Before explaining returns to scale it will be instructive to make clear the distinction between change in the scale and changes in factor proportions. The difference between the changes in scale and changes in factor proportions will become clear from the study of where the two factors labour and capital have been measured on the X axis and Y-axis respectively. We suppose that only labour and capital are required to produce a particular product. An Isoquants map has been drawn. A point S has been taken on the Y –axis ad the horizontal line ST parallel to X axis has been drawn. OS represents the amount of capital which remains fixed along the line ST. as we move towards right on the line ST the amount of labour varies while the amount of capital remains fixed at OS. In other words proportion between the two factors undergoes a change along the line ST the ratio of the variable factor labour to the fixed factor capital rises as we move towards right on the line St. thus the movement along the line ST represents variation in factor proportions. Likewise a vertical line GH parallel to the Y-axis has been drawn which also indicated changes in facto proportions. But in this case the quantity of labour remains fixed while the quantity of capital varies.
Now, draw a straight line OP passing through the origin. It will be seen that along the line OP the inputs of both the factors labour and capital vary moreover because the lineup is a straight line through the origin the ratio between the two factors along OP remains the same throughout. Thus the upward movement along the line Op indicates the increase in the absolute amounts of two factors employed with the proportion between two factors remaining unchanged. Assuming that only labour and capital are needed produce a product then the increase the two factor along the line OP represents the increase into eh scale since along the line Op both the factors increase in the same proportion and therefore proportion between the two factor remains unaltered. If any other straight line through the original such as OQ or is drawn it will show like the line Op the changes in the scale but it will represent a different given proportion of factor which remains the same along the line. That is the various straight lines through the origin will indicate different proportions between the two factors but on each line the proportion between the two factors remains the same throughout.