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

Grade 12 Social Studies Worksheet

Circle the best answer.

1. Read this first

   Use this

   Cards A and B on a firm's output (all made up for practice). Card A, "A workshop's costs (made up)". Written for this sheet. Table, columns Units made in a day | Total cost: 0 | $20; 1 | $32; 2 | $41; 3 | $49; 4 | $62; 5 | $79; 6 | $101. The $20 is owed even if the workshop makes nothing. Card B, "Prices (made up)". Written for this sheet. Summary in our words, not a quotation: the workshop sells each unit at the market price, which it cannot change. The price is $20 at first, later $11, and later still $24.

2. 1.

   Zee uses cards A and B. How many units should the workshop make when the price is $20?

   • Four: average cost per unit is lowest at four units, $15.50, so that is the right output
   • Five: the 5th unit adds $17 of cost and sells for $20, but the 6th would add $22
   • Two: the first units are the cheapest to make, so output should stop where costs are lowest
   • Six: the price of $20 is above the average cost of the first units, so more output pays
3. 2.

   The price falls to $11. Pia uses cards A and B. What should the workshop do?

   • Close down: at $11 the workshop cannot cover its $20 cost, so it should make nothing
   • Make six: with a price this low, the workshop should make as many units as it can to spread the $20
   • Make three: that loses $16, less than the $20 owed if it makes none
   • Make five: the price is above the cost of the first units, so output should rise to five

4. Use this

   Cards A and B on income tax and overtime (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. Each rate applies only to the part of income inside its bracket. Card B, "Ola's overtime (made up)". Written for this sheet. Summary in our words, not a quotation: Ola is single and has $46,010 of taxable income. Ola is offered overtime at $30 an hour, up to $3,000 in all (100 hours). Ola values an hour of free time at $24.

5. 3.

   Esme uses cards A and B. How much of the $3,000 does Ola keep if all 100 hours are worked?

   • Under $1,000: the overtime pushes Ola's whole income into the 22 percent bracket and the tax jumps
   • About $2,640: all $3,000 is taxed at 12 percent, the rate Ola's $46,010 already pays
   • About $2,340: all $3,000 is taxed at 22 percent, since the overtime lifts Ola into that bracket
   • About $2,454: part of the pay is taxed at 12 percent and the rest at 22 percent, $546 in all
6. 4.

   Jun works out how many overtime hours are worth taking for Ola, using cards A and B. What is the best number?

   • About 38 hours: those hours keep $26.40 each, but hours beyond keep only $23.40, below Ola's $24
   • None: Ola's marginal rate is 22 percent, and a $30 hour then keeps $23.40, below Ola's $24
   • All 100: the whole $3,000 leaves $2,454, or $24.54 an hour, which is above Ola's $24
   • Cannot be decided: Ola's value of free time is a feeling, so no number of overtime hours can be worked out
7. 5.

   A reporter says Ola's overtime will push all of Ola's income into the 22 percent bracket and cut take-home pay. Ren checks card A. What is the verdict?

   • Wrong: only the overtime above $47,150 is taxed at 22 percent, so extra pay always raises take-home
   • Right in part: the extra tax would exceed the pay for the first hours, so Ola should skip those hours
   • Wrong, because overtime is taxed under a different system and the brackets on card A do not apply to it
   • Right: income above $47,150 is taxed at 22 percent, so all of Ola's pay is now taxed at that rate

8. Use this

   Cards A to C on trade between two countries (all made up for practice). Card A, "Output in one worker-day (made up)". Written for this sheet. Table, columns | Grain (tons) | Cloth (bolts), each worker-day makes one or the other: Country M | 12 | 6; Country N | 3 | 3. Card B, "A proposal (made up)". Written for this sheet. Summary in our words, not a quotation: M offers N 1.5 tons of grain for each bolt of cloth. A third speaker says M should make its own cloth, since M is better at both goods. Card C, "A second proposal (made up)". Written for this sheet. Summary in our words, not a quotation: N offers M 2.5 tons of grain for each bolt of cloth.

9. 6.

   Bo compares the two proposals on cards B and C. Which statement is best supported?

   • N's offer gains both countries, since 2.5 is more than 2 and N is giving up more
   • Both offers gain both countries, since each country gets the good it wanted from the other
   • M's offer of 1.5 tons gains both, but N's offer of 2.5 tons would cost M more than it saves
   • M's offer hurts N, since N is paid 1.5 tons for cloth that took N less work than that to make
10. 7.

    Tala tests the third speaker's claim on card B with card A. What is the best verdict?

    • Strong: M makes more of both goods, so it gains nothing by buying cloth from another country
    • Weak: M cannot make grain and cloth in the same worker-day, so the claim is about timing
    • Strong: N gains from the trade, which shows M has nothing left to gain from it
    • Weak: trading at 1.5 tons a bolt gets M cloth for less than the 2 tons it costs to make

11. Use this

    Cards A to C on paying students to read (all made up for practice). Card A, "A reading reward (made up)". Written for this sheet. Summary in our words, not a quotation: 600 students were assigned by lottery to a reward group or a comparison group. The reward group was paid $2 for each book read. Over the semester the reward group read 9.0 books on average and the comparison group read 6.5. Test scores were 71 in both groups. Card B, "After the rewards stopped (made up)". Written for this sheet. Summary in our words, not a quotation: the next semester, with no rewards for either group, the former reward group read 5.8 books on average and the comparison group read 6.4. Card C, "Two views (made up)". Written for this sheet. Summary in our words, not a quotation: Speaker H says rewards work, since students read more. Speaker J says rewards make reading a chore, so students read less later.

12. 8.

    Ari weighs speakers H and J on card C against cards A and B. Which statement fits the evidence best?

    • Neither: test scores were 71 in both groups, so reading changed nothing and neither speaker has a point
    • H is right: the reward group read 2.5 more books, which shows rewards raise reading for good
    • J is right: the reward group later read less than the comparison group, so the rewards caused the drop
    • Both have a point: rewards raised reading by 2.5 books, then reading fell below the comparison group's
13. 9.

    Noah works out the cost per extra book in card A. What does it suggest about the program?

    • The cost is about $2.80 for each extra book, since 2.5 extra books are bought with $7
    • About $7.20 for each extra book, since $2 is paid on all 9.0 books but only 2.5 are extra
    • The cost is $2 for each extra book, which is the price the program pays for each book read
    • The cost is $18 for each extra book, the total paid to a student for the semester
14. 10.

    Speaker J says rewards cause students to read less later. What evidence would most help Kira test the claim?

    • Whether reading fell more in students whose rewards were taken away than in students who were never rewarded
    • Whether students in the reward group liked the books they read, since liking would explain later reading
    • Whether test scores of the comparison group changed in the second semester, since scores may have moved
    • Whether the 600 students were assigned by lottery, since the lottery decides whether the groups differ