The paper discusses the application of the Bayesian stochastic frontier cost functions as a tool for assessing and comparing the cost efficiency of firms. The analysis is based on the microeconomic production theory and the concept of inefficiency that is related to the existence of inner mechanisms responsible for observing costs higher than indicated by theory, given technical and economic environment of firms. The stochastic cost frontier a llows to estimate individual cost efficiency and to precisely decompose the observed cost into theoretical categories, such as minimal excessive or systematic cost, which play crucial role in assessing the economic behavior of firms. From the empirical perspective the most important is the minimal cost, which denotes the cost that is indispensable to achieve the observed production level giv en technology, input prices, cost effects of random variability. The Bayesian estimation of stochastic cost frontiers for panel data allows to treat a number of issues unsolved on the classical ground, such as stability of empirical results, assessment of the uncertainty of cost categories and efficiency coefficients. As a fundamental tool for the analysis we present the Bayesian random effects mode l with constant efficiency distribution. The methodology is illustrated with the cost function for the 14 firms operating in the electricity distribution sector observed over 6 years.