What is Balanced Growth Path

 In a steady state, there is balanced growth. That is, output and capital grow at the same rate: call it g.

Balanced growth refers to an allocation where output grows at a constant rate and capital-output ratio, the interest rate, and factor shares remain constant

A balanced growth path is a situation where each variable in the model is growing at a constant rate.

A balanced growth path is a path along which the quantities Y; K; and C are positive and grow at constant rates (not necessarily positive and not necessarily the same). 

(i) if there is balanced growth, then gY = gK = gC; and the ratios Y=K; C=K; and C=Y are constant; 

(ii) if Y=K and C=Y are constant, then Y; K; and C grow at the same constant rate, i.e., not only is there balanced growth, but the growth rates of Y; K; and C are the same.

The steady state level of capital per unit of effective labour, k* , is the level of capital per unit of effective labour that equates break even investment and actual investment i.e., sf(k*)=(n+g+δ)k*.

The golden rule level of capital per unit of effective labour, kG , is the steady state level of capital per unit of effective labour that would maximize the steady state value of consumption per unit of effective labour.