We investigate an infinite horizon bargaining problem in which a firm
and a worker bargain over two dimensions, quality and wage. The worker
has private information about his type. Only the uninformed firm make
s an offer and it can offer a menu of quality-wage contracts instead o
f single one. We show that for all discount factors, the unique sequen
tial equilibrium outcome is separating without delay; the firm separat
es the types of worker with a menu of contracts in the first period. O
ur result shows that in multi-dimensional bargaining, the ''Coase Conj
ecture'' holds in the sense that the game ends in the first period. Bu
t it fails in the sense that the uninformed party can preserve the ent
ire bargaining power.