The solution involves deriving a quadratic approximation of the representative household’s utility function around the efficient steady state.
Derive the log-linearized consumption Euler equation for a representative household with habit persistence in consumption (external habits). Solution Manual Gali Monetary Policy
(with habits) is obtained by rearranging: [ c_t = E_t[c_t+1] + h (c_t-1 - E_t[c_t]) - \frac1\sigma (r_t - \rho) ] The solution involves deriving a quadratic approximation of