『Abstract
　The production and the depletion of mineral resources, and especially oil and fossil fuels, has been an object of extensive predictive modeling. These predictions are often derived from Hubbert's model which is based on the fitting of the experimental data to a symmetric, bell-shaped curve. Although this model describes several historical cases, in particular, crude oil production in the lower 48 US states, not all theoretical models for the “mineral economy” are based on symmetric curves. also, not much attention has been dedicated so far to the mechanisms which lead to such a behavior. In particular, scarce attention has been dedicated to the factors which may make the production curve asymmetric, e.g. a decline in production more abrupt than the growth. In the present paper, the author uses a stochastic model to examine factors affecting these phenomena. The results of the simulations indicate that the production curves of a non-renewable resource may be asymmetric in dependence on factors such as the search strategy or the presence of technological improvements. Considering worldwide oil production, the simulations indicate that the after-peak downward slope might turn out to be considerably more steep than the upward slope, something that could have unpleasant effects on the economy.

Keywords: Hubbert; Oil depletion; Mineral economy』

1. Introduction
2. Models for the mineral economy
3. Results and discussion
4. Conclusion
Acknowledgements
References