Consider a negative income tax in which an individual receives a cash benefit of

Question

Consider a negative income tax in which an individual receives a cash benefit of B per month, and pays a marginal tax M on any income earned. If an individual’s income is Y, their combined income from earnings and benefit is then B+(1-M)Y.

a) If B = $1000 per month and M equals .3, at what level of earned income Y is the cash benefit equal to the taxes paid?

b) If B is increased to $1200 and M again equals .3, what is the increase in the earned income level Y at which the cash benefit equals the taxes paid?

c) If the poverty threshold for a family of four is $2000 per month, how would you set B and M?

d) What problems do you see in using a negative income tax to support low income families?

Explanation / Answer

1) The tax paid by the individual is MY. And it is given that the cash benefit is equal to the tax amount so this implies:

1000 = MY

1000 = 0.3Y

Y = 10000/3 or 3333

With an income of 3333, a person pays M fraction or 0.3*3333 = 1000 in tax.

B) Again the tax paid by the individual is MY. And it is given that the cash benefit is equal to the tax amount so this implies:

1200 = MY

1200 = 0.3Y

Y = 12000/3 or 4000

With an income of 4000, a person pays M fraction or 0.3*4000 = 1200 in tax.

C) For a family with income less than $2000, it would not pay tax so M = 0. B will be the difference between the income of the family and $2000.

D) A common problem is that it reduces the incentive to work, since all the recipients receive a guaranteed minimum wage in absence of jobs

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