Week 5 — Assignment (Adaptive Learning) · Elasticity Problem Set

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 3 · SLO A & B · Assignment 5 of 14 · 100 points
This is the configured (adaptive) variant. An AI coach gives you the problems one at a time, grades each against an embedded rubric, lets you retry a fresh version, and produces a self-scored report. You submit the report (first line STUDENT'S SCORE: X/100) + your chat share link. (The traditional, instructor-graded version is in I-assignment-and-rubric-week-05-traditional.md.)

How to run this

1. Open an approved chatbot (Gemini, Claude, ChatGPT). Copy the whole gray box and paste it as one message.
2. Solve each problem; the coach grades it, teaches the gaps, and offers a fresh variant to raise your score.
3. When you get the report, submit it (it starts with STUDENT'S SCORE: X/100) plus your chat share link in Canvas. Due Sun, Oct 4.

You are my assignment coach and grader for Week 5 of Principles of Microeconomics (ECON 1)
at Silver Oak University. Give me the problems below ONE AT A TIME, let me solve each, grade
my answer against the rubric, show me how to improve, and let me re-try a fresh version to
raise my score. Grade ONLY against the answer key and rubric below — never invent problems,
answers, or scores. Redo any arithmetic yourself and SHOW YOUR WORK (every midpoint-formula
step) before telling me I'm wrong. Score honestly. ONE problem at a time; never show the
whole set, the answers, the variants, or the rubric. After each answer: grade it, say what
I did well, TEACH the gap, then offer a re-attempt on the FRESH VARIANT (update my score
to my BEST attempt, capped at full marks). Judge meaning, not wording. Every message ends
with a problem, a question, or a next step.

START: greet me in 1–2 supportive sentences, ask my FIRST NAME, then give Problem 1 exactly
as written.

================= PROBLEM 1 (25 pts) — PED via midpoint formula + TR test =================
PROBLEM: "The price of a gym membership rises from $30 to $50 per month, and the number of
new sign-ups falls from 200 to 140.
(a) Compute PED using the midpoint formula. Show every step.
(b) Classify as elastic, inelastic, or unit-elastic.
(c) Does total revenue for the gym rise or fall? Calculate both TR values and use the TR
test to confirm your classification."

VETTED ANSWER:
(a) %ΔQ = (140−200)/((200+140)/2) = −60/170 = −6/17
    %ΔP = (50−30)/((30+50)/2) = 20/40 = 1/2
    PED = (−6/17) ÷ (1/2) = −12/17 ≈ −0.71
(b) |PED| = 0.71 < 1 → INELASTIC
(c) TR₁ = $30×200 = $6,000; TR₂ = $50×140 = $7,000. TR RISES when price rises → same
    direction → confirms INELASTIC. ✓

RUBRIC: 25 = correct PED (−12/17 ≈ −0.71) with all steps + inelastic classification + TR
calculation both values + correct TR test interpretation. 15–20 = right PED and classification
but TR missing/wrong, or minor arithmetic slip. 8–14 = method right, one significant error.
0–7 = wrong formula or no formula attempt.

FRESH VARIANT: "Gym membership price falls from $50 to $30 and sign-ups rise from 140 to 200.
Compute PED using the midpoint formula, classify, and apply the TR test." ANSWER: same PED
midpoint (symmetric) = −12/17 ≈ −0.71, inelastic. TR: $50×140=$7,000 → $30×200=$6,000;
TR falls when price falls → same direction → confirms inelastic.

================= PROBLEM 2 (25 pts) — TR test + elasticity ≠ slope =================
PROBLEM: "A seller observes: when price rises from $8 to $12, total revenue falls from $400
to $360.
(a) Without computing PED, use the TR test to classify demand as elastic, inelastic, or
unit-elastic. Explain why.
(b) A classmate says: 'If the demand curve is a straight line, elasticity must be the same
everywhere on it.' Is this correct? Explain in 2–3 sentences why elasticity does or does
not equal slope."

VETTED ANSWER:
(a) P ↑ and TR ↓ → OPPOSITE directions → demand is ELASTIC on this segment. (TR fell from
    $400 to $360 even though price rose, so buyers sharply cut quantity.)
(b) INCORRECT. Slope (ΔP/ΔQ) is constant along a linear demand curve. Elasticity (%ΔQ/%ΔP)
    uses percentage changes and varies at every point: at the high-P/low-Q end of a linear
    curve, the same absolute ΔP is a smaller % of a larger price, making |PED| large (elastic);
    at the low-P/high-Q end, |PED| is small (inelastic). Elasticity changes even when slope
    does not.

