Vertical integration and the licensing of innovation with a fixed fee or a royalty

In this paper, we analyse a situation where a patent holder is considered as an upstream firm that can license its innovation to some downstream companies that compete on a final market with differentiated products. Licensing contract may be based either on a royalty or a fixed fee. The patent holder can either be independant or vertically integrated with one of the downstream companies. We show that a licence based on a royalty works better with vertical integration, and that consequently, the patent holder have some interest to vertically integrate if it enables him to apply a royalty based license. The effect of vertical integration on the social surplus can be either positive or negative.LICENSING; INNOVATION; VERTICAL INTEGRATION

Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations

Barker recently proved new weak-strong uniqueness results for the Navier-Stokes equations based on a criterion involving Besov spaces and a proof through interpolation between Besov-H{\"o}lder spaces and L 2. We improve slightly his results by considering Besov-Morrey spaces and interpolation between Besov-Morrey spaces and L 2 uloc. Let u 0 a divergence-free vector field on R 3. We shall consider weak solutions to the Cauchy initial value problem for the Navier-Stokes equations which satisfy energy estimates. The differential Navier-Stokes equations read as $\partial$ t u + u. $\nabla$ u = $\Delta$ u -- $\nabla$p div u = 0 u(0, .) = u 0

Downstream labeling and upstream price competition

The paper analyses the economic consequences of labeling in a setting with two vertically related markets. Labeling on the downstream market affects upstream price competition through two effects : a differentiation effect and a ranking effect. The magnitude of these two effects determines who in the supply chain will receive the benefits and who will bear the burden of labeling. For instance, whenever the ranking effect dominates the differentiation effect, the low quality upstream firm loses from labeling while all downstream actors are individually better off. By decreasing the low quality input price, the label acts then as a subsidy which assures an increase of the downstream market welfare. This analysis furthers our understanding of the economic consequences of the public labeling in cases like restaurants or GMOs.LABEL;IMPERFECT CONSUMER INFORMATION;VERTICAL PRODUCT DIFFERENTIATION;VERTICAL RELATIONS;REGULATION

Real Interpolation method, Lorentz spaces and refined Sobolev inequalities

In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities

Credence goods, experts and risk aversion

The existing literature in expert-customer relationship concludes that when: i) consumers are homogenous, ii) consumers are committed with an an expert once this one made a recommendation, and iii) the type of treatment provided is verifiable, an expert finds optimal to serve efficiently his customers. This work shows that the previous result may not occur when consumers are not risk-neutral. Our result, that holds in a monopoly setting and under Bertrand competition, suggests that risk averse consumers have more likely to be mistreated by experts.CREDENCE GOODS;EXPERT SERVICES;RISK AVERSION

Spin wave theory for 2D disordered hard-core bosons

A spin-wave (SW) approach for hard-core bosons is presented to treat the problem of two dimensional boson localization in a random potential. After a short review of the method to compute 1/S-corrected observables, the case of random on-site energy is discussed. Whereas the mean-field solution does not display a Bose glass (BG) phase, 1/S corrections do capture BG physics. In particular, the localization of SW excitations is discussed through the inverse participation ratio.Comment: TIDS15 conferenc

Local stability of energy estimates for the Navier--Stokes equations

We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures