12th grade Think at the margin: one more unit, its extra cost and extra benefit worksheet

Think at the margin: one more unit, its extra cost and extra benefit

Grade 12 Social Studies Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Cards A and B on study time (all made up for practice). Card A, "Rosa's study time (made up)". Written for this sheet. Table, columns Hour of study | Extra test points it adds: 1st | 12; 2nd | 8; 3rd | 5; 4th | 2. Card B, "What an hour costs (made up)". Written for this sheet. Summary in our words, not a quotation: each hour Rosa studies means one less hour of babysitting at $6 an hour. Rosa values each test point at $1. Later the babysitting pay falls to $4 an hour.

2. 1.

   Ari reads cards A and B. How many hours should Rosa study at $6 an hour?

   • One: the 1st hour adds the most points, $12, so Rosa should stop after the best hour
   • Four: every hour adds some points, so Rosa should keep studying until the points stop
   • Two: the 2nd hour adds $8 of value, above its $6 cost, but the 3rd adds only $5
   • Three: the 3 hours add 25 points in total, which is more than the $18 they cost
3. 2.

   Babysitting pay falls to $4 an hour. Esme uses card A. How does Rosa's best number of study hours change?

   • It falls to one, since a babysitting pay of $4 means studying is a smaller gain than before
   • It stays at two, since the number of hours depends on the points each hour adds and not on its $4 cost
   • It rises to three: the 3rd hour adds $5, above its new $4 cost, but the 4th adds only $2
   • It rises to four, since a $4 cost makes each hour worth taking until the points run out
4. 3.

   A friend says four hours bring 27 points, or 6.75 a point per hour, well above $6, so Rosa should study four hours. Jun tests this. What is the verdict?

   • Wrong: 6.75 is not a whole number, so the friend's average cannot be used for hours of study
   • Right: the 4th hour adds $2, and any gain at all is worth having when studying is the goal
   • Right: four hours add $27 in all, an average of $6.75 an hour, which beats the $6 cost of an hour
   • Wrong: the average hour adds $6.75, but the 4th hour adds only $2, below its $6 cost

5. Use this

   Cards A and B on two bakers (all made up for practice). Card A, "Two bakers (made up)". Written for this sheet. Table, columns | Loaves in a day | Cakes in a day (each baker does one or the other, or splits the day): Rosa | 12 | 6; Tim | 4 | 4. Card B, "Rosa's idea (made up)". Written for this sheet. Summary in our words, not a quotation: Rosa bakes more of both than Tim, so she says she should bake everything and leave Tim out.

6. 4.

   Pia reads card A. Who gives up less to bake a cake, and what does each give up?

   • Neither: Rosa is better at both, so Tim has nothing he gives up less to bake than she does
   • Rosa: she bakes 6 cakes a day to Tim's 4, so she gives up less to bake a cake
   • Tim: a cake costs him 1 loaf, while it costs Rosa 2 loaves
   • Rosa: a cake costs her 12 loaves in a day, fewer than the 24 cakes she could not bake
7. 5.

   Tim bakes only cakes and Rosa only loaves, and they trade 3 loaves for 2 cakes. Zee checks the trade. Does each baker gain?

   • Rosa alone gains, since she is better at both jobs and receives the cakes she wanted
   • Neither gains, since they swap 3 loaves for 2 cakes and what one gets the other gives up
   • Yes: Rosa pays 1.5 loaves a cake instead of 2, and Tim gets 1.5 loaves a cake instead of 1
   • Tim alone gains, since he bakes the cakes and receives loaves that Rosa found easy to make
8. 6.

   Kira tests Rosa's idea on card B with card A. What is the verdict?

   • Strong: Tim bakes less of both, so leaving Tim out costs Rosa nothing she would miss
   • Weak: trading loaves for cakes costs Rosa 1.5 loaves a cake instead of 2, so she ends with more
   • Weak: Rosa should bake nothing and let Tim do the baking, since Tim's cakes are cheaper
   • Strong: Rosa makes more of both goods per day, so she would produce more by working alone

9. Use this

   Cards A and B on income tax (card A is IRS data; card B is made up). Card A, "Federal income tax brackets for 2024, single filers". Source: Internal Revenue Service, IRS provides tax inflation adjustments for tax year 2024 (irs.gov), read Nov 14, 2026. Summary in our words, not a quotation: the rate is 10 percent on taxable income up to $11,600; 12 percent on the part over $11,600 up to $47,150; 22 percent on the part over $47,150 up to $100,525; and 24 percent on the part over $100,525 up to $191,950. Each rate applies only to the part of income inside its bracket. Card B, "Noor's year (made up)". Written for this sheet. Summary in our words, not a quotation: Noor is single and has $50,000 of taxable income in 2024. Noor is offered a $1,000 bonus for a weekend of extra work.

10. 7.

    Milo reads cards A and B. How much of the $1,000 bonus does Noor keep, and why?

    • $780: the bonus falls in the 22 percent bracket, so $220 goes to tax
    • About −$4,000: the bonus lifts Noor's whole pay into the 22 percent bracket, so tax jumps
    • $880: the bonus is taxed at the 12 percent rate that most of Noor's income pays
    • $760: the bonus is taxed at 24 percent, the next bracket, because it is a large extra payment
11. 8.

    Noor values the free weekend at $850. Luz uses cards A and B. Should Noor take the bonus work?

    • No: after tax the weekend pays $780, less than the $850 Noor puts on the free time
    • Yes: the bonus is $1,000, which is more than the $850 Noor puts on the free weekend
    • No: tax takes over half of a bonus, so extra work does not pay for Noor
    • Yes: the bonus is taxed at the 12 percent rate, so Noor keeps $880, more than $850

12. Use this

    Card A on a ticket and a shift (all made up for practice). Card A, "Lena's evening (made up)". Written for this sheet. Summary in our words, not a quotation: Lena paid $40 for a concert ticket that cannot be refunded or sold. On the night Lena has a cold, and the concert is now worth $20 to Lena. A cafe offers Lena a shift at the same time, paying $60. The shift costs Lena $25 in effort.

13. 9.

    Noah reads card A. What should Lena do, and why?

    • Go to the concert: Lena paid $40, and skipping it would waste that money
    • Go to the concert: it is worth $20 to Lena tonight, and the shift is just a chore
    • Work the shift: it nets $35, more than the concert's $20, and the $40 ticket is spent either way
    • Work the shift because it pays $60, more than the $40 the ticket cost Lena
14. 10.

    Ren lists four claims about card A. Which one goes beyond what the card shows?

    • Going to the concert means giving up a shift that would net Lena $35
    • The shift pays $60 and costs Lena $25 in effort, a net of $35
    • Buying the ticket was a mistake, because Lena now loses $40 whatever Lena does
    • The $40 for the ticket cannot be recovered, whether Lena goes to the concert or not