Consider an economy with two agents who differ in their innate earning

ability, denoted by w and w for the high-ability individual and the lowability

individual, respectively, where w > w 0. Both individuals share

the same preferences given by U(c,l) = c -l2 / 2, where c denotes

consumption and l denotes labor (the price of c is normalized to 1).

Income is subject to a proportional income tax denoted by 0 < t <1.

Moreover, the government is enacting a supplementary-security-income

policy (SSI) according to which, any individual whose (net) income is

lower than a specified level of income, I, is entitled to supplementary

income support up to this level of income (I is a minimal level of

income guaranteed by the government).

1) Draw the budget constraint faced by both individuals.

2) What would be the effective MTR for individuals entitled to SSI?

Demonstrate how the SSI program may adversely affect

individuals' incentives to participate in the labor market.

3) Suppose the government is seeking to maximize the well-being of

the least well-off individual in the economy. Formulate the

constrained optimization problem of the government. Assume that

a fiscal deficit is not allowed. (Hint: There are two incentive

constraints for the two individuals. Each individual can choose

either a level of income that is entitled to SSI or a higher level of

income that is not entitled to SSI. The choice is optimal!)

4) Show that the incentive constraint of the low-ability individual is

satisfied as a strict inequality.

5) Show that the revenue constraint of the government is satisfied as

equality.

6) Show that the incentive constraint of the high-ability individual is

satisfied as equality; hence, the optimal tax rate is given by:

t =1/3. Calculate social welfare.

7) Show that when w = 0, an optimal linear income tax system (as

discussed in class) is dominated by the SSI program. Explain!