T. W. Swan Economic Growth

In Chart (1), the line $$\frac{Y}{L}$$ Y L shows real output per worker, in a given productive environment, as a function of $$\frac{K}{L}$$ K L (the slope of $$\frac{Y}{L}$$ Y L rises from left to right, because each unit of labour is more productive the larger the capital stock it has to work with. (Consider only the heavier inked lines for the moment.) The other three curves can all be derived without any additional data once the Curve $$\frac{Y}{L}$$ Y L is known. $$\frac{Y}{K}$$ Y K , real output per unit of capital, is obtained simply by dividing $$\frac{Y}{L}$$ Y L at any point by the corresponding value of $$\frac{K}{l}$$ K l . The curve $$R$$ R shows the marginal productivityproductivity" of capital $$\left(=\frac{dY}{dK}\right)$$ = dY dK —the rate of return in terms of product $$Y$$ Y for a small increase in $$K$$ K , unaccompanied by any increase in $$L$$ L ; the level of $$R$$ R is the slope of $$\frac{Y}{L}$$ Y L at the corresponding point.