  By applying copositivity criterion to the scalar potential of the economical
$3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions
at tree level. Although these are a large number of intricate inequalities for
the dimensionless parameters of the scalar potential, we present general
enlightening relations in this work. Additionally, we use constraints coming
from the minimization of the scalar potential by means of the orbit space
method, the positivity of the squared masses of the extra scalars, the Higgs
boson mass, the $Z'$ gauge boson mass and its mixing angle with the SM $Z$
boson in order to further restrict the parameter space of this model.
