Country Travel Economy
Turnpike theorems set of outputs. Turnpike theorems analyse the conditions under which the fastest growth path from one set of outputs to the other will involve moving along, or, more accurately, moving close to, the maximal balanced growth path. The significance of the analysis lies in the point that if, under a wide range of circumstances, the maximal balanced growth path does have this ˜turnpike’ property, then it must play a central role in models which plan for optimal growth. In fact, the theorems do not establish the extreme turnpike property of our motoring example, in that it is not in general best to move as quickly as possible to the maximal balanced growth path, move along it, then come off as close as possible to the final destination. Rather, the theorems prove weaker propositions of the following type: provided that the terminal date is ˜sufficiently’ far away, the optimal growth path will require that ˜much’ of the time be spent travelling ˜close’ to the maximal balanced growth path (where of course the terms ˜sufficiently’, ˜much’ and ˜close’ are given precise mathematical expression). Given the two end points, the optimal path between them will curve away from the straight line joining them, in the direction of the maximal balanced growth path. (Note that in the economic model, there is no disadvantage in travelling across country.) Thus the significance of the maximal balanced growth path to planning economic growth is established, but in a more limited sense than would be so if the full turnpike property were to hold.
Unavoidable costs fixed costs; marginal cost.
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