Question

HI, I need a help with the part (b) of this question. I have the solution guide book but it won't help me. I want a detail explanation. Here is the problem:

1. 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 ⅓, 400, and 600 hours, respectively, under this program.

(a). Draw the budget constraint (trading off leisure and consumption spending) that faces any worker under this program.

(b). 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%. Draw the budget constraint facing any worker under the proposed new program.

Answer 1

ANSWER:

a, The budget constraint for the original program is enclosed as graph -1.

When zero hours worked (2,000 hours leisure), a worker is able to consume $3,000, the guaranteed income level. After 1,000 hours of work, the benefits will decline to zero (50% of $6,000 in income).

b ,

The budget constraint for the proposed program is enclosed as graph -2.

When zero hours worked (2,000 hours of leisure), the worker is able to consume the lower $2,000 guarantee. She can work for up to 500 hours without any reductions in the benefits thus if works for 500 hours will be able to consume $5,000 (= $2,000 + $6/hr x 500 hrs) and has 1,500 hours of leisure. After an additional 2,000/3 = 666.67 hours, i.e. the total of about 1,133.33 hours of work or 833.33 hours of leisure will not gain any benefits. The benefits reduced to $2,000 (=50% * $6hr * 2000/3 hrs = 50%*4000). The dashed line displays the original budget constraint.