On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology
This paper provides an economic and mathematical analysis of the long-run profit maximization problem of a monopolist with linear demand and a two-input Cobb-Douglas technology to derive the conditions that guarantee the solution to this problem. In addition, the conditions under which the closed-fo...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2025-01-01
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| Series: | Croatian Operational Research Review |
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| Online Access: | https://hrcak.srce.hr/file/473282 |
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| author | Zrinka Lukač Mira Krpan Vedran Kojić |
| author_facet | Zrinka Lukač Mira Krpan Vedran Kojić |
| author_sort | Zrinka Lukač |
| collection | DOAJ |
| description | This paper provides an economic and mathematical analysis of the long-run profit maximization problem of a monopolist with linear demand and a two-input Cobb-Douglas technology to derive the conditions that guarantee the solution to this problem. In addition, the conditions under which the closed-form solution can be derived and the conditions under which the monopolist's profit is positive are discussed. Whenever the problem has a unique solution, the closed-form defines the profit function well for the given demand function. The closed-form solution to the problem depends on the returns to scale. The problem has a unique solution for decreasing returns to scale, for which in general no closed-form can be found. On the other hand, the closed-form of the unique solution can easily be found for constant returns to scale. However, three sub-cases are identified for the case of increasing returns to scale. The analysis is supported by economic interpretations and numerical illustrations. |
| format | Article |
| id | doaj-art-963185965f344a67a0655d577a3f52c0 |
| institution | Kabale University |
| issn | 1848-0225 1848-9931 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj-art-963185965f344a67a0655d577a3f52c02025-08-20T03:28:29ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312025-01-0116211312610.17535/crorr.2025.0010On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technologyZrinka Lukač0Mira Krpan1Vedran Kojić2Faculty of Economics and Business, University of Zagreb, Zagreb, CroatiaFaculty of Economics and Business, University of Zagreb, Zagreb, CroatiaFaculty of Economics and Business, University of Zagreb, Zagreb, CroatiaThis paper provides an economic and mathematical analysis of the long-run profit maximization problem of a monopolist with linear demand and a two-input Cobb-Douglas technology to derive the conditions that guarantee the solution to this problem. In addition, the conditions under which the closed-form solution can be derived and the conditions under which the monopolist's profit is positive are discussed. Whenever the problem has a unique solution, the closed-form defines the profit function well for the given demand function. The closed-form solution to the problem depends on the returns to scale. The problem has a unique solution for decreasing returns to scale, for which in general no closed-form can be found. On the other hand, the closed-form of the unique solution can easily be found for constant returns to scale. However, three sub-cases are identified for the case of increasing returns to scale. The analysis is supported by economic interpretations and numerical illustrations.https://hrcak.srce.hr/file/473282closed–form solutionCobb-Douglas technologylinear demand functionlong-run profit maximizationmonopoly |
| spellingShingle | Zrinka Lukač Mira Krpan Vedran Kojić On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology Croatian Operational Research Review closed–form solution Cobb-Douglas technology linear demand function long-run profit maximization monopoly |
| title | On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology |
| title_full | On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology |
| title_fullStr | On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology |
| title_full_unstemmed | On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology |
| title_short | On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology |
| title_sort | on the closed form solution of the monopolist long run profit maximization problem with linear demand and cobb douglas technology |
| topic | closed–form solution Cobb-Douglas technology linear demand function long-run profit maximization monopoly |
| url | https://hrcak.srce.hr/file/473282 |
| work_keys_str_mv | AT zrinkalukac ontheclosedformsolutionofthemonopolistlongrunprofitmaximizationproblemwithlineardemandandcobbdouglastechnology AT mirakrpan ontheclosedformsolutionofthemonopolistlongrunprofitmaximizationproblemwithlineardemandandcobbdouglastechnology AT vedrankojic ontheclosedformsolutionofthemonopolistlongrunprofitmaximizationproblemwithlineardemandandcobbdouglastechnology |