Why Developing Countries Cannot Achieve Growth and Greater Equality of Income Simultaneously

I came about this ‘proof’ while investigating the following problem: Imagine that there are four people in a country. Three of these people earn $1 and one person earns $2. Hence, the total income in the economy is $5. As a result of economic growth, an extra unit of income enters the economy and now the situation is that two people earn $1 and two people earn $2. The question is whether the second situation is more of less equal than the first.

In order to solve this problem, we must first decide how we will measure equality. The Gini coefficient – derived from the Lorenz Curve – is a commonly used and widely accepted measure of inequality and so I will use it as my inequality measuring tool.

As mentioned, the Gini coefficient (GC) is derived from the Lorenz Curve. The Lorenz Curve is the curve that tracks how the cumulative percentage of national income (y-axis) changes as you ‘accumulate’ the total population (from poorest to richest). On the below diagram, the GC can be calculated as the proportion of area a/area a+b. Clearly, the higher the ratio, the more unequal the country is as the Lorenz Curve is further from the line of perfect equality.

Now that the definitions are out of the way, let’s get down to the problem. If we plot the Lorenz curve for scenario 1 and 2 (scenario 1 is three people $1, one person $2; scenario 2 is 2 people $1, 2 people $2) we find that the GC for scenario 1 is 0.15 and the GC for scenario 2 is 0.166. In other words, the second scenario is more unequal than the first. At first this can seem counter-intuitive as total income in the economy has increased and all the extra earnings went to someone who was formerly ‘poor’. The implications of this are that in a country where more than half the people are ‘poor’, any increase in output (which is the same as an increase in income as national income = national output) up until the point where half the people are poor and half are rich will inevitably lead to rising inequality.

If we take this problem a step further and say that, as a result of further growth, the scenario changes to the following: three people earning $2 and only one person earning $1. In this case, our intuition is right – the third scenario is more equal than the second. Indeed the GC for this situation is 0.11 which is even lower than scenario 1. Clearly scenario 3 is the best out of all three as average income is the higher and there is the least income inequality.

What these three scenarios show us (and the same effects can be seen using different numbers) is that, with no government intervention to redistribute income, if a country with more than half the population poor (most developing nations) grows, there will be an inevitable rise in inequality up until the point where half the population are poor and half are rich. Beyond this point, inequality reduces more rapidly than it rose in the first place.

This example suggests several things. Firstly, as most developing countries have a GC that they would hate to increase, having a completely free economy with no progressive tax structure is harmful as it will lead to further inequality and further social tensions. Also, the fact that equality improves after the 50:50 mark leads me to believe that developing countries should be less alarmed when they see a rising GC as the above scenarios suggest that this will fall if the poor are continually being elevated to the ranks of the ‘well off’. Finally, this example suggests that in a country where the GC is high to begin with (perhaps greater than 0.6), and government tax policies are non-existent or ineffective (maybe in a lawless or incredibly corrupt state), it may actually, in the interests of social harmony, be unwise for that country to pursue growth!

Note: A natural reaction to the situation that I have presented is to say that it is unrealistic for all of the ‘extra’ $1 of income to have gone to a formerly ‘poor’ guy. In real life a large chunk of this extra $1 goes to the ‘rich’ person who already had $2. This is very true. However, the fact that inequality initially increases even in this rosy, best-case situation is helpful in proving my point that, in real-life (which is far worse that this best-case situation) inequality will definitely rise at first.

Note on the Note: Some of you may question my calling the situation ‘best-case’ in the paragraph above. Surely the best-case situation is that the extra $1 is split evenly between the ‘poor’ people – doing this will certainly reduce the Gini coefficient. While this is correct, it is grossly unrealistic. To understand why this is true, it is important first to bear in mind that each individual in my scenarios would represent tens (or even hundreds) of millions of people in an actual economy. It is impossible for government policies to simultaneously benefit these teeming masses and to the same degree. Therefore, it would be too unrealistic to split the extra income evenly between the poor.