Liquidity Constrained Competing Auctions

When goods are sold through competing auctions, what e¤ect does monetary policy have on the equilibrium allocation? To answer, we extend the competing auctions framework in several ways: buyers choose how much money they bring to an auction, the quantities traded at the auctions are endogenous, and sellers can charge a fee (either positive or negative) to buyers participating in their auction. We present two di¤erent speci?cations of the model. In the ?rst model, sellers post a quantity they wish to sell and a fee, and allow the price to be determined by an auction. In the second model, sellers post a price and a fee and allow the quantity sold to be determined by an auction. When sellers post a quantity and buyers bid prices, the Friedman rule implements the ?rst best and, in this case, no fee is charged by sellers. Sellers charge buyers a participation fee as soon as the nominal interest rate is positive, and marginal increments in money growth decrease both the posted quantity and buyers?entry. The use of auction fees reduces welfare in this environment. When sellers post a price and buyers bid quantities, the Friedman rule is optimal but does not yield the ?rst best as agents trade an ine¢ ciently low quantity in multilateral matches and an ine¢ ciently high quantity in pairwise matches. Marginal increments in money growth decrease the posted real price and the quantities traded. When the interest rate is low, sellers pay buyers who participate in their auction, which increases welfare. When the interest rate is high, sellers charge buyers who participate in their auction, which reduces welfare.