JNU SSS 2017 Question 41: Keynesian cross and the multiplier

Consider a closed economy without government spending or taxes. The equilibrium value of output in each period is determined by the equality of (the value of) output and expenditure. Saving in period $t$ is given by $S(t) = s \cdot Y(t)$ and investment expenditure in period $t + 1$ is given by $I(t + 1) = a + b \cdot Y(t)$, for all values of $t$. $a$ is a positive constant, $s$ and $b$ are positive constants less than unity and $Y(t)$ is the value of output in period $t$. What relation must hold between the values of $s$ and $b$ for there to exist a value of output in this economy, which once achieved in a time period will continue to persist in subsequent periods of time?