How is investment per worker represented in relation to output?

Investment per worker is critical in macroeconomic models, especially in the context of growth theory. The correct representation of investment per worker in relation to output is articulated via the equation ( i = sf(k) ).

In this formula, ( i ) represents investment per worker, ( s ) denotes the savings rate, and ( f(k) ) is the output per worker function, where ( k ) stands for capital per worker. The equation indicates that the investment per worker is determined by the fraction of output that is being saved (the savings rate) multiplied by the output generated per worker.

This relationship emphasizes the critical connection between savings and investment in driving economic growth. The output per worker function ( f(k) ) captures the productivity of capital in relation to labor, illustrating how additional capital increases output. Therefore, the investment per worker is directly tied to both the savings behavior of the economy and the productive capabilities reflected in the output per worker.

Alternative representations do not accurately capture this concept by either misdefining the relationship between output, capital, and investment, or by misrepresenting the nature of savings and output conversion. For instance, while other expressions may involve production functions or total output, they do not specifically address the per worker