This work uses various model frameworks to study the evolution of equilibria in an open loop evolving economy in which the model characteristics evolve without any directional restrictions except for continuity. Applying mathematical methods, it is shown that equilibria can always be adapted in a piecewise gradual, non bang-bang way. Furthermore, the analysis provides a complete characterization of the structure of the equilibrium price set of evolving exchange economies. The results allow to derive policy implications for a gradual, frictionless tuning of equilibrium values for open loop evolving economies. The analysis is innovative in both its approach and its results. It contributes to bridging the gap between the traditional static, closed loop, dynamic equilibrium approach and the idea of open loop evolution which has become an attractive concept in economics in recent years.