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, 333.3, 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%. (a) Draw the budget constraint facing any worker under the proposed new program. (10 points) (b) Which of the four workers do you expect to work more under the new program? Who do you expect to work less? Are there any workers for whom you cannot tell if they will work more or less? (5 points as bonus)