Introduction

The Solow-Swan model explains long-run economic growth by tracking how a country's capital stock evolves over time. Developed independently by Robert Solow and Trevor Swan in 1956, it shows that an economy converges to a unique steady state determined by the savings rate, depreciation, and population and technology growth — regardless of where it starts.

The Solow-Swan model is the bedrock of modern growth theory. It answers one of the most fundamental questions in economics: why are some countries rich and others poor, and what determines the long-run standard of living of a nation?

At its core, the model says: capital accumulates when investment exceeds depreciation. Over time, an economy converges to a unique steady state — a point where output per worker stops growing (absent technological progress). The speed and destination of that journey depend on the savings rate, population growth, and technology.

Despite being built on stark simplifying assumptions, the model generates powerful, testable predictions about cross-country income differences, the returns to saving, and the nature of economic convergence.

Before writing any equation, three core economic mechanisms build the model's intuition.

Capital — factories, machines, infrastructure — enables workers to produce more. But capital has two competing forces acting on it: investment adds to the capital stock, and depreciation wears it down.

The capital stock grows when investment outpaces depreciation:

As more capital is added to a fixed number of workers, each additional unit contributes less to output than the last. This diminishing marginal product of capital is what prevents growth from compounding forever.

As capital accumulates, the benefit of adding more weakens while the cost of maintaining it grows proportionally. Eventually these forces balance.

The model's elegance comes from analysing everything per unit of effective labour. This collapses a two-dimensional problem (capital + labour) into a one-dimensional one.

Define $k = K/(AL)$ (capital per effective worker) and $y = Y/(AL)$ (output per effective worker). The entire dynamics of the economy are then described by the evolution of $k$ alone.