This paper deals with the critical elastic behavior of a two-dimensional micropolar (or "granular") network with randomly rigid or elastic bonds. It presents a new derivation of Feng's inequalities $1l{s}^{\ensuremath{'}}ls$ in the context of micropolar elasticity (where $s$ is the conductivity exponent, ${s}^{\ensuremath{'}}$ the elastic-moduli exponent). In addition, an exact calculation on a fractal model suggests that ${s}^{\ensuremath{'}}=s\ensuremath{-}{\ensuremath{\Delta}}^{S}$, where ${\ensuremath{\Delta}}^{S}$ is a correction of order 20%. This correction results from the rotations of the rigid clusters, and differs from the "eccentricity" correction ${\ensuremath{\Delta}}^{E}$ found in the elastic case.