In this article, we analyze the use of descending clock auctions in the implementation of a minimum pricing policy. This type of auction has been used by the Brazilian government policy of support for agricultural prices since 1997. We propose a clock auction model along the lines used by the Brazilian government and derive its main implications. Based on data from auctions already held and implications of the theoretical model, we conclude that the following factors are crucial to minimize the costs of implementing a minimum price policy via auctions: the choice of product to be auctioned, amount auctioned, reserve price, and the rules used in the implementation of the auction.