4. Consider an income guarantee program with an income guarantee of $3,000 and a

Question

4. Consider an income guarantee program with an income guarantee of $3,000 and a benefit reduction rate of 50%. A person can work up to 2,000 hours per year at $6 per hour. Alice, Bob, Calvin, and Deborah work for 100, 333 %, 400, and 600 hours, respectively, under this program. The government is considering altering the program to improve work incentives. Its proposal has two pieces. First, it will lower the guarantee to $2,000. Second, it will not reduce benefits for the first $3,000 earned by the workers. After this, it will reduce benefits at a reduction rate of 50%.

Explanation / Answer

c. Workers working fewer than 500 hours see their hourly wage effectively doubled under the plan. The substitution effect therefore tends to make Alice, Bob, and Calvin all work more. One can calculate that the two budget constraints cross at 333 1/3 hours of work, or 1,666 2/3 hours of leisure. The income effect is thus different for these three workers. Alice was working less than 333 1/3 hours under the old policy, so the policy change effectively makes her poorer. She consumes less of all normal goods, including leisure, so this also makes her work more. We can unambiguously conclude that she will work more. Bob was working exactly 333 1/3 hours, so he feels no income effect. We can conclude from the substitution effect alone that he too will work more. Calvin was working more than 333 1/3 hours before, so this policy change effectively makes him richer. He will therefore tend to work less due to the income effect. We cannot tell if the substitution effect or the income effect is stronger, so we cannot tell if Calvin will work more or less. Finally, Deborah was working 600 hours before. Under both policies, the effective wage of someone working this many hours is $3/hr (since 50 percent of income is offset by reduced benefits). There is no substitution effect for her. However, she experiences an increase in income. We conclude that she will work less.

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