This paper studies a buyer (e.g., a government agency) offering a proc
urement contract to a number of privately informed suppliers. The buye
r has private information about her demand for the product to be procu
red. The optimal mechanisms for all types of the buyer are examined. I
t is optimal for the buyer to reveal her demand information through th
e contract offer and use a first-price sealed-bid auction procedure to
award the contract, announcing her reserve price in advance. Any seco
nd-price auction is shown to yield less expected surplus for the buyer
than the optimal first-price auction does when the buyer's marginal w
illingness to pay decreases with quantity.