Here is a review of some of the math you will use. A welfare program's payment to a zero private income family is its guaranteed income. In my lecture, I called this G. The drop in payment for every dollar earned in private income is called the benefit reduction rate and symbolized r. So with an r of 15% or 0.15, the payment drops 15 cents for every dollar earned.

The welfare payment for any private income earned then can be found with the equation Payment = G - (r x Private Income). For example, if r is 15%, G is $10,000 and the person earns $60,000, then the payment they receive is Payment = $10,000 -(0.15 x $60,000) = $10,000 - $9,000 = $1,000. To find the income at which the payment goes to 0 for a given G and r, set the payment equal to zero, plug in the G and r, then solve the algebraic equation for the Private Income.

Also remember for this homework that people have a choice between working and not working. Unless working pays enough more than not working to be worth it, people will choose not to work. How much more is enough to be "worth it" is given in the problems.

Now you are ready - have at it!

A country has no welfare program and 4 of its people are earning the income given in the Old Private Income column of the table below. Their poverty line is $25,000.

Now the country starts a simple welfare program that pays everyone below the poverty line enough to rise to the poverty line. No one above the poverty line receives any payment. In terms of the math equations above, the guaranteed income is $25,000 and the benefit reduction rate is 1.00 or 100%.

Fill in the boxes with the question numbers (of course you won't actually have a box you are filling in; you will merely write that question number in your textbox). Assume people will not work unless they make $10,000 more by working than not working. Old Private Income is how much the person was earning at their job before the welfare program started. New Private Income is how much they earn at their job after the welfare program has started. Total income will be their New Private Income plus their Government Payment.

The person does not have the ability to get a raise (so their private income will not go up), only to decide if they wish to work or not based on if working is worth it or not. Remember from above, people only work if their total income after welfare is at least $10,000 higher than not working. For this part of the homework, you may not find it necessary to actually use the math equation. You can use it, but you can also just realize that the person will be paid whatever amount is necessary to get them to $25,000 total income (total income being new private income plus government payment). People earning above $25,000 on their own are paid nothing by the government, nor do they pay anything to the government.

Old Private Income	New Private Income	Government Payment	Total Income
$0			Question #1
$20,000	Question #2	Question #3
$30,000	Question #4		Question #5
$40,000		Question #6

Now instead there is a program that only reduces the welfare payment by 10% of the private income. Assume everyone works and earns as much as before because of the strong incentive built in to continue working. Assume the payment to zero income people is enough to raise them to the poverty line. The payment to everyone else is determined by the equation already given to find the value of welfare payments. People above the poverty line are eligible for payments. Again answer the question number with the number that would go in that box of the table.

Old Private Income	New Private Income	Government Payment	Total Income
$0
$20,000	Question #7		Question #8
$40,000	Question #9	Question #10

Question #11) For the welfare program with a G = $25,000 and an r = 10%, how much will someone have to earn at their job before the welfare payment drops to $0?