time_series.tex

$$ m_t [u'(f(x_t))   - v'(m_t) ] \leq \beta u'(f(x_{t+1})) \theta_{t+1}, \quad = \ {\rm if} \ m_t < \bar m. \EQN eqn_chang4000 $$

$$ \theta_t = u'(f(x_t)) (m_t + x_t), \EQN eqn_chang5a $$


$$ - x_t = m_t (1-h_t).  \EQN eqn_chang2 $$