Question

Write the equation for the basic production function (Solow model) that macroeconomists use to understand GDP in the long run and give a written definition of each variable in the equation.

Answer 1

All firms in the economy produce output using the same production technology that takes in capital and labor as inputs. Therefore, the level of output (represented by Y), the level of capital (represented by K), and the level of labor (represented by L) are all linked through the production function equation Y = aF(K,L).

The Solow Growth Model assumes that the production function exhibits constant-returns-to-scale (CRS). Under such an assumption, if we double the level of capital stock and double the level of labor, we exactly double the level of output. As a result, much of the mathematical analysis of the Solow model focuses on output per worker and capital per worker instead of aggregate output and aggregate capital stock.