Limits to the private enforcement of antitrust law

Following Regulation No. 1/2003 EC which permits the substitution of decentralised and private enforcement for centralised and public enforcement of Articles 81 and 82 EC, the European Commission in December 2005 presented a Green Paper on "damages actions for breach of the EC antitrust rules". The purpose of this initiative is to foster private tort suits by victims of anti-competitive behaviour. However, there are limits to the private enforcement of antitrust law through actions for damages, since the harm is typically shifted to a large number of final victims who are badly informed or face a rational disincentive to sue for damages.Our paper focuses on a so far neglected aspect of loss diffusion which results from hardcore price cartels. Under reasonable conditions the owners of production factors are also affected by price cartels, whereas consumers are typically affected less than is commonly assumed.

A probabilistic model for the equilibration of an ideal gas

I present a generalization of the Ehrenfest urn model that is aimed at simulating the approach to equilibrium in a dilute gas. The present model differs from the original one in two respects: 1) the two boxes have different volumes and are divided into identical cells with either multiple or single occupancy; 2) particles, which carry also a velocity vector, are subjected to random, but elastic, collisions, both mutual and against the container walls. I show, both analytically and numerically, that the number and energy of particles in a given urn evolve eventually to an equilibrium probability density $W$ which, depending on cell occupancy, is binomial or hypergeometric in the particle number and beta-like in the energy. Moreover, the Boltzmann entropy $\ln W$ takes precisely the same form as the thermodynamic entropy of an ideal gas. This exercise can be useful for pedagogical purposes in that it provides, although in an extremely simplified case, a probabilistic justification for the maximum-entropy principle.Comment: 9 pages, 2 figure