Nonlinear input-output balance and Young duality: Analysis of COVID-19 macroeconomic impact on Kazakhstan

Abstract

We discuss the possibilities of the new approach to the interindustry
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.