18.3 Mathematical methods and models in economics

Problem: The model of intersectoral balance, where the product intended for domestic and final consumption in period \( t \), is determined by the output in the subsequent period \( t+1 \) assuming a constant share of domestic consumption by each industry, will have the form: \[ \left\{\begin{array}{l} x(t+1)=0,5 x(t)+0,1 y(t)+40 \\ y(t+1)=0,4 x(t)+0,5 y(t)+60 \end{array}\right. \] At the initial moment of time the gross output of each of the industries is \( x(0)=100, y(0)=100 \). It is required to calculate the vector of the gross output of each of the industries at the moment \( t=2 \), if the final consumption components increase by \( 30 \% \) for each period.