Shape of tile Scale Line
The following diagram (Fig. 19.9) shows how variations in the amounts of the factors used and in the output obtained determine the shape of the scale line. Suppose the return is constant so that doubling the amount of each factor results in doubling of the output.That is. a certain proportionate change in the amount of each factor used ‘leads to the change in the output exactly in the same proportion

In a situation like this. the scale lines will be straight through the origin. P’ Q’ R’ S’ . PQRS and P” _ Q” R” S” arc the three straight scales lines. The returns to scale along each scale line on the equal product map are constant. This is shown by the fact that the distance between the three equal product curves along each scale line is the same, i.e., OP = PQ = QR = RS and OP’ = P’ Q’ = R’ S’ , and so on. In a diagram like this, given relative factor prices, i.e., with a constant price slope, not only are the returns to scale constant but the returns to outlay are also constant. Similarly, the returns to scale and returns to outlay are interchangeable and the same. But if there is an equal product map where the relative prices are not constant and where the returns are not constant, the returns to scale and returns to outlay will not be the same. ‘When as the output changes, the proportion between factors also changes, it will be necessary to speak of returns to outlay instead of returns to scale. However, here for the sake of convenience and easy understanding, we assume that .proportion between the factors remains constant, whatever the scale of production.

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