Regularity of a general equilibrium in a model with infinite past and future

We develop easy-to-verify conditions assuring that comparative statics in a general equilibrium model where time is a real line is feasible, i.e., the implicit function theorem is applicable. Consider an equilibrium equation, $Upsilon(k,E)=k$ of a model where an equilibrium variable (k) is a continuous bounded function of time, real line, and the policy parameter (E) is a locally integrable function of time. The key conditions are time invariance of the equilibrium map $Upsilon$ and the requirement that the Fourier transform of the derivative of the map $Upsilon$ with respect to the equilibrium variable k does not return unity. Further, in a general constant-returns-to-scale production and homogeneous life-time-utility overlapping generations model we show that the first condition is satisfied at a balanced growth equilibrium and the second condition is satisfied for ``almost all'' policies that give rise to such equilibria.