Different types of procurement auctions may result in different level of social welfare even if they select the same seller or service provider. This happens when firms in an auction bid market prices at which they want to sell in the aftermarket. This paper compares levels of welfare that first-price and second-price auctions generate in the aftermarket. It is shown that the monotonicity of an augmented market demand elasticity in price is the main driving factor. The paper builds on the model of price competition with private costs (Spulber, 1995) and extends it into the aftermarket social welfare analysis and comparison with the original Bertrand competition model.