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All Journal GEMA EKONOMI Imajiner: Jurnal Matematika dan Pendidikan Matematika Revitalisasi : Jurnal Ilmu Manajemen Jurnal Ekonomi Bisnis Manajemen Prima Action Research Literate (ARL) Al-MIKRAJ: Jurnal studi Islam dan Humaniora Abdimas Indonesian Journal Innovative: Journal Of Social Science Research Journal of Economics and Management Scienties Jurnal Cendekia Ilmiah
Eka Purwanda, Eka
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Religion Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Environmental Science Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Mathematics Public Health Social Sciences Other

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Model Matematis dan Analisis Statistik Indeks Efisiensi Investasi Pariwisata (T-CLEI) Musafa, Musafa; Purwanda, Eka
Imajiner: Jurnal Matematika dan Pendidikan Matematika Vol 8, No 3 (2026): Imajiner: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/imajiner.v8i3.27460

Abstract

This study develops a mathematical and statistical framework for analyzing tourism investment efficiency through the Tourism Capital–Leverage Efficiency Index (T-CLEI). The model is formulated as a fractional optimization problem using a Cobb-Douglas profit function and analyzed via differential calculus, Hessian matrix analysis, and logarithmic transformation. Existence and uniqueness of the optimal solution are rigorously proven using the Extreme Value Theorem and concavity analysis. A statistical framework applying the Delta Method provides first-order approximations for the expectation and variance of T-CLEI, enabling confidence interval construction. The central theorem establishes that the optimal solution is unique when the sum of output elasticities satisfies β + γ  1. The model contributes for tourism investment efficiency analysis with potential for empirical validation on panel data.
Co-Authors Aditya Aditya Akhmadi Akhmadi Arnovita, Dyah Kusuma Bachtiar, Renata Aghnia Farida Yuliaty Firdaus, Angga Eriksa Hasanah, Siti Romlah Jujun Junaedi Manurung, Muranny Nurshyaliha Martin Agusta Mudzakky, Fachrizza Mulyawati, Tin Musafa Musafa Pandu Prihanantyo, Andika Putri, Gita Dhitawati Qirom, Hafizzul setyaji, deny teguh Soamole, Syukri Sofia, Etty Suherman, Enang Susilawati, lena Titin Herawati Vip Paramarta