<![CDATA[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.]]>
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