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 is true for an economy where there is no depreciatibn
to capital stock, there is no population growth and technological progress does not &e
place. Let us assume for the time being that there is no population
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