This paper is aimed at providing a direct proof of the Cease conjectur
e when the existence of a second-hand market ensures the possibility o
f arbitrage for the consumers; in this context, the problem is stated
as an optimal control problem. The commitment strategy and the no-comm
itment strategy of the monopolist are respectively found. The latter w
hich is analysed by dynamic programming gives the Cease conjecture res
ult. (C) 1998 Elsevier Science S.A.