Harrod Domar
ECON 1910 Spring 2012 Lind / Willumsen
Short solution proposal to the compulsory assignment in ECON1910
Problem 1: Harrod-Domar vs. Solow. In the Harrod-Domar model a change in the savings rate (s) has a permanent effect on the growth rate of GDP per capita, while in the Solow model a change in the savings rate has only a temporary effect on the growth rate of GDP per capita. Why is this the case? Answer: The main difference between the Harrod-Domar (HD) model and the Solow model is that HD assumes constant marginal returns to capital, while Solow assumes decreasing marginal returns to capital. The reason that a change in the savings rate has a permanent effect in HD, while only a temporary effect in Solow, is exactly due to the differences in assumptions on the marginal returns to capital. To see why, assume that we initially are in the steady state in the Solow model, where investments exactly are equal to break-even investments (i.e. the amount of investments syt are equal to (n + δ)kt , the amount of investment that needs to be undertaken in order for the capital stock per capita next period to be the same size as today). If we increase the savings rate in the Solow model from s to s , we will in the next period have more capital per capita than before, as depreciation (δ), population growth (n) and capital today (kt ) are the same, i.e. break-even investments today do not change. This additional capital will generate more output next period (a fraction s of which is saved), but we will also need to invest more next period if we were to keep capital constant at this new level since the new break-even investment level (n + δ)kt+1 > (n + δ)kt since kt+1 > kt . It will now (in period t + 1) also be the case that investments are higher than the new break-even investment level, but less so than last period because the marginal product of capital is lower at the new and higher level of k. As the marginal product of capital decreases as k gets larger, while the ‘cost’
Short solution proposal to the compulsory assignment in ECON1910
Problem 1: Harrod-Domar vs. Solow. In the Harrod-Domar model a change in the savings rate (s) has a permanent effect on the growth rate of GDP per capita, while in the Solow model a change in the savings rate has only a temporary effect on the growth rate of GDP per capita. Why is this the case? Answer: The main difference between the Harrod-Domar (HD) model and the Solow model is that HD assumes constant marginal returns to capital, while Solow assumes decreasing marginal returns to capital. The reason that a change in the savings rate has a permanent effect in HD, while only a temporary effect in Solow, is exactly due to the differences in assumptions on the marginal returns to capital. To see why, assume that we initially are in the steady state in the Solow model, where investments exactly are equal to break-even investments (i.e. the amount of investments syt are equal to (n + δ)kt , the amount of investment that needs to be undertaken in order for the capital stock per capita next period to be the same size as today). If we increase the savings rate in the Solow model from s to s , we will in the next period have more capital per capita than before, as depreciation (δ), population growth (n) and capital today (kt ) are the same, i.e. break-even investments today do not change. This additional capital will generate more output next period (a fraction s of which is saved), but we will also need to invest more next period if we were to keep capital constant at this new level since the new break-even investment level (n + δ)kt+1 > (n + δ)kt since kt+1 > kt . It will now (in period t + 1) also be the case that investments are higher than the new break-even investment level, but less so than last period because the marginal product of capital is lower at the new and higher level of k. As the marginal product of capital decreases as k gets larger, while the ‘cost’