Final answer:
To find an expression for Yt, substitute the expressions for Ct and It into the equation for Yt. Calculate Y1, Y2, and so on using the equation Yt = 0.8Yt-1 + 600. The system is stable as it converges to a steady-state value.
Step-by-step explanation:
The two-sector model is represented by the equations:
Yt = Ct + It
Ct = 0.7Yt-1 + 400
It = 0.1Yt-1 + 200
To find an expression for Yt, we can substitute the expressions for Ct and It into the equation for Yt:
Yt = 0.7Yt-1 + 400 + 0.1Yt-1 + 200
Simplifying the equation, we get:
Yt = 0.8Yt-1 + 600
Given that Y0 = 3000, we can calculate Y1, Y2, and so on using the equation:
Yt = 0.8Yt-1 + 600
Therefore, Y1 = 0.8 * 3000 + 600 = 3000 + 600 = 3600
Similarly, Y2 = 0.8 * 3600 + 600 = 2880 + 600 = 4200
Y3 = 0.8 * 4200 + 600 = 3360 + 600 = 4800
...
The system is stable because it converges to a steady-state value, which is 6000 in this case.