?
Optimal behavior of agents in a piecewise linear taxation environment
Tikhon V. Bogachev
In press
We study analytical properties of the optimal income taxation model.
In this model we consider the maximization of {\it utility} of an agent of the given type.
The real meaning of the utility is the net profit of the legal entity.
The mathematical consideration of the taxation optimization uses methods of probability theory,
functional analysis and optimal control.
The totality of all agents in the economy is represented by the probability space of their types.
Optimal income taxation differs from commodity taxation, another branch of the optimal tax theory.
Actual taxes are commonly linear or segmented, which naturally suggests us to consider such cases in this research.
To be more precise, we describe the general
piecewise linear taxation model with increasing linear coefficients.
The latter is necessary for the tax function to be convex.
An explicit description of optimal functioning of agents depending on their types is obtained.
In particular, we consider optimal labour effort and optimal utility.
Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102
We study the additive theory of arbitrary figures in linear spaces, that is, the theory of
addition extended to sets of vectors. Our main result is the following: if a linear space is infinite,
then the additive theory of figures admits interpreting second-order arithmetic and, therefore, it has
such or higher degree of undecidability. For countably infinite spaces, ...
Added: May 1, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
IEEE, 2026.
Added: April 21, 2026
Galkin O., Galkina S., Ястребова И. Ю., Журнал Средневолжского математического общества 2026 Т. 28 № №1 С. 11–30
Polynomials of least deviation from zero play an important role in the theory and practice of numerical methods. They can be used to solve problems of optimizing the properties of various computational algorithms. Our work is devoted to the study of polynomials of least deviation from zero on a ray in the exponential norm. In ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Petrov I., Doklady Mathematics 2026 Vol. Volume 112 P. S103–S110
This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent ...
Added: April 17, 2026
A. V. Pereskokov, Theoretical and Mathematical Physics 2026 Vol. 226 No. 3 P. 470–484
We consider the spectral problem for a hydrogen atom in orthogonal electric and magnetic fields with
an additional self-consistent field. We obtain an asymptotic expansion of self-consistent energy levels.
We find an asymptotic expansion of asymptotic eigenfunctions near the sphere |q| = 2. We calculate the
asymptotics of their norm in the space L2(R3). ...
Added: April 12, 2026
Kolachev N., Адамский А. И., Drozdov D. et al., Моделирование и анализ данных 2026 Т. 16 № 1 С. 157–176
Context and relevance. Despite the widespread adoption of the competency-based approach in higher education, a gap remains between the understanding of competence as a dynamic process and the tools available for its design and management. Dominant practices of learning outcomes assessment rely on static “snapshots,” which limits the possibilities for forecasting and purposeful development of competence. ...
Added: April 10, 2026
Kuchumova (Paramonova) Y. A., Galle B., Gamage D., / Series SSRN "Available at SSRN 5093851". 2025.
We examine when it is optimal to employ sales or VAT-type taxes as complements to a labor income tax. We find a Ramsey-type result in which each tax instrument should be imposed in inverse proportion to the combined elasticity of real and avoidance responses to the respective tax. Contrary to some prior results, we find ...
Added: January 21, 2026
M. L. Blank, Polyakov M. O., Problems of Information Transmission 2024 Vol. 60 No. 1 P. 53–70
A new and relatively elementary approach is proposed for solving
the problem of fair division of a continuous resource (measurable space,
pie, etc.) between several participants, the selection criteria
of which are described by charges (signed measures).
The setting of the problem with charges is considered for
the first time. The problem comes down to analyzing the properties
of the trajectories ...
Added: January 16, 2025
Bogachev T., Popova S., Математические заметки 2021 Т. 109 № 2 С. 170–179
We consider the problem of maximization of an integral functional on the space of increasing functions, which is motivated by economic concerns for tax mechanisms optimization. An analytical description of the optimal value is obtained, as well as an approximation method for finding the solution. ...
Added: February 13, 2021
Mamedli M., Норкина О.А., Журнал Новой экономической ассоциации 2019 № 3(43) С. 34–56
One of the key issues of optimal fiscal policy is public goods financing. Financial repression is commonly used by governments as an implicit taxation of financial sector along with explicit labor and capital taxes. In this paper we consider the optimal choice of benevolent government in an overlapping generations’ model with an endogenous labor supply ...
Added: October 28, 2019
Tsitovich I. I., Информационные процессы 2018 Т. 18 № 4 С. 335–365
In the paper, we consider the score value of some functional of conditionally normally distributed random variables, which is linked to the problem of the sequential hypothesis testing. It is ascertained that the evaluation was limited in growth, which is responsible for setting the average length of observations. ...
Added: September 4, 2019
Radionov S., Pospelov I. G., HSE Economic Journal 2015 Vol. 19 No. 3 P. 386–394
We consider standard monopolistic competition models in the spirit of Dixit
and Stiglitz or Melitz with aggregate consumer's preferences defined by two well known classes of utility functions – the implicitly defined Kimball utility function
and the variable elasticity of substitution utility function. These two classes gene ralize classical constant elasticity of substitution utility function and overcome its
lack of ...
Added: October 18, 2015
Норкина О. А., Pekarski S. E., Журнал Новой экономической ассоциации 2015 № 28 С. 31–55
Under fiscal stress the government often turns to practice of financial repression to lower the debt service cost. Captive pension fund is one of the targets for enlarging the demand for public debt. We propose an extension of the overlapping generations model with the fully-funded pension system and fiscal policy to question the optimality of ...
Added: October 14, 2015
Kazakov A., Lerman L. M., Kulagin N., Mathematical Modeling of Natural Phenomena 2013 Vol. 8 No. 5 P. 155–172
We demonstrate that a piecewise linear slow-fast Hamiltonian system with an equilibrium of the saddle-center type can have a sequence of small parameter values for which a one-round homoclinic orbit to this equilibrium exists. This contrasts with the well-known findings by Amick and McLeod and others that solutions of such type do not exist in ...
Added: March 29, 2015
Kurakin A. A., Мир России: Социология, этнология 2014 Т. 23 № 3 С. 175–185
The review of Johanna Bockman’s ‘Markets in the Name of Socialism: The Left- Wing Origins of Neoliberalism’ focuses the relationships between Western and Soviet economic sciences. Bockman emphasizes that historically there was no insurmountable gap between the analysis of market and planned economies: mathematical analysis made Soviet and Western economists similar to each other. For ...
Added: July 24, 2014