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There will be a poverty trap whenever the scope for growing income or wealth at a very fast rate is limited for those who have too little to invest, but expands dramatically for those who can invest a bit more. On the other hand, if the potential for fast growth is high among the poor, and then tapers off as one gets richer, there is no poverty trap. —— Banerjee and Duflo

Firstly, as shown in the figure 1, there are ‘poverty trap zone’ and ‘outside the poverty trap zone’ and the curve shapes like an ‘S’. The point on the 45 degree diagonal line suggests that ‘income today equals to income tomorrow’. In terms of people in the poverty trap zone, ‘income in the future’ is lower than ‘income today’, thus becoming poorer and poorer as time goes — poverty trap until reaching point P; in terms of people outside the poverty trap, it is easy to distinguish that ‘income in the future’ is much greater than ‘income today’ by observing the curve being above the diagonal line, signalling that these people are getting richer and richer.

I personally agrees with the authors’ opinion that theories are only just theories. To make every poverty trap solvable with effective measures, assessment should be made ‘case by case’. As we cannot know what is the consumption and saving patterns of poor people, the attention given towards sanitation, education by the poor and etc.

References

1. Figure 2-4: The S-Shape Curve and the Poverty Trap. Source: (Banerjee and Duflo 2011) 
2. Poor economics, Banerjee and Duflo, 2011