We analyze the real case of two firms evaluating a shift from a ''risk
and revenue sharing agreement'' to a supplying agreement. From the po
int of view of economic theory, this is a constrained bilateral monopo
ly problem. At the first stage, the two firms take sequential decision
s of price and demand, with price being represented not only as a simp
le level, but also as a more realistic price schedule. In this more ge
neral case we solve a variational problem by transforming it - with no
restrictions - into a classical mathematical programming one. At the
second stage, the two firms an allowed to bargain over a couple price-
quantity instead of taking separate decisions about them. As expected,
bargaining is efficient with respect to the constant price case. In t
he price schedule case however efficiency does not hold without furthe
r conditions.