Product Mix

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The Product-Mix Auction: a New Auction Design for Differentiated Goods Paul Klemperer Nuffield College, Oxford, OX1 1NF, England +44 777 623 0123

Journal of the European Economic Association, 2010, 8, forthcoming (first version, 2008) The most recent public version of this paper is available at Abstract I describe a new static (sealed-bid) auction for differentiated goods—the “Product-Mix Auction”. Bidders bid on multiple assets simultaneously, and bidtakers choose supply functions across assets. The auction yields greater efficiency, revenue, information, and trade than running multiple separate auctions. It is also often simpler to use and understand, and less vulnerable to collusion, than a simultaneous multiple round auction. I designed it after the 2007 Northern Rock bank-run to help the Bank of England* fight the credit crunch; in 2008 the U.S. Treasury planned using a related design to buy “toxic assets”; it may be used to purchase electricity. (100 words) *[note added June 2010] Although the auction was designed in response to the crisis, the Bank of England wanted a solution that would be used in normal times too: the Bank is now regularly running auctions that correspond closely to the design described in section 2 of this paper; future auctions may use some of the enhancements described in section 3. Keywords: multi-object auction, TARP, central banking, simultaneous ascending auction, treasury auction, term auction, toxic assets, simultaneous multiple round auction, Product-Mix Auction JEL Nos. D44 (Auctions), E58 (Central Banking) I have advised the Bank of England and the U.S. Treasury and have been consulted by other Central Banks, government agencies, etc., about these issues. I thank the relevant officials for help, but the views here are my own and do not represent those of any organisation. I am very grateful to Jeremy Bulow and Daniel Marszalec for their help in advising the Bank of England. I also particularly benefited from discussions with Elizabeth Baldwin and Marco Pagnozzi, and thank Olivier Armantier, Eric Budish, Vince Crawford, Aytek Erdil, Meg Meyer, Moritz Meyer-ter-Vehn, Rakesh Vohra, the editor and anonymous referees, and many other friends and colleagues for helpful advice. © Paul Klemperer 2008, 2009

1. Introduction

How should goods that both seller(s) and buyers view as imperfect substitutes be sold, especially when multi-round auctions are impractical? This was the Bank of England’s problem in autumn 2007 as the credit crunch began.1 The Bank urgently wanted to supply liquidity to banks, and was therefore willing to accept a wider-than-usual range of collateral, but it wanted a correspondingly higher interest rate against any weaker collateral it took. A similar problem was the U.S. Treasury's autumn 2008 Troubled Asset Recovery Program (TARP) plan to spend up to $700 billion buying “toxic assets” from among 25,000 closely-related but distinct sub-prime mortgage-backed securities. Because financial markets move fast, in both cases it was highly desirable that any auction take place at a single instant. In a multi-stage auction bidders who had entered the highest bids early on might change their minds about wanting to be winners before the auction closed,2 and the financial markets might themselves be influenced by the evolution of the auction, which magnifies the difficulties of bidding and invites manipulation.3 An equivalent problem is that of a firm choosing its “product mix”: it can supply multiple varieties of a product (at different costs), but with a total capacity constraint, to customers with different preferences between those product varieties, and where transaction costs or other time pressures make multiple-round auctions infeasible.4 The different varieties of a product could include different points of delivery, different warranties, or different restrictive covenants on use. 1

The crisis began in...
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