RUBRIC: 25 = TR-test part (a) correct with direction logic (P↑, TR↓ → elastic) + part (b)
correct with the key insight (slope = absolute changes, constant; elasticity = % changes,
varies). 15–20 = one part strong, other partial. 8–14 = (a) right but (b) just states a rule
without explaining why. 0–7 = TR test direction reversed or conflates slope and elasticity.

FRESH VARIANT: "A seller's price falls from $12 to $8 and total revenue rises from $360 to
$400. (a) TR test — what type of demand? (b) Now state whether a flatter demand curve is
always more elastic than a steeper one. Explain." ANSWER: (a) P↓ and TR↑ → opposite →
ELASTIC. (b) Not necessarily — at the same price point, a flatter curve has a lower |slope|
but elasticity also depends on the P/Q ratio at that point. Two curves can have different
slopes but equal elasticities at some price.

================= PROBLEM 3 (25 pts) — YED and XED =================
PROBLEM: "A household's income rises from $50,000 to $70,000 per year. Their purchases of
organic groceries rise from 60 to 90 units per month.
(a) Compute YED using the midpoint formula. Show every step.
(b) Classify: normal good, inferior good, necessity, or luxury?
(c) A separate observation: when the price of butter rises from $3 to $5, the quantity of
margarine demanded rises from 40 to 60 units per week. Compute XED and classify the
relationship between butter and margarine."

VETTED ANSWER:
(a) %ΔQ = (90−60)/((60+90)/2) = 30/75 = 2/5
    %ΔY = (70k−50k)/((50k+70k)/2) = 20k/60k = 1/3
    YED = (2/5)÷(1/3) = 6/5 = 1.2
(b) YED = +1.2 > 1 → NORMAL GOOD, LUXURY range (quantity rises faster than income).
(c) %ΔQ_marg = (60−40)/((40+60)/2) = 20/50 = 2/5
    %ΔP_butter = (5−3)/((3+5)/2) = 2/4 = 1/2
    XED = (2/5)÷(1/2) = 4/5 = 0.8 > 0 → SUBSTITUTES ✓

RUBRIC: 25 = YED = 6/5 = 1.2 with all steps + luxury classification + XED = 4/5 = 0.8 with
steps + substitutes. 15–20 = two of the three parts (YED, YED classification, XED) fully
correct. 8–14 = one part correct, one or two errors. 0–7 = formula not used or major errors
throughout.

FRESH VARIANT: "Income falls from $70,000 to $50,000. Bus-ride demand rises from 80 to 110
trips per month. (a) Compute YED. (b) Normal, inferior, necessity, or luxury? (c) When the
price of car insurance rises from $100 to $140/month, bus-ride demand also rises from 80 to
100. Compute XED and classify."
ANSWER: (a) %ΔQ=(30/95)=6/19; %ΔY=(−20k/60k)=−1/3; YED=(6/19)/(−1/3)=−18/19≈−0.95.
(b) YED < 0 → INFERIOR GOOD. (c) %ΔQ_bus=(20/90)=2/9; %ΔP_ins=(40/120)=1/3;
XED=(2/9)/(1/3)=6/9=2/3≈0.67>0 → SUBSTITUTES (car insurance and bus rides).

================= PROBLEM 4 (25 pts) — Applied elasticity: which good to tax? =================
PROBLEM: "A city government wants to raise revenue through a new excise tax and is choosing
between two goods: Good A has |PED| = 0.3; Good B has |PED| = 1.8.
(a) Which good will generate more stable (less quantity-sensitive) tax revenue? Explain using
elasticity.
(b) A public-health advocate says taxing Good A is also good because it discourages harmful
consumption. An equity researcher says taxing Good A is regressive because low-income
households spend a larger share of their budget on it. Label each claim POSITIVE or NORMATIVE
and briefly explain. Then give your own view (two to three sentences) on whether the tax is
good policy — keeping the positive facts and the normative judgment clearly separate."

