We model a sustainable supply chain with simultaneous consideration of greening and Corporate Social Responsibility by supplier and buyer and analyze it for four different decision alternatives. In the first two cases, a single supply chain agent looks after both greening and social responsibility, in the other two cases, one agent takes one of the responsibilities. We compared these four cases by considering both full information and asymmetric information about the buyer's marginal production cost. Using the supplier Stackelberg game, we obtained the optimal values of decision variables under both information scenarios. The supplier negotiates with the buyer using the wholesale price contract or the linear two-part tariff contract. The second one is the dominating choice. For this contract the value of information is also higher for all decision alternatives. We have revealed the conditions under which the supplier would be benefited by choosing the greening effort and where the buyer would be benefited by taking up social responsibility. Further, we have designed a cut-off policy and found that the supplier and buyer can trade without conflicts only at a high level of consumer sensitivity towards greening and social responsiveness. This result suggests that if sustainability is left completely on consumer pressure, then the supplier and the buyer may not incorporate sustainability in the supply chain practices. We could specify those consumer sensitivity levels under which there must be government regulations to derive sustainability.