Solowmodel

The Solow model, named after Robert Solow, is a foundational neoclassical framework for analyzing long-run economic growth with exogenous technological progress. It combines a production technology with a controlled accumulation of capital, recognizing diminishing returns to capital.

The production function F(K, AL) has constant returns to scale, where K is physical capital, L is labor, and A represents technology (productivity). By defining per-effective-worker variables y = Y/(AL) and k = K/(AL), the model can be written as y = f(k). The evolution of capital per effective worker is governed by dk/dt = s f(k) − (n + g + δ) k, where s is the saving rate, δ is depreciation, n is population growth, and g is the growth rate of technology.

A steady state occurs when dk/dt = 0, implying s f(k*) = (n + g + δ) k*. In this steady state, output per worker is y* = f(k*), and consumption per worker is c* = (1 − s) f(k*). Because technology grows at rate g, long-run growth in per-capita terms is determined by g rather than by s, once the steady state is reached. The model predicts conditional convergence: economies with similar s, n, and g but different initial k will tend to converge in per-capita income.

Implications include the influence of the saving rate on the steady-state level of capital and output, the effects of higher population growth or slower depreciation on steady-state capital, and the golden rule for maximizing consumption, which occurs when f′(k) = δ + n + g. The Solow model provides a baseline for growth accounting and has been extended to include human capital, technology spillovers, and endogenous growth mechanisms.