... p, t ) , then and if , then p t p t t t that Proposition 4. 2 In intertemporal centralized pricing (4. 2)- (4. 3), (4. 5)- (4. 6) and (4. 7), if the supply chain is profitable, i.e., P>p>c, and there is ... neither of the two 4. 2 INTERTEMPORAL PRODUCTION/PRICING COMPETITION 167 Proposition 4. 1 In intertemporal centralized pricing (4. 2)- (4. 3), (4. 5) (4. 6) and (4. 7), if the supply chain is profitable, ... m(t ), t dt m m (4. 4) s.t m(t) 0, q(w(t)+m(t),t) (4. 5) (4. 6) Formulations (4. 1)- (4. 6) assume non-cooperative behavior of the supply chain members which affects the overall supply chain performance...