Demand reduction and initial endowments in consignment auctions

Consignment auctions, in which bidders first receive free initial endowments of a good and must then consign them to a subsequent uniform price auction, are often used in emissions allowance trading for the environmental regulation of greenhouse gas emissions. We study consignment auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We first characterize the equilibrium outcome and then examine the effects of initial endowments and total supply. If bidders' initial endowments increase or the total supply decreases, the equilibrium price increases whereas the social welfare and the auctioneer's revenue may increase or decrease. In particular, the revenue may increase even though fewer units remain in the hands of the auctioneer since an increase in initial endowments can prevent the low price equilibrium resulting from demand reduction.