Maximizing Tax Revenue for Profit-Maximizing Monopolist with the CES Production Function and Linear Demand as a Stackelberg Game Problem

Zrinka Lukač (), Krunoslav Puljić and Vedran Kojić
Additional contact information
Zrinka Lukač: Faculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, Croatia
Krunoslav Puljić: Faculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, Croatia
Vedran Kojić: Faculty of Economics & Business, University of Zagreb, Trg J. F. Kennedyja 6, 10 000 Zagreb, Croatia

Mathematics, 2025, vol. 13, issue 5, 1-19

Abstract: 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.

Keywords: optimal taxation; CES production function; linear demand; bilevel programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/825/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/825/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:825-:d:1603111

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().