Savings under neoclassical and endogneous model

[pianok]

I am confused with the whole savings thing in economics..it says under the neoclassical model that the level of savings has no effect on thr long term growth but the savings rate would increase productivity.and it says in the curriculum that “although the savings rate increases both y and k,it has no impact on steady growth rates of output per capita and output”
my first question is does the savings rate affect or not the growth??
Second under the endogeneous model, it says increasing the savings rate permanenty increases the rate of economic growth. and this also leads to constant returns to capital.
Can someone explain to me the relation between the savings rate and the constant returns to capital???and is it capital or capital to labor??

 

[MrSmart]

Under the neoclassical model, we assume that the marginal product of capital is equal to the cost of capital on the long run. So MPK = r = αY/K.
An increase in savings would stimulate capital accumlation through lower real interest rates, because more supply of liquiduty pumped into the banking sector means banks are in a better position to distribute less interest on your deposits. This lower interest rate would reduce your borrowing cost for creating capital investements, so r drops below the current level of MPK, which leaves you with MPK>r. But since we assume that capital accumlation keeps piling up until it’s not profitable anymore to do so, then capital deepining will happen untill MPK drops down to r and MPK=r again. Which means that you’ve increased your K/L by moving up the production curve, and your level of Y/L also improves. But this is not a long term solution for steady growth rates, as savings rate can change, and the amount of capital you accumlate in the economy to grow is capped by the real interest rates. So unless savings can grow in perpetuity (to keep driving down interest rates), and MPK does not reach zero with ever increasing capital (which it does from dimishing marginal returns), it is not a sustainable source of long term growth. And output-to-capital is constant at the sustaiable growth rate.
A shift of the production curve upward through technological innovation is however, sustainable. Coupled with increasing proportion of labor to output. As more labor share to output means more room for capital deepining, and thus higher marginal productivity of capital (developing countries).
The endogenous model takes it from the opposite side. It tells you that investment in capital has a spillover effect on technology (the better the resource allocation, the more innovation you get on investments). And so capital deepining is not capped by r, since more capital creates more technology, leaving you in a viscious cycle of ever expanding growth without the need for population growth. In other words increases in TFP is implied with increases in K. So even if savings keep increasing, income per person keeps on rising, and real interest rates keep dropping to compensate for the endogenous cycle of more capital -> more technology -> more income -> more saving -> less cost of borrowing -> more capital…etc, then interest rates eventually drop to zero, but capital investments at this point still can shift you up the production curve, and not capped by MPK = 0 = r.
Hope this helps.

 

[pianok]

ok first thanks a lot for the effort you have put into this…its does make a lot of sense now.
Second how did you understand all this??? is it written somewhere in the curriculum?
Third, i wanna conclude something and plz correct me if im wrong:
So in the neoclassical model, savings do increase the productivity just temporarily and saving rates are not stable and it is only a temprary thing. (but countries with higher savings rate do enjoy higher growth??? kz thats whats mentioned in schweser).
Under the endogeneous model, since the growth doesnt have a limit and can always increase then savings will lead to a higher growth.
Thanks a lot for your help i do appreciate it

 

[MrSmart]

Just understand what the graphs and formulas mean, then take it on a long term frame to assess sustainability (variable goes to infinity).
In the neoclassical model, a higher savings rate will permenantly increase the level of output, and productivity (Y and Y/L respectively) if the savings rate stay at that level permenantly as well (moving from developing to developed economic states). It’s more about sustainability, than temporary or permenant states. The difference is that in the neoclassical model, capital accumlation will stop increasing output as MPK goes to zero from the diminishing marginal productivity of capital, while in the endogenous growth model, more capital spillsover another Cobb Douglas factor of production (TFP) without directly changing it, while keeping L constant in both models. So MPK goes to zero and Y/L reaches a ceiling with infinitely more capital (assuming savings rate keep moving up permenantly beyond the model’s assumption of a constant αY/K at some level r), while in the endogenous model, MPK can still go to zero, but Y/L and Y keep increasing at a sustainable rate as TFP increases with changes in capital as well (not assumed in the neoclassical model).
In other words, more savings will increase income per person at a lesser rate as you increase capital in the neoclassical model until it doesn’t increase income anymore at some point far along the production curve. While more savings will keep increasing income per person as you increase capital in the endogenous model, so it’s sustainable. Even if we assume that MPK = 0 = r in both models (which isn’t realistic in the real world).