The economic simulation design is, given performance requirements, designing the simulation of a linear system and distributing precision among the instruments such that the computational cost is minimized without violating the simulation accuracy. In this paper, we consider the simulation of a large-scale linear system in digital devices with fixed-point arithmetic and finite wordlength. Given the output variance upperbound, we focus on finding an optimal realization and the allocation of wordlength among A/D converter, computer and sensors. This problem is in general not convex because of the scaling constraint. By exploring the special structure of this joint optimization problem and under mild assumptions, we simplify this problem and find the optimal coordinate transformation and the wordlength allocation scheme simultaneously by solving LMIs (linear matrix inequalities). Numerical results are given which compare this new realization with the balanced realization and random realizations.