Suppose that the government introduces an income maintenance program for low-income people that offers a basic grant of \(\$ 200\) per month, but that for any earnings above \(\$ 100\), the grant is reduced dollar-for-dollar (that is, the marginal tax rate is 100 percent).

a. Assume that Lois can earn \(\$ 10\) per hour and has no other income. Sketch her annual budget constraint with and without the program in effect. Carefully label the axes, intercepts, and all kink points. At how many hours of work is the grant reduced to zero?

b. According to economic theory, what would happen to Lois's hours worked and total income if the government instituted this welfare plan?

c. Suppose that the government decides to keep the monthly base grant at \(\$ 200\), but to lower the implicit marginal tax rate on earnings to 66.67 percent. Draw the new budget constraint.

d. Relative to the first plan, how will introduction of the new plan affect Lois's hours of work and total income?