Mathematical Modeling and Optimization of Nepal’s Export–Import Dynamics for Sustainable Economic Growth

Abstract

Nepal presents one of the most instructive external-balance puzzles in the developing world: five decades of progressive trade liberalization have coexisted with a secular deterioration of the trade balance, from a deficit of roughly five percent of GDP in the mid-1970s to nearly twenty-eight percent in 2024, while exports contracted from about fifteen percent of GDP at their turn-of-the-century peak to under seven percent. This paper constructs a fully articulated mathematical framework to explain this trajectory and to design a correction. We develop a continuous-time dynamic model of the external accounts in which the net international investment position and the real effective exchange rate co-evolve under an intertemporal solvency constraint, we characterize the equilibrium structure of the resulting planar system, and we prove that the unregulated economy lies on a saddle path along which external solvency is restored only through implausibly large real depreciations. The model is then enriched with lagged volume adjustment, which delivers a Marshall–Lerner-consistent J-curve with an impact deterioration of 1.65 percentage points of GDP and a break-even horizon of roughly eight and a half quarters. Cointegration and error-correction representations, a structural gravity block, and a Kalman-filtered stochastic extension provide the econometric and filtering scaffolding for calibration. Finally, we solve a discounted linear-quadratic optimal control problem in closed form: the Hamiltonian system decouples into stable and unstable eigenvalue pairs summing to the discount rate, the value function solves an algebraic Riccati equation exactly, and the resulting linear feedback rule cuts the discounted external-adjustment loss by about sixty-one percent over a fifty-year horizon relative to passive drift. Numerical experiments, including a sensitivity surface over structural elasticities and stochastic fan charts under real-exchange-rate diffusion, quantify the fragility of unmanaged adjustment and the robustness of the optimized policy.