AbstractOur model minimizes the discounted cost of meeting projected Canadian oil demand from the currently inexpensive but limited conventional oil, more expensive tar sands and still more expensive imports. We limit the rates of increase of the three sources of supply and impose non‐negativity constraints on two of the state variables, conventional supply and imports. The optimal control is generalized bang‐bang, but the set of extreme points depends on the status of the state constraints. All possible optimal sequences of extreme point controls are determined. Implications for tar sands development policy are discussed, along with economic interpretations and additions to the theory of exhaustible resour
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