Question

True or false and why?

1. In the Harrod-Domar model of economic growth, a country’s per capita growth rate depends on its rate of savings, whereas in the Solow model the savings rate has no effect on the per capita growth rate.

Answer 1

False

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.

This is so because the two models have different assumptions on the marginal returns of capital. While the Harrod-Domar (HD) model assumes that there are constant marginal returns to capital, the Solow model on the other hand, assumes decreasing marginal returns to capital.

Assume that we initially are in the steady state in the Solow model, where sy =  (n + δ)k, i.e. the investment amount is equal to 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)k_t+1 > (n + δ)k_t since k_t+1 > k_t .
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’ of higher k in terms of higher break-even investments increases linearly with k, the temporary effect on growth of the change in s will gradually level off until we reach the new steady state, where growth again is 0.

The last argument does not hold for the HD model. In the HD model the marginal product of capital per capita is constant, and hence a permanent change in s will have a permanent effect on the growth rate of the economy.