Models of economic growth

Growth models turn stories about accumulation into equations. Harrod-Domar says growth equals the saving rate divided by the capital-output ratio: save more or use capital more efficiently, and growth rises. Solow adds diminishing returns to capital and technology, predicting that economies converge to a steady state where growth comes only from technological progress. Worked example: with a saving rate of 12% and a capital-output ratio of 3, Harrod-Domar growth is 12/3 = 4% a year; and in Solow with saving rate 0.2, depreciation 0.05 and output per worker y = k^0.5, the steady state solves 0.2 x sqrt(k) = 0.05k, giving sqrt(k) = 4, so k = 16 and y = 4.