  It is possible to extract values for critical couplings and gamma_string in
matrix models by deriving a renormalization group equation for the variation of
the of the free energy as the size N of the matrices in the theory is varied.
In this paper we derive a ``renormalization group equation'' for the Penner
model by direct differentiation of the partition function and show that it
reproduces the correct values of the critical coupling and gamma_string and is
consistent with the logarithmic corrections present for g=0,1.
