Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem
The optimization of taxation and profit maximization constitute two fundamental and interconnected problems, inherently entwined as firms navigate within a given tax framework. Nonetheless, existing literature commonly treats these problems separately, focusing either on optimal taxation or on profi...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/5/825 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850051817711337472 |
|---|---|
| author | Zrinka Lukač Krunoslav Puljić Vedran Kojić |
| author_facet | Zrinka Lukač Krunoslav Puljić Vedran Kojić |
| author_sort | Zrinka Lukač |
| collection | DOAJ |
| description | The optimization of taxation and profit maximization constitute two fundamental and interconnected problems, inherently entwined as firms navigate within a given tax framework. Nonetheless, existing literature commonly treats these problems separately, focusing either on optimal taxation or on profit maximization independently. This paper endeavors to unify these problems by formulating a bilevel model wherein the government assumes the role of a leader, and the profit-maximizing monopolist acts as a follower. The model assumes technology given by a constant elasticity of substitution (CES) production function, with market prices following a linear demand curve. Since the solution for a general case with an arbitrary degree of homogeneity cannot be determined explicitly, analytical expressions for the tax revenue function, profit function, optimal tax rates, and optimal input levels are derived for scenarios with degrees of homogeneity set to values 0.5 for decreasing and 1 for constant returns to scale. Several illustrative numerical examples are presented alongside corresponding graphical representations. The last example, with a degree of homogeneity set to value 2, shows that the optimal solution is achievable under monopolist assumption even with increasing returns to scale, a scenario impossible under perfect competition. The paper ends with discussions on sensitivity analysis of the change in the optimal solution with regard to the change in the producer’s price. |
| format | Article |
| id | doaj-art-8a5f931f382e41ac8b6313101152c1b2 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8a5f931f382e41ac8b6313101152c1b22025-08-20T02:53:02ZengMDPI AGMathematics2227-73902025-02-0113582510.3390/math13050825Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game ProblemZrinka Lukač0Krunoslav Puljić1Vedran Kojić2Faculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, CroatiaFaculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, CroatiaFaculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, CroatiaThe optimization of taxation and profit maximization constitute two fundamental and interconnected problems, inherently entwined as firms navigate within a given tax framework. Nonetheless, existing literature commonly treats these problems separately, focusing either on optimal taxation or on profit maximization independently. This paper endeavors to unify these problems by formulating a bilevel model wherein the government assumes the role of a leader, and the profit-maximizing monopolist acts as a follower. The model assumes technology given by a constant elasticity of substitution (CES) production function, with market prices following a linear demand curve. Since the solution for a general case with an arbitrary degree of homogeneity cannot be determined explicitly, analytical expressions for the tax revenue function, profit function, optimal tax rates, and optimal input levels are derived for scenarios with degrees of homogeneity set to values 0.5 for decreasing and 1 for constant returns to scale. Several illustrative numerical examples are presented alongside corresponding graphical representations. The last example, with a degree of homogeneity set to value 2, shows that the optimal solution is achievable under monopolist assumption even with increasing returns to scale, a scenario impossible under perfect competition. The paper ends with discussions on sensitivity analysis of the change in the optimal solution with regard to the change in the producer’s price.https://www.mdpi.com/2227-7390/13/5/825optimal taxationCES production functionlinear demandbilevel programming |
| spellingShingle | Zrinka Lukač Krunoslav Puljić Vedran Kojić Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem Mathematics optimal taxation CES production function linear demand bilevel programming |
| title | Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem |
| title_full | Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem |
| title_fullStr | Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem |
| title_full_unstemmed | Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem |
| title_short | Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem |
| title_sort | maximizing tax revenue for profit maximizing monopolist with the ces production function and linear demand as a stackelberg game problem |
| topic | optimal taxation CES production function linear demand bilevel programming |
| url | https://www.mdpi.com/2227-7390/13/5/825 |
| work_keys_str_mv | AT zrinkalukac maximizingtaxrevenueforprofitmaximizingmonopolistwiththecesproductionfunctionandlineardemandasastackelberggameproblem AT krunoslavpuljic maximizingtaxrevenueforprofitmaximizingmonopolistwiththecesproductionfunctionandlineardemandasastackelberggameproblem AT vedrankojic maximizingtaxrevenueforprofitmaximizingmonopolistwiththecesproductionfunctionandlineardemandasastackelberggameproblem |