A regulator usually has less information (about costs, technology, etc) than the firm it regulates. This can lead to strategic behaviour and inefficient results. While cost-plus regulation will lead to cost overruns, price cap systems can lead to huge rents for efficient firms. Optimal regulation must take into account these incentives and may not achieve first best levels of efficiency, but will trade off efficiency gains and distributional concerns.
Laffont & Tirole (1986) Journal of Political Economy