Consider a society of 100 inhabitants composed by two types of individuals. Half of them are poor and have a yearly income of 10,000 dollars, and half of them are rich, with an annual income of 90,000 dollars. The government plans to tax annual income at a flat rate in order to redistribute it with a lump sum transferT

per person that is equal for all members of the society. However, for a positive tax rate of

over annual income, there is a

2

leak in the bucket. Thus, for each dollar of income taxed, the total tax revenue collected is equal to

2

. Assume0

.

Solve in terms of

andT

, the total income that a poor individual has after taxes are collected and transfers are made.

Solve in terms of

andT

, the total income that a rich individual has after taxes are collected and transfers are made.

Assuming that the government needs to balance the budget, solve the budget constraint of the government, and solve for the lump sum transferT

in terms of

.

To show demonstrate that you have solved these constraints, assume for a moment that=0.2

What would be the total income of poor?