What does the formula k = sf(k) - (depreciation + n)k represent?

The formula k = sf(k) - (depreciation + n)k represents the change in capital per worker, which is an essential concept in macroeconomic growth models, particularly in the Solow Growth Model.

In this equation, "k" signifies the capital per worker, "s" is the savings rate, "f(k)" is the production function that describes how output depends on capital, "depreciation" refers to the rate at which capital loses its value over time, and "n" is the population growth rate. The term "sf(k)" denotes the total investment in new capital, while "(depreciation + n)k" accounts for the capital that must be replaced due to depreciation and to equip new workers entering the labor force.

The change in capital per worker is central to understanding how economies grow over time. When investment exceeds the combined losses from depreciation and the need to support a growing workforce (n), the capital per worker increases, fostering higher productivity and output. Conversely, if depreciation and new worker requirements surpass investment, capital per worker diminishes, indicating a decline in productivity.

This framework allows economists to analyze how various factors, such as changes in savings rates or technology, influence capital accumulation and economic growth.