In year 1, the owner of the mine will generate an output level of 90 tons. This is illustrated below in figure 1. This illustrated in figure 2 below. In Hotelling's perfectly competitive model, resources are treated as assets within a mine owner's portfolio. Profit maximising mine owners must decide between extracting today or extracting in the future.
Substitution occurs until no gains can be made from shifting extraction from one period to another.
Assets in the mine will be depleted and the proceeds will be invested where better returns are available. As stated previously, the market rate of interest is the proxy for returns on alternative assets. Thus, the owner of the mine will be indifferent between depletion and liquidation when the value of assets in the mine appreciate at the same rate as the market rate of interest. Hotelling's analysis can be illustrated by returning to the numerical example. Hotelling used the calculus of variations to maximise total surplus subject to the finite resource constraint.