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Mathematics
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Mathematical Modeling and Applications in Industrial Organization
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Mathematical Modeling and Applications in Industrial Organization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 1 September 2024 | Viewed by 11586

Special Issue Editors

Dr. Natalia Aizenberg

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Guest Editor
Department of Electric Power System, Melentiev Energy Systems Institute SB RAS, 664033 Irkutsk, Russia
Interests: industrial organisation; game theory; modeling of economics; energy economics
Prof. Dr. Sergey Dzuba

E-Mail Website
Guest Editor
Department of Economic Science of School of Economics and Management, Far Eastern Federal University (FEFU), 690922 Vladivostok, Russia
Interests: network and agent-based models in economics; information theory applications; corporate finance; theory of the firm

Special Issue Information

Dear Colleagues,

We are pleased to announce a Special Issue of the journal Mathematics entitled “Mathematical Modeling and Applications in Industrial Organization”. It is a fast-moving field of the economy that requires new research, both theoretical and practical. This Special Issue covers a wide range of problems in economic analysis based on mathematical models using a variety of tools, including econometric and cluster analysis. Research is encouraged that includes the modeling of the complex processes in the operation and quality of different markets, firm problems, regulation issues, and innovation. We will give preference to submissions that develop new mathematical approaches to modeling and analysis in industrial organizations.

Dr. Natalia Aizenberg
Prof. Dr. Sergey Dzuba
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Economic modeling
  • Industrial organization
  • Imperfect competition
  • Monopolistic competition
  • Applied econometrics
  • Econometric issues
  • Time series
  • Investments
  • R&D (research and development) models
  • Energy markets
  • Electricity markets

Published Papers (6 papers)

