We investigated the consequences of variable potential softness on elastic properties, using the repulsive inverse power potential. With this potential the softness can be changed continuously from very soft to extremely steep or hard. An explicit formula for the equation of state is derived and discussed. It is shown how this formula can be exploited to determine the infinite frequency elastic properties of the inverse power fluid. Explicit formulae for the elastic constants, the high-frequency elastic moduli, the longitudinal- and transverse-wave velocities and Poisson's ratio are obtained. Their behaviour in the steeply repulsive limit is discussed. It is demonstrated that the softness directly determines the Poisson's ratio, and it is shown that in order to decrease the value of the Poisson's ratio a harder potential interaction must be applied.