Abstract:
The global macroeconomic shocks of the last decade entail the restructuring of national
production networks and induce processes of input substitution. We suggest mathematical tools of
Young duality for variational inequalities for studying these processes. Based on the tools we provide,
a new mathematical model of a production network with several final consumers is created. The
model is formulated as a pair of conjugated problems: a complementarity problem for optimal resource allocation with neoclassical production functions and the Young dual problem for equilibrium
price indices on network products. The solution of these problems gives an equilibrium point in the
space of network inter-industry flows and price indices on goods. Based on our previous results, we
suggest an algorithm for model identification with an official economic statistic in the case of constant
elasticity of substitution production functions. We give an explicit solution to the complementarity
problems in this case and develop the algorithm of the inter-industry flows scenario projection. Since
the algorithm needs the scenario projection of final sales structure as its input, we suggest a modified
methodology that allows the calculation of scenario shifts in final consumer spending. To do this,
we employ the generalized nonparametric method of demand analysis. As a result, we develop
new technology for scenario calculation of a national input–output table, including shifts in final
consumer spending. The technology takes into account a substitution of inputs in the network and is
based on officially published national statistics data. The application of the methodology to study tax
collection scenarios for Kazakhstan’s production network is demonstrated.
