We consider a symmetric information auction setting in which bidders, even if they fail to obtain the good, care about the price paid by the winner. First, if bidders care about the price independently from the identity of the winner, this affects the second-price auction but not the first-price auction. In broader specifications, we observe though that the first-price auction can be affected by the presence of some types of price-externalities. Nevertheless, in comparison with the first-price auction, the second-price auction exacerbates the effects of price-externalities whatever their types. Thus, there is no equivalence between the two auction formats.