What is meant by steady state in the Solow model? Explain how Golden Rule is different from steady state.

 A steady state is a situation in which the economy’s output per worker, consumption per worker, and capital stock per worker are constant that is, in the steady state; output, consumption, and capital do not change over time.

According to the Solow model, investment per unit of effective labour equals saving per unit of effective labour.

i= sy

Since y = f(k) we can write equation (1)

i=sf(k)

The above shows the relationship between existing capital stock (k) and accumulation of new capital (i) expressed in ‘per effective labour’ term. As we know, increase in capital stock is due to investment. Thus, the difference between capital stock in two successive years is equal to investment that has taken place during the year. In other words, the rate of /growth capital stock is equal to the rate of investment.

In per effective labour term, we can express (2) as k=sf(k) where k refers to the growth rate in k (In general we put a dot over a variable to represent its growth rate). The above equilibrium condition is true for an economy where there is no depreciation to capital stock, there is no population growth and technological progress does not take place.

Growth of Capital and Steady State The Solow model assumes that existing capital depreciates at the rate Thus, each year amount of capital is depreciated. Investment and depreciation act in opposite directions and the growth in capital stock is net of the two quantities. 

since i=sf(k(t))

k(t)=sf(k(t)) – sk(t)

From equation (4) we infer that capital stock rises when remains constant when falls when sfk(t))<8k(t) and sf(k(t)) = 8k(t).

The two curves, saving and depreciation curves, intersect at point X, where capital stock is ki and depreciation equals investment.

At this point there is no growth in capital stock hence, output also remains steady, k* is therefore known as the steady state level of capital. There are two unique features of the steady state: (i) economy in steady state will remain, until there is change in any other variable, and (ii) economy will always move towards the steady state.

For example, if the economy starts at level of capital, where k1 <k*, investment exceeds depreciation. As a result, capital stock k1, along with output f(K) rises till k reaches k.

On the other hand, if the economy starts at k2, level of capital, which is greater than k, investment is less than depreciation.  Consequently, there is a decline in capital stock and output in the economy until steady state capital, that is, k is reached.

Once the economy attains the steady state there is no pressure on k to increase or decrease hence, the economy stays there. Thus, the Solow model does not explain sustained economic growth. An economy with a high saving rate will have higher level of output and capital as compared to a country with low rate of saving.

Thus, saving rate is an important determinant of an economy’s output and capital Saving rate may vary across countries due to plethora of reasons like development of financial markets, tax policy, cultural differences, retirement policies, political stability and political institutions Population Growth and Steady State To analyse the effect of population growth we expand the Solow model.

We now consider the case where population and the labour force grow at a constant rate n. When labour force grows, additional capital is required to maintain the same level of k. Hence, the economy should have adequate investments to take care depreciation (8k) as well as population growth (nk). In order to introduce n we modify equation (4) as

k (t) =sf(k(t))-(n+8)k(t)

For steady state the amount of investment required must not only cover depreciation (Ok) but also provide new workers with capital (nk). Break-even investment now would be (n+8)k. The steady sate is achieved at the point of intersection of investment and (n+8)k curves. The line ok in Fig. 2.4 accordingly is adjusted to represent.

The steady state is reached in a similar manner. If k1 < k* investment is greater then break even investment so k and y rise. on the other hand k2 > k*, k declines till is reaches k*. Population growth succeeds in explaining sustained economic growth in an economy. In this framework, however, output per effective labour remains unchanged.

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