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Turnover tax. A tax levied as a proportion of the price of a commodity on each sale in the distribution chain; also called a cascade tax. value added tax.

Turnpike theorems. Propositions about the nature of optimal paths of economic growth for an economy. Suppose one wants to get from location A to a reasonably distant location B, neither of which may be at a motorway access point, and which may be connected by an ordinary road network. Given the speed differential between travel on a motorway and on an ordinary road, and given the distance between A and B, the quickest way of making the trip may be to drive from A to the motorway, travel along it, and then leave it and drive to B. This is a very simple example of the kind of proposition presented by the turnpike theorems (turnpike’ is the American term for a motorway). The analogue to the motorway is the maximal balanced growth path of the economy, i.e. a time-path of outputs of each industrial sector of the economy which has the two properties that: (a) at each point in time supply of each output is equal to its demand, so that the economy is continuously in equilibrium, and (b) the growth rate of the economy (which, in the kind of model analysed, is the common growth rate of each industrial sector) is greater than that along any other balanced growth path. The counterpart to location A is the current set of outputs in the economy; and the counterpart to location B is a future desired

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