## Tuesday, January 9, 2007

### Negative Income Tax - Part 2

In a comment to my previous post, Rohit, a good friend of mine, explained where I went wrong.
Using Rohit's variables:
1. F: The government provided a fixed payment to every individual.
2. I: Income earned other then the fixed government payment.
3. R: A flat tax rate of positive income tax.
To make it simple let R be a decimal number i.e. for 50% rate it is 0.5, for 25% it is 0.25.4. E: Total take home earning of an Individual

E= I – R*I + F

If Income (I) = 40, then with Rohit's formula then Earning is 40 - 0.5*40 + 60 = 80.

Let's understand what the formula means. We know for Income less than 60.

Earning = Income + Government Support

Government support is reduced by certain rate (1/2 on our example) for every dollar in inccome.
i.e. Government Support = F - R*I

Therefore, E = I + F - R*I <----- the formula Rohit uses. Or is R = 1/2 then E = F + 0.5I Let's say if the government only "reimburses" upto the amount that a person falls short of \$60. Howeverm if Income is greater than 60 then E=I. To represent it in simple code:
IF I > F
E = I
ELSE

E = I + F - R*I
ENDIF

for F = 60, I = 60, R = 0.5; E = 90

We can clearly see that if a person gets \$60 then there is a strong dis-incentive for him to get a higher paying job unless the job pays more than \$90 (50% increase in pay, which might be very difficult to get). This is a major point of attack for NIT opponents

#### 2 comments:

1. In the version of NIT I am talking of, F never ends.

That is F will always be there, even if you start earning a billion dollar.

Going back to the formula
E=I-RI+F=I-(RI-F) =I-V

V is the amount you pay to the government out of your income.

V < 0 if I < F/R
V > 0 if I > F/R

The effective rate of income tax, r, is V/I
r=V/I

r < 0 if I < F/R
r > 0 if I > F/R

Thus for low Incomes (I) the tax is negative and for high incomes it is positive.

Any Ways

A Technical discussion does not do full justice to the issue.
Economics is a Positive science and Empirical Evidence will always outweigh theoretical justification.

The effect of NIT is subject to Empirical Verification.

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