Factor intensity and order of resource extraction

This paper characterizes the optimal time paths of extraction of several nonrenewable resource deposits with different costs of extraction when the extracted resource can be converted into productive capital and the extraction process, as well as the production of the substitute, requires two primary factors of production. Under a technological assumption granting that the time paths of primary factor prices are monotonic, we show that, for each pair (lower cost/higher cost) of deposits, an intensity condition is necessary in order to have discontinuous extraction of the lower cost deposit. We also show that the same condition is sufficient for discontinuous extraction of the lower cost deposit, provided the stock of the lower cost deposit is sufficiently large and the stocks of all other deposits are sufficiently small.