If an economy has capital that is less than the golden rule level of capital, can we reach the golden rule without increasing the savings rate?

Question

This question is in context of this problem I was trying to solve:

The answer given is (a). But I think the answer is (C). My arguments are as follows:

• First, the golden rule level of capital corresponds to one and only one savings rate, $ s^* $.
• Thus, to reach $ s^* $, we need to increase the savings rate (since the economy starts off below the golden rule of capital accumulation steady state).
• Increasing savings reduces consumption initially.
• But increased savings stimulate investment, which increases production, which ultimately increases income and thus **increases consumption in the long run.

Is my answer correct, speaking strictly in terms of academic Solow Model theory and with the information given in the question? If wrong, why?

Answer 1

Your reasoning is exactly correct and the answer should be C.

We are told to begin "from a steady state which is below the golden rule of capital accumulation". So, $s<s_g$, where $s$ is the initial savings rate and $s_g$ is the golden-rule savings rate.

Suppose that at period $250$, our savings rate jumps from $s$ to $s_g$. Then the evolution of per-capita consumption looks like this:

Google spreadsheet where you can play with the numbers.

Answer 2

Yes the answer should be C. I have attached an image showing the variation with time of the variables $y$(per capita output), $c$(per capita consumption) and $i$(per capita investment). I am assuming at $t=t_0$ the savings rate is increased.

The consumption per capita initially will fall because the savings rate has increased. Eventually it must go above the initial per capita consumption because of the Golden Rule condition.

Cheers!