We propose a Bayesian approach to estimating productive capital stocks and depreciation rates within the production function framework, using annual data on output, employment and investment only. Productive capital stock is a concept related to the input of capital services to production, in contrast to the more common net capital stock estimates, representing market value of fixed assets. We formulate a full Bayesian model and employ it in a series of illustrative empirical examples. We find that parameters of our model, from which the time-path of capital is derived, are weakly identified with the data at hand. Nevertheless, estimation is feasible with the use of prior information on the production function parameters and the characteristics of productivity growth. We show how precision of the estimates can be improved by augmenting the model with an equation for the rate of return.

The article presents the possibility of using the Cobb-Douglas production function for planning in a turbulent environment. A case study was carried out – the Cobb-Douglas function was used to examine the condition of the Polish hard coal mining industry and the progress which has been made after undertaking certain activities aimed at increasing the competitiveness of coal companies over recent years. Only the correct and confirmed identification of the causes of irregularities in the production process can allow for the introduction of effective remedies. The effectiveness of the solutions proposed by the author has been confirmed thanks to the simulation during which the impact of the proposed production strategy on the parameters of the CD function was examined. Three variants of production functions models were created and production productivity rates and marginal substitution rates were determined. The results enabled the verification of the progress of restructuring as well as identification of the origin of the observed problems and comparison of the current state with the results of analyses carried out in previous years. Scenarios of possible trend developments for the factors introduced into the function model in order to present remedial measures that could improve the process of hard coal extraction were created. The scenarios were created using the ARIMA class models. Which scenario is the most favourable was determined. A computer program, created by the author, for optimising the level and use of labor resources at the level of the entire coal company has been presented.