Why some countires are so rich while others are mired in poverty??

 Before starting to explain the phenomenon as to why their a a difference in status of countries. Firstly we need to understand in what terms we are saying that a country is rich and other is poor. Is it standard of living, employment, aggregate income of a country or inflation and several other economic indicators.

To clear the point it is standard of living of people of country which is stated in terms of real GDP per capita i.e. on an average income of a person in a country.

Before going into details, we need to understand a comprehensive model named as Solow Growth Model named after the famous economist Robert Solow. We need to clearly understand the assumptions prior to diving into the mode.

Assumptions

• Production function exhibits Diminishing Marginal return to Capital
• We assume 2 inputs in the production function - Capital and Labor
• Two other important inputs are Natural Resources and Human capitsl (but at this point of time we will not consider these two inputs)
• We will assume that growth in "Technology"  is  not there.

Production function :  Y =  A F(K,L)

Assuming y = Y/L and k = K/L, we can rewrite the equation as y = f (k) as we are interested in analyzing output per labor.

Also as we know that  Saving = Investment = s f (k) where s = saving rate

The change in capital stock per worker :

dk = Investment (sf(k)) - depreciation in capital (d*k) - rate of increase in population growth (n) * k

    Increase in population requires additional capital
    We need to maintain the condition on existing machines/ capital stock
    Investment on capital will help in increasing capital stock 

At steady state dk = 0
hence,   sf (k) =  ( n + d ) k

Key findings :

1. At steady state output / worker and capital / worker is constant i.e. growth is zero. 

2. You can see clearly from the graph that if saving rate is high :  Steady state capital / worker and output / worker will be high.

3. While if rate of depreciation of capital or population growth (n) is high standard of living will be low. 

4. Steady state growth in total output of a country is n i.e. population growth

So countries with high population growth and low saving rate are poorer. 

      ######  Keep in mind that we excluded  the effect of technological growth in this model. ######

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