Saturday, December 10, 2005

Subsidies and Logic!

"Arey bhai, some of the richest people in India are politicans!" Hands stretching out and eyes winking, "itna saara paisa banate hain!"

"Really! So if you are in Indian politics, there are good chances of being rich OR is it that if you are rich in India there is a pretty good chance that you are a politican!"

"Kya fark padta hai?"

There is a difference.

Let us take the case of subsidies (electricity/water/PDS kuch bhi...)

Last year about 50 people got these subsidies (label S). The system can accommodate only 50 subsidy requests. 35 of them were deserving (labelled POOR) and the rest 15 were not deserving of it (labelled RICH).

At first sight, we find that 30% of the people getting the subsidies are not deserving of it, i.e. the RICH category.

However, the more interesting question might be this. Given that you are not deserving of the subsidy (i.e. RICH), what is the probability that you will get the subsidy? Now you have the data of people applying for the subsidies. About 20 RICH people and 80 POOR people.

Let me concise that data.

20 RICH people applied and 15 RICH ones are receiving the subsidy. A little grease here and there, you know!

80 POOR people applied and 35 RICH ones are receiving the subsidy. The system still works, you see!

There are two interesting questions.

1> What is the chance of getting subsidy given that you are rich?
2> What is the chance of being rich given that you get subsidy?

Take a moment to reflect.

The answer to one of them is 0.3 and the other is 0.75.

P(RICH /S) = 15/50= 0.3
P(S/RICH) = 15/20= 0.75
/ stands for given

In laymen terms, 30% of those receiving subsidies are rich but more importantly, there is a 75% chance of the rich receiving subsidy, if they apply. A little application of conditional probability gives us an idea of the distortion of incentives involved.

You can apply the same logic to backward communities applying for government employment. No wonder it is worth forging one's community status because of the increased probability of receving government benefits.

Data in above example is only indicative for purposes of displaying conditional probability and any errors in above logic will be appreciated.

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