DSE 2015 Question 17: Business cycles and rational expectations

With $C_t=\alpha Y^e_t$ ($0<\alpha<1$) and $I_t=\gamma(Y^e_t)^2$ ($\gamma>0$), output is demand-determined ($Y_t=C_t+I_t$). Under static expectations, starting from any $Y_0\ne\tfrac{1-\alpha}{\gamma}$, in the long run actual output