We study equilibrium in hedonic markets, when consumers and suppliers have
reservation utilities, and the utility functions are separable with respect to
price. There is one indivisible good, which comes in different qualities; each
consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types,
supplier types and qualities can be either discrete of continuous, in which
case they are allowed to be multidimensional. Prices play a double role: they
keep some agents out of the market, and they match the remaining ones pairwise.
We define equilibrium prices and equilibrium distributions, and we prove that
equilibria exist, we investigate to what extend equilibrium prices and
distributions are unique, and we prove that equilibria are efficient. In the
particular case when there is a continuum of types, and a generalized
Spence-Mirrlees condition is satisfied, we prove the existence of a pure
equilibrium, where demand distributions are in fact demand functions, and we
show to what extent it is unique. The proofs rely on convex analysis, and care
has been given to illustrate the theory with examples.
