Bidding Theory and the Treasury Bill Auction: Does Price Discrimination Increase Bill Prices?

R ECENT DISCUSSIONS by Milton Friedman [4] and Deane Carson [2] have independently suggested that the Treasury should abandon the policy of price discrimination in the weekly auction of 91-day and 182-day Treasury bills. They would substitute a simulated purely competitive auction in which all bids are filled at a uniform market-clearing price determined by the intersection of the offer quantity and the demand array of submitted bids. Andrew Brimmer [ 1, p. 181 ] challenged this view, arguing in favor of price discrimination on the ground that efficient ". resource allocation should be subordinated to the minimization of interest cost to the Treasury. . . ." This conclusion requires the assumption, stated explicitly by Brimmer [1, p. 178] that, "Through auctioning new bills (at discriminatory prices), the United States Treasury receives higher prices than it could get by selling these issues at a single price." This paper is not directed to the question of whether the Treasury should or should not practice in the public sector what the Clayton Act prohibits in the private sector. The paper is concerned exclusively with the theoretical question of whether the Treasury would necessarily receive higher prices by employing price discrimination than it could get by selling the issues at a single price. From a theory of bidding under uncertainty, which seems to apply naturally to the Treasury auction, it will be shown that buyers may be expected to enter lower bids under price discrimination than they would for a simulated competitive auction. If this analysis is accepted, it suggests that the Treasury may actually get less revenue from a given bill offering under price discrimination than under a competitive auction. Various approaches might be used in attemDting to build a model of bidding behavior in the bill auction. My approach will assume that bidders desire to maximize expected utility, where the expectation is over a subjective probability density function for the lowest accepted bid. That is, whether we are designing a discriminatory auction model or a purely competitive auction, each bidder is assumed to associate a subjective probability with each possible value for the minimum successful bid. Within this framework, three models will be discussed. Model I assumes each bidder has a fixed specified limit price at which he is willing to buy a specified quantity of bills. I intend this model to serve as an abstract representation of the behavior of non-dealer participants in the bill auction -banks, corporations and insurance companies -who act more or less as final holders of the bills. It is assumed in Model II that each bidder attaches a subjective probability density to the price at which he can resell new bills bought at auction from the Treasury. I think of this model as applying to the government security dealers who participate in the auction. Such dealers face not only the uncertainty, experienced by all bidders, as to where the low bid will fall, but also uncertainty as to the price that can be obtained by retailing the new bills in the secondary market for outstanding bills. In both Models I and II, the decision variable is the bid price. Model III is a generalization of II in which the decision variables are the bid price and the quantity of bills to be specified in the bid. From Models I and II, it is possible to show, unambiguously, that an individual will make at least as low a bid (and most probably lower) in a discriminatory auction as in a single-price competitive auction. From Model III, which seems to be less tractable, the case rests with an example in which an individual's bid price is less, and the quantity of bills specified in the bid is less, under discrimination.