Let Co(p) be the class of all functions f defined in the unit disc D having a simple pole at z = p where 0 < p < 1 and analytic in D {p} with f (0) = 0 = f ́(0) − 1 such that f maps D onto a domain whose complement with respect to the extended complex plane is a bounded convex set. These functions are called concave univalent functions. Each f ∈ Co(p) has the following Taylor expansion: (Farmula Presented) In this article, we first determine the regions of variability of the difference of successive coefficients (an+1 − an) for n ≽ 3 . We also find sharp upper bounds of the Toeplitz determinants, the entries of which are the Taylor coefficients of functions in Co(p) .