A comprehensive, self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism

In this contribution we review in a rigorous, yet comprehensive fashion the assessment of the one-body reduced density matrices derived from the most used single-reference excited-state calculation methods in the framework of the equation-of-motion formalism. Those methods are separated into two types: those which involve the coupling of a deexcitation operator to a single-excitation transition operator, and those which do not involve such a coupling. The case of many-body auxiliary wave functions for excited states is also addressed. For each of these approaches we were interested in deriving the elements of the one-body transition and difference density matrices, and to highlight their particular structure. This has been accomplished by applying a decomposition of integrals involving one-determinant quantum electronic states on which two or three pairs of second quantization operators can act. Such a decomposition has been done according to a corollary to Wick's theorem, which is brought in a comprehensive and detailed manner. A comment is also given about the consequences of using the equation-of-motion formulation in this context, and the two types of excited-state calculation methods (with and without coupling excitations to deexcitations) are finally compared from the point of view of the structure of their transition and difference density matrices

Multiproduct Monopolist and Full-line Forcing: The Efficiency Argument Revisited

Shaffer (1991) shows that a multiproduct monopolist selling differentiated products through a unique retailer cannot earn monopoly profit using brand specific two-part tariffs and that full-line forcing restores monopoly power. We extend this analysis to more general contracts and shows that full-line forcing is efficient as it increases both industry profits and consumers' surplus.

Portfolio Effects and Merger Control: Full-line Forcing as an Entry Deterrence Strategy.

The ''portfolio effect theory'' developed by the European Commission in merger control is at the center of a fierce international row with the US authorities who believe that this theory has no economic foundations. This paper aims to provide a counter-argument and shows that full-line forcing may be used by the holder a comprehensive range of products as an entry deterrence device to maintain its monopoly power. However, due to buyer power on the retail market, this will happen only if entry is not profitable for the industry as a whole. The effects on consumer welfare are ambiguous. Full-line forcing will reduce prices in the first period, but as it helps maintaining monopoly power, is harmful in the long-term.Portfolio effects, competition policy, full-line forcing, entry deterrence.

Bilateral Control with Vertical Contracts

A supplier is known to be subject to opportunism when contracting secretly with downstream competitors, particularly when downstream firms have "passive beliefs." We stress that in many situations, an equilibrium with passive beliefs may not exist and passive beliefs appear less plausible than "wary beliefs", introduced by McAfee and Schwartz, that account for multilateral deviations. We show that in a broad range of situations, equilibria with wary beliefs exist and reflect opportunism. Last, we confirm the insight, derived by O'Brien and Shaffer using a more ad-hoc equilibrium concept, that RPM eliminates the scope for opportunism.Opportunism, Secret Contracts, Beliefs, Resale Price Maintenance

Optimal Audit Policy and Heterogenous Agents

Frauds can be explained not only in terms of individual willingness to cheat, but may also be driven by opportunities to behave dishonestly. The audit policy should therefore be different for different categories of agents. This paper focuses on the optimal audit policy when there are two categories of agents and shows that the auditor adopts different policies depending on its budget. When resources are quite limited, the auditor sets identical audit probabilities for both types. On the other hand, in most of the cases, the authority should first ensure that people with lower opportunities choose not to commit an offence.Fraud, audit, opportunities, budget allocation.