Map of Hemmet on His mathematical model derived from the basic identity that savings must equal investment, S = I. Assume that savings is a fixed fraction of income, so s = (S/Y), and divide both sides of the equation by Y. Then take the right-hand side and multiply by (dY/dY) and get (S/Y) = (dY/Y)(I/dY), or s = GC (in Harrod’s terms), where G = (dY/Y) is the growth rate of national income and C = (I/dY) is the incremental capital-labor ratio (remember that Investment is the change in the capital stock, so I = dK). So this equation, s = GC, is as much a tautology as S = I. The theory only enters with some modest behavioral assumptions: if growth is faster than expected, then this can only occur if C is lower than expected. If firms, seeing their desired capital-output ratio decline, respond with more investment, then the system is clearly unstable. An unexpected increase in income growth will increase investment, or vice versa. Map of Hemmet 2016.
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