18.2 Mathematical methods and models in economics

Problem: Let's suppose that \( y(t) \) is the national income at time \( t \). The consumption \( c(t) \) lags relative to \( y(t) \) according to the law \( c(t+1)=0,84 y(t)+4 \sin 0,7 t \). An entrepreneur makes investments if the increase of the national income is stable, i.e., \( i(t+2)=1,96(y(t+1)-y(t)) \). An equilibrium state is achieved under the following condition: \( y(t+2)=c(t++2)+i(t+2) \). Find the function of the national income under equilibrium conditions at time \( t \).