The Optimal Timing of New Plants for Oil from the Alberta Tar Sands

In this paper we use an optimal control model to examine whether early exploitation of the vast Alberta tar sands resource may be justified due to constraints on the availability of construction resources for tar sands plants. We model conventional oil as an exhaustible resource whose unit production cost increases with cumulative production, and tar sands oil as a virtually inexhaustible resource (a backstop) having constant unit production cost initially much higher than that of conventional oil. There is a finite, time-dependent maximum rate of increase in tar sands production capacity. The problem involves a state-space constraint inasmuch as the tar sands production rate (a state variable) cannot exceed the exogeneous demand rate at any time. In a discounted cost formulation for sufficiently large finite, or infinite, planning periods, we show that the optimal policy is to use conventional oil alone until some critical time and then expand tar sands capacity at a maximum rate until it equals total demand, after which all demand is met through tar sands oil alone. We discuss an unexpected “cost overshoot”—the unit cost of conventional oil exceeds that of tar sands oil at the time of transition to total reliance on the tar sands backstop. Using plausible functional forms and parameter values, we conclude that construction of new tar sands plants should be deferred for several years, although other considerations not dealt with in our examination may have a significant effect on this conclusion.