Derive the conditions for steady state in the Solow model. What are its implications? In what
respects is the golden rule different from the steady state?
Investment per unit of effective labour equals saving per unitlof effective labotir:
i = sy—(1)
Since y = f(k) we can write equation (1) as
The above shows the relationship between existing capital stock (k) and accumulatibn of new capital (i) expressed in'per effective labour' term.
As you know, increase in capital stock is due to investment. Thus the diffaence betw&n capital stock in two successive years is equal to investment that has taken place duribg the year. In other words, the rate of growth capital stock is equal to the rate of investmebtt. In per effective labour term, we can express (2) as
k = sf (k) .. .(3)
where k refers to the growth rate in k (In general we put a dot over a variableto represent its growth rate). I
The above equilibrium condition
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