The paper develops a nonlinear input-output model for analyzing medium-term changes in production networks under external shocks. The theoretical framework is formulated for a general class of neoclassical production functions and combines an optimal resource-allocation problem with Young dual equilibrium price equations. Unlike the classical linear input-output balance with fixed coefficients, the proposed approach allows endogenous changes in technological coefficients caused by shifts in relative prices and substitution effects. For the applied analysis, a model with nested Cobb-Douglas-CES technologies is constructed for Kazakhstan using official symmetric input-output tables. Identification and calibration of the model provide estimates of substitution elasticities for aggregated sectoral complexes of the economy. The model is then tested on input-output data for 2012-2024 and compared with the linear Cobb-Douglas balance model. The numerical results show that the nonlinear model provides more accurate medium-term reconstruction, especially for sectors with more flexible substitution mechanisms.