How much Capital per Worker is the Best for the Economy? The Golden Rule of Capital

What can we say about economic policy and long-run growth? To keep matters simple, let us assume that the government can—by proper fiscal and monetary policies—set and keep the economy’s
savings-investment rate s at whatever level it wishes. What level should the government choose for the economy’s savings rate?

It seems reasonable to assume that the government’s objective is to maximize the well-being of the individuals who make up the society by maximizing the amount of goods and services that they can
consume. Let us, for the moment, simplify things further and say that consumption C is equal to total production Y minus investment I:

C = Y-I
I =sY

Higher savings rate so not mean Higher Prosperity always/ The best savings rate is that which maximises the consumption for the economy. Let us assume that the change in capital /worker is given by Delta(k)

Then Delta(k) =  Investment - Depreciation (of the capital)

Delta(k) = (Savings Rate)(Production/worker)- (Depreciation Rate)(capital/worker)

At steady state left hand side term is zero
Consumption/worker = (Production/worker) – Depreciation.
So to maximize consumption we have
Marginal Production = Depreciation Rate


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