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The Harrod-Domar model, built on work by Roy Harrod (1939) and Evsey Domar (1946), assumes output is proportional to the capital stock, Y = K/v, where v is a fixed capital-output ratio. Since investment equals saving, the capital stock grows by sY − δK each year, which gives the growth rate g = s/v − δ. Growth therefore rises with the saving rate and falls with the amount of capital needed per unit of output. Development agencies used this logic for decades to compute a "financing gap" between the investment needed for a target growth rate and domestic saving, to be filled by foreign aid or borrowing. Its fixed capital-output ratio and neglect of productivity and institutions are its main weaknesses.
Compute growth for a few combinations of saving rates and capital-output ratios, then reverse the calculation to find the saving or aid needed for a target growth rate. Then compare the model's prediction with cases where high investment did not produce fast growth. That comparison motivates the Solow model and the later emphasis on productivity and institutions.
After World War II, economists wanted a simple way to think about how poor countries could grow. The Harrod-Domar model gave one. It grew out of Roy Harrod's 1939 essay on dynamic theory and Evsey Domar's 1946 paper on capital expansion, and it became the backbone of what development textbooks call linear-stages theories.
The model rests on two assumptions. First, output is proportional to capital: Y = K/v, where v is the capital-output ratio, the amount of capital needed to produce one unit of output per year. Second, from the saving-investment identity, the part of output that is saved becomes new capital. If s is the saving rate and δ the depreciation rate, the change in capital is ΔK = sY − δK. Dividing by K, and using Y/K = 1/v, gives the growth rate of capital, and therefore of output: g = s/v − δ.
The formula says two things. Saving more speeds growth. And economies that need less capital per unit of output grow faster from the same saving. With s = 20%, v = 4, and no depreciation, the economy grows 5% a year.
Planners ran the formula backward. If the target growth rate is g, required investment is (g + δ)v. Subtract domestic saving, and what remains is the financing gap, to be filled by foreign aid or capital inflows. A country targeting 7% growth with v = 3 needs to invest 21% of GDP; if it saves 15%, the gap is 6%. The Marshall Plan's success in rebuilding Western Europe seemed to support the idea that capital was the missing ingredient. W. W. Rostow's 1960 *The Stages of Economic Growth* similarly stressed raising investment to reach a "take-off."
The model's weaknesses became clear with experience. Its fixed capital-output ratio rules out diminishing returns, which Robert Solow's 1956 model introduced. In Solow's model a higher saving rate raises income per worker but not long-run growth, which depends on technological progress. Saving is also not sufficient: postwar Europe had skilled workers, institutions, and markets that many poorer countries lacked, so the same capital produced much less elsewhere. And aid need not become investment at all. William Easterly's 1999 study argued that the financing-gap model, still used by international institutions, had little support in the data. The model remains useful as a first account of why saving and investment matter, and as a reminder of what that account leaves out.