Nonlinear input-output balance and Young duality: analysis of Covid-19 macroeconomic impact on Kazakhstan

We discuss the possibilities of the new approach to the inter-industry linkages modeling for the analysis of regional macroeconomic effects of Covid-19. Our approach is based on the mathematical framework of nonlinear input-output balance that allows to find the equilibrium point in the set of industry inputs and prices by solving the primal nonlinear resource allocation problem and the Young dual problem of prices formation. We identify and calibrate the model on the base of aggregated official input-output statistics of Kazakhstan. Given the scenario conditions for primal factors prices and final consumption in the economy the model allows to evaluate the new competitive equilibrium in the production network. The advantage of the model is non-linearity of balances and technologies that allows substitution of industry inputs. In the case of technologies with constant elasticity of substitution (CES) we apply the model to analysis of macroeconomic responses of the Kazakhstan economy to the Covid-19 pandemic.