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Research

23 pages, 881 KiB  
Article
How to Determine the Optimal Number of Cardiologists in a Region?
by Artur Nagapetyan, Alexander Drozd and Dmitry Subbotovsky
Mathematics 2023, 11(21), 4422; https://doi.org/10.3390/math11214422 - 25 Oct 2023
Viewed by 1084
Abstract
This paper proposes an approach to determining the optimal number of medical specialists in a particular territory. According to the author’s theoretical model, in order to maximise public welfare, the marginal contribution of the last physician recruited to the growth of the public [...] Read more.
This paper proposes an approach to determining the optimal number of medical specialists in a particular territory. According to the author’s theoretical model, in order to maximise public welfare, the marginal contribution of the last physician recruited to the growth of the public utility function should be equal to the marginal cost of attracting them and providing conditions for their work. To empirically assess the contribution of physicians to the number of lives saved, the CVD mortality rate is modelled using the instrumental variable method. At the level of provision of cardiologists in the amount of 1 per 100,000 people, their marginal contribution to the number of lives saved is not less than 124 per 100,000 people, with a further decrease of 10 per 100,000 people with an increase in the level of provision of one unit. The use of the obtained results will increase the validity of managerial decisions and improve the determination of the optimal number of doctors when choosing between alternative possibilities of spending money on hiring doctors with different profiles or other expenses, especially in the case of limited resources. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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24 pages, 2410 KiB  
Article
Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime
by Helder Rojas, Artem Logachov and Anatoly Yambartsev
Mathematics 2023, 11(20), 4235; https://doi.org/10.3390/math11204235 - 10 Oct 2023
Viewed by 717
Abstract
We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our [...] Read more.
We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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13 pages, 274 KiB  
Article
The Open Monopolistic Competition Models: Market Equilibrium and Social Optimality
by Igor Bykadorov
Mathematics 2023, 11(19), 4172; https://doi.org/10.3390/math11194172 - 5 Oct 2023
Viewed by 832
Abstract
We study the monopolistic competition model of Dixit–Stiglitz–Krugman with additive separable utility and transport costs of “iceberg types”. The production costs are not necessary linear. We study two concepts: market equilibrium and social optimality. There are well-known facts in the closed economy under [...] Read more.
We study the monopolistic competition model of Dixit–Stiglitz–Krugman with additive separable utility and transport costs of “iceberg types”. The production costs are not necessary linear. We study two concepts: market equilibrium and social optimality. There are well-known facts in the closed economy under monopolistic competition: (1) “in market equilibrium, the elasticity of revenue equals the elasticity of total costs” and (2) “in social optimality, the elasticity of utility equals the elasticity of total costs”. Moreover, earlier Prof. Sergey Kokovin (HSE University, Russia) generated the idea that (3) “the search for equilibrium is equivalent to the problem of optimization, but revenue, not utility”. For the case of several countries, it turns out that facts (1) and (2) and prediction (3) remain mostly true. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
16 pages, 1730 KiB  
Article
Advance Dynamic Panel Second-Generation Two-Step System Generalized Method of Movement Modeling: Applications in Economic Stability-Shadow Economy Nexus with a Special Case of Kingdom of Saudi Arabia
by Mohd Ziaur Rehman, Shabeer Khan, Mohsin Ali, Faheem Ur Rehman, Wadi B. Alonazi and Mohammed Aljuaid
Mathematics 2023, 11(1), 85; https://doi.org/10.3390/math11010085 - 26 Dec 2022
Cited by 1 | Viewed by 1941
Abstract
Applying an advance dynamic panel second-generation two-step system generalized method of movement modeling, this study endeavors to bridge the gap in the literature by examining the association between shadow economy and economic stability in multiple countries with a special case of the Kingdom [...] Read more.
Applying an advance dynamic panel second-generation two-step system generalized method of movement modeling, this study endeavors to bridge the gap in the literature by examining the association between shadow economy and economic stability in multiple countries with a special case of the Kingdom of Saudi Arabia. The study has been motivated by the evidence that the shadow economy is a persistent source of the decline in tax revenue, which is the main source of funds for any economy to run welfare packages for the public. In addition, it also impacts the economy’s financial stability and amplifies the losses. Saudi Arabia is selected as a special case given its global significance and participation in the group of the fastest growing economies in the world. Thus, this study finds a negative association between the shadow economy and economic stability in the case of the full sample and a sub sample of Saudi Arabia. In other words, our study supports the point of view of those scholars who claim that the shadow economy is harmful to the economy. Based on the empirical findings, the study recommends that policymakers need to give importance to the shadow economy while formulating economic stability policies in the case of a full sample, especially in Saudi Arabia. Similarly, the robustness of the results is tested using different model specifications and alternative estimation techniques. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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16 pages, 1335 KiB  
Article
A Profit Maximization Inventory Model: Stock-Linked Demand Considering Salvage Value with Tolerable Deferred Payments
by Amisha Patel, Isha Talati, Ankit D. Oza, Dumitru Doru Burduhos-Nergis and Diana Petronela Burduhos-Nergis
Mathematics 2022, 10(20), 3830; https://doi.org/10.3390/math10203830 - 17 Oct 2022
Viewed by 1578
Abstract
Every business owner wishes that all sales were made on a cash basis, but in a cutthroat market, it is not always feasible. To entice buyers to purchase their goods, dealers may need to offer sales with credit terms. Unfortunately, selling with deferred [...] Read more.
Every business owner wishes that all sales were made on a cash basis, but in a cutthroat market, it is not always feasible. To entice buyers to purchase their goods, dealers may need to offer sales with credit terms. Unfortunately, selling with deferred payment conditions introduces a completely new facet of business management. Additionally, the salvage amount or value is significant for determining depreciation and can have an impact on the company’s overall depreciable amount used in its depreciation schedule. This study looks at an inventory model with the best possible pricing and ordering policy for retailers. Research is derived from when inventory is subjected to a constant deterioration rate and associated with appropriate salvage value. A perishable payments strategy inventory model is created, with the demand as a function of the stock level as well as selling price. Manufacturers provide to the retailer a tolerable deferred payment scheme to repay against the purchase products. That the cycle length and order size will rise under tolerable deferred period is refuted. The study’s goal is to determine the optimal replenishment cycle length and selling price to optimize retailer’s net income. With reference to cycle length and selling price, we developed an algorithm with a numerical example to optimize the net profit. The results are mathematically proven, and data is provided to validate the aforementioned model. Numerical examples are used to validate the model, and sensitivity analysis was performed. Using mathematical tools, a 3D graph will be used to demonstrate the concavity of the objective function. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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21 pages, 4083 KiB  
Article
Cluster Analysis of Financial Strategies of Companies
by Sergey Dzuba and Denis Krylov
Mathematics 2021, 9(24), 3192; https://doi.org/10.3390/math9243192 - 10 Dec 2021
Cited by 12 | Viewed by 4127
Abstract
Measuring the value of companies and assessing their risk often relies on econometric methods that consider companies as a set of objects under study, homogeneous in the sense of their use of financial strategies. This paper shows that cluster analysis methods can divide [...] Read more.
Measuring the value of companies and assessing their risk often relies on econometric methods that consider companies as a set of objects under study, homogeneous in the sense of their use of financial strategies. This paper shows that cluster analysis methods can divide companies into classes according to financial strategies that they employ. This indicates that homogeneity can be considered within these classes, while between-class companies should rather be perceived as heterogeneous. The clustering of companies has to be performed on quite a dense set of strategies, which requires a combination of formal and heuristic methods. To divide companies into classes, we used financial coefficients characterizing strategies for the 2030 largest non-financial companies within the time period from 2006 to 2018. As a result, a stable division into seven clusters/strategies was obtained. We revealed that some strategies were more characteristic for the companies of high-tech economy, while others were typical for the companies in basic industries. The dynamics of clusters is characterized by an increase in the share of risky strategies. A good meaningful interpretation of the resulting clustering confirms its consistency. The identified clusters can be used as dummy variables in econometric studies of companies to improve the quality of the results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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