Question

Economic growth theory has the golden law of savings rate. What good, according to the theory, would it be if the savings rate followed the golden rule? What happens if the savings rate is higher than the golden rule?

Answer 1

The golden law of savings rate is acknowledged to Edmund Phelps. According to the  Solow growth model, a steady 100% savings rate means that all income is invested to generate capital for future production, which implies a steady state with zero consumption level. while savings rate of 0% implies no new investment capital is created, and the  capital stock with no replacement ( all consumed). This implies an unsustainable steady state except at zero output, which implies a consumption level of zero.which is not possible.  The solow maodel says that in between these two extremes that there has to be a Golden Rule of savings whre suatainable higohest percapita consumption is possible at constant state. A steady state growth means a  higher savings and a higher capital-to-labor ratio to achieve a higher per capita income but this doesn not guarantee higher per capita consumption , so it is important to find the level of capital-to-labor ratio that provides at the maximum possible per capita consumption to ensure a steady state of growth. Golden rule provides solution to this as it says that an economy will reach the optimum growth rate at the point where each generation saves and invests at the level that it wishes the previous generation would have invested. So as per the rule  each generation shall save that fraction of income that past generations shall have saved for of future generations. This condition requires that the rate of interest on savings ( profits on investment) equals the rate of growth of an economy. Given that (Savings equals investment) the per capita consumption (c ) as the difference between the per capita income and the per capita savings/investment c = f (k ) –sf (k ). Equilibrium is attained at the point where the growth rate of capital labour ratio equals to zero. So the rate of profit equals the growth rate of the economy, because at the steady state growth rate, the growth rate of output equals the growth rate of labor force. by following the golden rule at a given rate of saving, the economy will have a  steady-state growth in the long run with constant per capita consumption . The Golden Rule level of capital represents the level that maximizes consumption in the steady state.

A saving rate higher than the golden-rule saving rate is inefficient. The consumption is lower in the short run which will create capital accumulation in short run and will  lead to faster economic growth only in the short run. An increase in the saving rate raises growth until the economy reaches the new steady state. So  a high saving rate does not mean a high rate of growth forever. So if current generations save more and consume less it may benefit in short run but in the the long-run steady-state consumption per capita is reduced below the golden-rule value it will be inefficient.