What is the simplified form of the production function expressed per worker?

The production function expressed per worker shows how output is related to the amount of capital available per worker. The correct form is represented as ( y = f(k) ), where ( y ) denotes output per worker, and ( k ) represents capital per worker. This reflects the foundational concept in macroeconomics where output depends on the inputs used in production, specifically capital and labor.

In this context, ( f(k) ) implies that as the quantity of capital per worker increases, the output per worker will likewise increase, illustrating the relationship between capital deepening and productivity. This aligns with the standard model of economic growth where the productivity of labor is tied to its access to capital, hence the function ( f ) captures the idea of diminishing returns to capital in a production setting.

The other choices do not capture this relationship accurately regarding output per worker. For instance, the equation ( y = K/L ) represents output per worker in terms of total capital and total labor directly but lacks the functional form that expresses the relationship in terms of productivity and capital intensity. Equations like ( y = c + i ) or ( y = I + C ) represent different relationships, focusing on components of national income or expenditure rather than the