Elsevier

Research in Economics

Volume 63, Issue 3, September 2009, Pages 160-164
Research in Economics

Fixed versus variable supply in the public provision of goods

https://doi.org/10.1016/j.rie.2009.06.002Get rights and content

Abstract

Using discriminatory price auctions with variable supply, we explore a situation in which a corruptible public employee is in charge of producing and allocating a finite number of goods among consumers with uniformly distributed valuations. The negative effects of corruption are lower when the employee‘s task is to “provide at least q0 goods” than when the employee is required to “provide exactly q0 goods”.

Introduction

Corruption is a complex phenomenon with many implications, both economic and social. Depending on the situations to which it is related, and on the causes that generate it, corruption can appear in a wide variety of forms, sometimes extremely different from one another. The immediate implication is that we cannot understand all corrupt behaviors and their effects using a unique model, hence the need for multiple tools in order to analyze the various forms of corruption. In this paper we use a model of discriminatory price auctions with variable supply to examine the behavior of a corruptible public employee in charge of providing goods and the implications of his corruptibility on the allocation of goods. We provide a solution for the simplified case of uniform distribution of both the marginal cost of producing the good and of the consumers’ valuations for the good.

Most of the existing literature on corruption in the public sector examines situations in which bribes are asked or cases in which bribes are proposed but the public employee has the capacity to manipulate only the exit of a single object auction, as in the case of privatization. However, when a public employee is in charge of producing and allocating a number of goods, there are situations in which bribes are proposed by the potential consumers in order to influence the provider’s decisions and the provider has some discretionality regarding the number of goods to produce. We consider that, if corruption is present in such situations, the best representation that we can give is by means of auctions. Depending upon how the public employee’s official task is formulated, such cases can be described using different types of auctions: the traditional discriminatory-price auction if the supply is fixed, and the variable supply auction when the quantity required is only indicative as a minimum compulsory supply. In the first case, the public employee can only serve the consumers in decreasing order of grafts. In the second case, the public employee can increase the supply of services above what he is required in exchange for a bribe.

Several recent theoretical studies have been dedicated to auctions with variable supply, (Lengwiler, 1999, McAdams, 2006), but they have generally focused on uniform price auctions, while leaving the discriminatory price auctions mostly to empirical studies. Lengwiler (1999) extended his analysis also to discriminatory price auctions but he studied a very specific setup in which the bidders do not compete with one another in the auctioning process. In this paper we propose a model in which the auctioning process is generated by the fact that consumers are rivals and consequently “struggle” to get the goods.

This model can also be used in a more general setup in which corruption is not present and the variable supply auction describes the behavior of a profit-maximizing private agent who has to make production decisions. However, the purpose of the present paper is to analyze certain corrupt behaviors in the public sector, which have not yet been fully characterized by the existing literature in the field and the variable supply auctions model is adequate for this purpose. In this case, corrupt public agents behave like private agents because they use the decision power with which they are invested, to achieve profit-maximization.

Section snippets

The model

A public employee is in charge of providing a service. As an example one can think of production licenses. Suppose the cost function of providing the goods is C(q)=C0+cmax{0,(qq0)}. This should be interpreted in the following way: producing a quantity of the good q lower than or equal to q0 costs the public employee only a fixed cost C0, which is common knowledge, while any additional unit implies a constant marginal cost c. The marginal cost is private information. However, it is common

Equilibrium and outcomes

Fixed supply. The situation in which the Government announces that exactly q0 production licenses are to be delivered is perfectly described by a traditional discriminatory price auction. We use the existent results, derived by Vickrey (1962), to characterize this situation.

Variable supply. Suppose that the public employee can increase the number of services delivered. Given that a quantity q0=1 is always provided, the consumers compete in grafts for getting the good. However, in choosing their

Comparative analysis

In what follows we analyze the differences between the two cases: (i) when the Government imposes the public employee to deliver exactly q0 units (fixed supply) and (ii) when the Government announces variable supply. The main results for the case of fixed supply follow easily from known results in the traditional discriminatory price auctions. According to the work of Vickrey (1962), the bid of an individual who attaches value v to the good is: βF(v)=12v.

The central result, when comparing the

Conclusions

When evaluating the outcomes of fixed supply and variable supply auctions from the auctioneer’s point of view, the range of the marginal costs is very important. Low values of the marginal cost make the variable supply auction preferable. This is because, compared with a traditional auction, the expected profit from selling an additional good is higher than the unrealized revenues from receiving a lower bid for the first good. On the other hand, high values of the marginal cost make the fixed

Acknowledgements

I am grateful to my PhD advisor, Professor Marco LiCalzi, for his valuable suggestions and support.

References (3)

  • Y. Lengwiler

    The multiple unit auction with variable supply

    Economic Theory

    (1999)
There are more references available in the full text version of this article.

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