The impedance for a monopole antenna is derived and compared with the cases for wire dipole and double-sphere antennas. This derivation produces a new expression for the monopole antenna response function, $F_{m1}(x)$. The monopole, wire dipole, and double-sphere response functions are compared by modeling an antenna in Earth's ionospheric plasma (i.e. electrostatic and collisionless) and predicting the antenna capacitance and voltage power spectra for quasi-thermal noise (QTN) and shot noise. The monopole antenna current distribution is assumed to be a half-triangular current distribution (considering only the positive half of the triangular distribution). The predictions for the shot noise and capacitance presented problems, as the integral over wavenumber-space or $k$-space did not converge for large values of $k$. The derived expression therefore remains a current problem and necessitates future work to determine a more general expression. In this paper we bring the problem of an appropriate analytic monopole antenna response function to the attention of the community and outline a number of tests that can be used to verify any future expression.