Question

Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per capita output y = AVkt with rate of depreciation of capital 8, investment it = sy. = sAvky, capital transition function kt+1 - k = SAVk - Okt, where s is savings ratio. 1. Putting per capita output (income) y on the y-axis and k on the x-axis, graph the curves for depre- ciation and investment. Label steady state capital k* and steady state output y'. 2. What factors determine the position of state capital k* and steady state output y*? 3. Graphically show a poor country that can grow fast, and a poor country that cannot grow. Explain their differences intuitively (Put it another way, why can one grow fast while the other cannot?). 4. If s increases in the economy, what does this mean intuitively? What would happen to steady state capital k* and steady state per capita income y*? What are the negative consequences of a higher s?

Answer 1

1).

Consider the given fig here we have measured “k” on the horizontal axis and “y” on the vertical axis. Now, “yt” show the output per worker for each possible “kt”. “it = s*yt” be the investment per worker for each possible “kt”.

yt d*kt yt = f(kt) y*1 it = s*yt kt k*1

Now, at the equilibrium “it” is equal to “d*kt”, => the change of “kt” is zero. So, here the steady state level of “kt” and “yt” are “k*1” and “y*1” respectively.

2).

Here the labor force are fixed, => there are two factor that effect the steady state level of “k” and “y” these are “s = savings rate” and “d = depreciation rate”.

If the savings rate increases implied the investment per worker increases, => “it” will rotate upward, => given the depreciation line the steady state capital per worker and output per worker both increases. If the depreciation rate increases implied the depreciation line increases, => “it” will rotate upward, => given the investment function the steady state capital per worker and output per worker both decreases.

3).

Consider the following fig where there are two counties having different savings rate.

d*k y=f(k) y1* v2* s1*y E1 s2*y E2 k2* k1*

So, country1 having higher savings rate and “country 2” having lower savings rate. So, the steady state equilibrium of “country1” is “E1” and of “country2” is “E2”. So, the steady state capital per worker of both country are “k1” and “k2 < k1” respectively. Similarly, the steady state output per worker of both country are “y1” and “y2 < y1” respectively. So, a country having higher savings rate having higher capital stock per worker and output per worker, => a country having higher savings rate having higher growth.

4).

Now, increase in the savings increases the investment per worker, => given the level depreciation of capital the change of capital per worker increases, => the level of capital per worker and output per worker increases. Now, the consumption per worker is given by, “c = (1-s)*y”, => if the savings rate increases (1-s) decreases the correct consumption decreases.