Recent developments in high reliability components for linear induction accelerators (LIA) make possible the use of these devices as economical power drives for very high gradient linear colliders. A particularly attractive realization of this ''two-beam accelerator'' approach is to configure the LIA as a monolithic relativistic klystron operating at 10 to 12 GHz with induction cells providing periodic reacceleration of the high current beam. Based upon a recent engineering design of a state-of-the-art, 10- to 20-MeV LIA at Lawrence Livermore National Laboratory, this paper presents an algorithm for scaling the cost of the relativistic klystron to the parameter regime of interest for the next generation high energy physics machines. The algorithm allows optimization of the collider luminosity with respect to cost by varying the characteristics (pulse length, drive current, repetition rate, etc.) of the klystron. It also allows us to explore cost sensitivities as a guide to research strategies for developing advanced accelerator technologies.