Optimal Public Utility Pricing: A Further Reconsideration

Pricing of public utilities has long been discussed after Hotteling (1947), and most preceding arguments have provided a negative answer to the question to attain a Pareto-efficient allocation in an economy with non-convex production possibilities. Contrasting to these, Kamiya (1995) provided an argument that it is possible to devise a pricing mechanism of non-convex technology good(s) such that the equilibrium allocation under the pricing mechanism is always Pareto-efficient. The present note intends to examine a small question to find how Kamiyafs arguemnt differs from the preceding, with an intention to clarify how the efficiency property of his pricing mechanism is secured. The reconsideration however leads to a negative result that Kamiyafs pricing mechanism will fail to assure the efficiency property in a simple illustrative economy considered by himself. We first confirms that the simple example given in Kamiya contradicts his main theorem, and then review Kamiyafs proving argument and examine where any slip remains.Public utility pricing, non-convex economy, Pareto-efficient allocation

Scale and confinement phase transitions in scale invariant SU(N)SU(N) scalar gauge theory

We consider scalegenesis, spontaneous scale symmetry breaking, by the scalar-bilinear condensation in $SU(N)$ scalar gauge theory. In an effective field theory approach to the scalar-bilinear condensation at finite temperature, we include the Polyakov loop to take into account the confinement effect. The theory with $N=3,4,5$ and $6$ is investigated, and we find that in all these cases the scale phase transition is a first-order phase transition. We also calculate the latent heat at and slightly below the critical temperature. Comparing the results with those obtained without the Polyakov loop effect, we find that the Polyakov effect can considerably increase the latent heat in some cases, which would mean a large increase in the energy density of the gravitational waves background, if it were produced by the scale phase transition.Comment: 20 pages, 15 figures, Version published in JHE

Affine Weyl groups, discrete dynamical systems and Painleve equations

A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application, some examples of difference and differential systems of Painleve type are discussed.Comment: AMSLaTeX, 16 page

Symmetries in the fourth Painleve equation and Okamoto polynomials

We propose a new representation of the fourth Painlev\'e equation in which the $A^{(1)}_2$-symmetries become clearly visible. By means of this representation, we clarify the internal relation between the fourth Painlev\'e equation and the modified KP hierarchy. We obtain in particular a complete description of the rational solutions of the fourth Painlev\'e equation in terms of Schur functions. This implies that the so-called Okamoto polynomials, which arise from the $\tau$-functions for rational solutions, are in fact expressible by the 3-reduced Schur functions.Comment: 25 pages, amslate

Birational Weyl group action arising from a nilpotent Poisson algebra

We propose a general method to realize an arbitrary Weyl group of Kac-Moody type as a group of birational canonical transformations, by means of a nilpotent Poisson algebra. We also give a Lie theoretic interpretation of this realization in terms of Kac-Moody Lie algebras and Kac-Moody groups.Comment: 31 pages, LaTe

Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system

We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the $R^2$ and $R_{\mu\nu}^2$ coupling constants, are relevant in case of higher derivative pure gravity. For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling constants become relevant. The relevant Yukawa coupling is crucial to realize the finite value of the Yukawa coupling constants in the standard model.Comment: Version published in JHEP; 75 pages, 10 figures, typos corrected, references adde