What calculation is used to derive the steady-state output per worker?

The steady-state output per worker is derived by evaluating the production function at the level of capital per worker, often denoted as k*. In macroeconomic theory, specifically in the Solow growth model, the production function relates the amount of capital available per worker to the overall output produced by those workers.

At the steady-state, the economy reaches a condition where capital per worker remains constant over time. This occurs when the amount of investment in new capital equals the amount of capital that wears out or depreciates. The steady-state output per worker, therefore, is fundamentally tied to the production function evaluated at this steady-state level of capital (k*).

Evaluating the production function at k* captures how much output can be generated per worker when the capital is neither increasing nor decreasing—essentially the long-run output level that an economy can sustain without external shocks impacting its capital stock. By focusing on this level, we can gain insights into the efficiency and productivity of the economy under conditions where growth stops, leading to a clearer understanding of output stability in the long term.