Research Joint Ventures and Optimal Emissions Taxation

This paper performs a comparison of two well known approaches for modelling R&D spillovers associated with investment in E-R&D, namely dAspremont-Jacquemin and Kamien-Muller-Zang. We show that there is little qualitative difference between the models in terms of total surplus delivered when selecting the optimal tax regime when there is precommitment under cooperative regimes in which firms coordinate expenditures to maximize joint profits. However, under non-cooperative regimes there is marked difference, with the model of Kamien- Muller-Zang leading to higher taxation rates when firms share information. Furthermore, we argue that the Kamien-Muller-Zang model is of questionable validity when modelling R&D on emissions reducing technology due to counter intuitive results showing a positive relationhip between R&D spillovers and emissions taxes.

Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order

Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes highly nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.Comment: 16 page

Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps

Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral polymers, there are two sorts of chirality: the first describes the usual cholesteric-like twist of the local director around a pitch axis, while the second favors the rotation of the local bond-orientational order and leads to a braiding of the polymers along an average direction. In the former case chirality can be manifested in a tilt grain boundary phase (TGB) analogous to the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are led to a new "moire" state with twisted bond order. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In this case the polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity, reminiscent of dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to [email protected]

Monopolization through acquisitions in a differentiated product industry

This article analyzes the incentive to merge in a context of price competition with horizontal product differentiation. In contrast to the results obtained by Kamien and Zang (1990), we show that merged equilibria can appear in this game. Moreover monopolization of the industry occurs with a high number of firms.cooperative game; mergers; oligopoly

Patent Licensing and Price Discrimination

We extend the Kamien and Tauman model of patent licensing by introducing heterogeneous licensees that differ in their marginal costs using the licensed technology. We show that price discrimination does not necessarily ensure an efficient allocation of licenses. Moreover, it is possible that more licenses are sold without rather than with price discrimination.Endogenous valuation

License Auctions with Royalty Contracts for (Winners and) Losers

This paper revisits the licensing of a non–drastic process innovation by an outside innovator to a Cournot oligopoly. We propose a new mechanism that combines a restrictive license auction with royalty licensing. This mechanism is more profitable than standard license auctions, auctioning royalty contracts, fixed–fee licensing, pure royalty licensing, and two-part tariffs. The key features are that royalty contracts are auctioned and that losers of the auction are granted the option to sign a royalty contract. Remarkably, combining royalties for winners and losers makes the integer constraint concerning the number of licenses irrelevant

License Auctions with Royalty Contracts for Losers

This paper revisits the standard analysis of licensing a cost reducing innovation by an outside innovator to a Cournot oligopoly. We propose a new mechanism that combines elements of a license auction with royalty licensing by granting the losers of the auction the option to sign a royalty contract. The optimal new mechanism eliminates the losses from exclusionary licensing without reducing bidders’ surplus; therefore, it is more profitable than both standard license auctions and pure royalty licensing. We also take into account that the number of licenses must be an integer, which is typically ignored in the literature

Aspects of Defect Topology in Smectic Liquid Crystals

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.Comment: 19 pages, 13 figure