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Loosening the poverty trap: reducing government assistance by 50 cents for every $1 earned

The graph shows a downward sloping line that extends from $28,000 on the y-axis to $18,000 on the y-axis (from 0 to 2,500 on the x-axis). Two points R and S appear on the line. Another line starts at (0, $20,000) and ends at (2,500, 0). A dashed plum line extends horizontally from $18,000 on the y-axis and meets with the vertical line extending from 2,500 on the x-axis. Another dashed plum line extends from $16,000 on the y-axis and intersects with the vertical line extending from 500 on the x-axis at point P. Beneath the x-axis is an arrow pointing to the right indicating leisure (hours) and an arrow pointing to the left indicating labor (hours).
On the original labor-leisure opportunity set, the lower budget set shown by the smaller dashed line in the figure, the preferred choice P is 500 hours of leisure and $16,000 of income. Then, the government created an antipoverty program that guarantees $18,000 in income even to those who work zero hours, shown by the larger dashed line. In addition, every $1 earned means phasing out 50 cents of benefits. This program leads to the higher budget set shown in the diagram. The hope is that this program will provide incentives to work the same or more hours, despite receiving income assistance. However, it is possible that the recipients will choose a point on the new budget set like S, with less work, more leisure, and greater income, or a point like R, with the same work and greater income.
The labor-leisure tradeoff with assistance reduced by 50 cents for every dollar earned
Amount Worked (hours) Total Earnings Government Support Total Income
0 0 $18,000 $18,000
500 $4,000 $16,000 $20,000
1,000 $8,000 $14,000 $22,000
1,500 $12,000 $12,000 $24,000
2,000 $16,000 $10,000 $26,000
2,500 $20,000 $8,000 $28,000

The next module will consider a variety of government support programs focused specifically on the poor, including welfare, SNAP (food supplement), Medicaid, and the earned income tax credit (EITC). Although these programs vary from state to state, it is generally a true statement that in many states from the 1960s into the 1980s, if poor people worked, their level of income barely rose—or did not rise at all—after the reduction in government support payments was factored in. The following Work It Out feature shows how this happens.

Calculating a budget constraint line

Jason earns $9.00 an hour, and a government antipoverty program provides a floor of $10,000 guaranteed income. The government reduces government support by $0.50 for each $1.00 earned. What are the horizontal and vertical intercepts of the budget constraint line? Assume the maximum hours for work or leisure is 2,500 hours.

Step 1. Determine the amount of the government guaranteed income. In this case, it is $10,000.

Step 2. Plot that guaranteed income as a horizontal line on the budget constraint line.

Step 3. Determine what Jason earns if he has no income and enjoys 2,500 hours of leisure. In this case, he will receive the guaranteed $10,000 (the horizontal intercept).

Step 4. Calculate how much Jason’s salary will be reduced by due to the reduction in government income. In Jason’s case, it will be reduced by one half. He will, in effect, net only $4.50 an hour.

Step 5. If Jason works 1,000 hours, at a maximum what income will Jason receive? Jason will get the government assistance of $10,000. He will net only $4.50 for every hour he chooses to work. If he works 1,000 hours at $4.50, his earned income is $4,500 plus the government income of $10,000. Thus the total maximum income (the vertical intercept) is $10,000 + $4,500 = $14,500.

Key concepts and summary

A poverty trap occurs when government-support payments for the poor decline as the poor earn more income. As a result, the poor do not end up with much more income when they work, because the loss of government support largely or completely offsets any income that is earned by working. The bite of the poverty trap can be reduced by phasing out government benefits more slowly, as well as by imposing requirements for work as a condition of receiving benefits and a time limit on benefits.

Problems

Susan is a single mother with three children. She can earn $8 per hour and works up to 2,000 hours per year. However, if she does not earn any income at all, she will receive government benefits totaling $16,000 per year. For every $1 of income she earns, her level of government support will be reduced by $1. Create a table, patterned after [link] . The first column should show Susan’s choices of how many hours to work per year, up to 2,000 hours. The second column should show her earnings from work. The third column should show her level of government support, given her earnings. The final column should show her total income, combining earnings and government support.

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Questions & Answers

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
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Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
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Aphelele
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Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
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Abubakar
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state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
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Method
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Amoon
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Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
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When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
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Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
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d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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Source:  OpenStax, Principles of economics. OpenStax CNX. Sep 19, 2014 Download for free at http://legacy.cnx.org/content/col11613/1.11
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