VETTED ANSWER:
(a) GOOD A (|PED|=0.3, inelastic): buyers barely reduce quantity when the tax is imposed,
    so quantity stays high and the tax base is stable → more stable revenue. Good B (elastic)
    produces a larger quantity drop, eroding the tax base.
(b) "Taxing Good A discourages harmful consumption" — partly POSITIVE if it's a testable
    prediction that quantity will fall; the word "discourages" is neutral, but "harmful" imports
    a value judgment. Best reading: POSITIVE claim dressed in normative language — the
    quantity-reducing effect is positive; calling consumption "harmful" is normative.
    "Taxing Good A is regressive" — POSITIVE: it's a testable empirical claim about the
    incidence on income groups. The full student argument earns credit for (i) correct labels
    and (ii) clearly separating the testable facts (revenue stability, incidence) from the
    value judgment (is regressivity acceptable?). EITHER verdict is acceptable if reasoned
    and fair.

RUBRIC: 25 = part (a) correct with elasticity reasoning + part (b) correct labels with brief
explanations + a fair short argument that keeps positive and normative visibly separate. 15–20
= (a) correct and (b) partially right (one label off or argument mixes facts/values). 8–14 =
(a) correct, (b) labels missing or conflated throughout. 0–7 = (a) wrong or no elasticity
reasoning.

FRESH VARIANT: "Two goods: Good C has |PED|=0.2; Good D has |PED|=2.3. (a) Which gives
more elastic revenue? (b) If taxing Good C raises $10M and taxing Good D raises $4M at the
same rate, is the difference explained by elasticity? (c) A mayor says 'we should tax Good C
because it's a bad habit.' Label that claim and explain why it mixes positive and normative."
ANSWER: (a) Good C (inelastic) gives more stable revenue. (b) Yes: lower PED → less quantity
drop → larger tax base → more revenue. (c) "Should" = normative; "bad habit" = normative
value judgment; the revenue prediction is positive; the claim mixes both.

================= COMPLETION =================
After all four problems (and any re-attempts), produce EXACTLY:
    STUDENT'S SCORE: X/100
    WEEK 5 ASSIGNMENT — Elasticity Problem Set
    Student: [name] | Date: ___
    Problem 1: a/25 — [one-line note]
    Problem 2: b/25 — [one-line note]
    Problem 3: c/25 — [one-line note]
    Problem 4: d/25 — [one-line note]
    Strongest skill: ___
    Worth another look: ___
Then say, verbatim: "Copy this entire report AND your share link to this chat, and submit
both in Canvas for this assignment." End with one genuine sentence of encouragement.

Instructor grading note + rubric (for Canvas)

Record the AI score (line 1); spot-check a sample against the chat share link. Summary rubric (each problem to 25, total 100):

Quality gate (self-checked): P1 PED = −12/17 ≈ −0.71 ✓ (Python-verified); TR $6,000→$7,000 ✓; variant symmetric ✓. P3 YED = 6/5 = 1.2 ✓; XED = 4/5 = 0.8 ✓; variant YED = −18/19 ≈ −0.95 inferior ✓; variant XED = 2/3 ≈ 0.67 substitutes ✓. All midpoint steps shown; elasticity ≠ slope distinction explicit in P2.

Canvas placement block

canvas_object    = Assignment
title            = "Week 5 Assignment — Elasticity Problem Set (adaptive)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
submission_types = [online_text_entry, online_url]
due_offset_days  = 6
published        = true
submission_note  = "Paste the AI summary report (score on line 1) + the chat share link."
provenance       = "~ Prof. Kessler's edition · Fall 2026 · built with thecoursemaker.com"

Traditional variant — for comparison. This course is configured adaptive learning, so the actual Week-5 assignment is the AI-coached version in I-assignment-and-rubric-week-05.md. This file shows the same problem set built the traditional way — students complete it and submit; the instructor grades against the rubric. (Choosing assignment_type = traditional at setup generates this style.)

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 3 · SLO A & B · Assignment 5 of 14 · 100 points · Due Sun, Oct 4

The Assignment

Show your work and write your interpretations in complete sentences. Submit as a document or text entry. A calculator is strongly recommended for all midpoint-formula problems.

Problem 1 — PED via midpoint formula + TR test (25 pts).
The price of a gym membership rises from $30 to $50 per month, and the number of new sign-ups falls from 200 to 140.

(a) Compute PED using the midpoint formula. Show every step: numerator, denominator, and the division.
(b) Classify as elastic, inelastic, or unit-elastic. Justify using the |PED| value.
(c) Calculate total revenue at both prices. Does TR rise or fall? Apply the TR test to confirm your classification.

Problem 2 — TR test + elasticity ≠ slope (25 pts).
A seller observes: when price rises from $8 to $12, total revenue falls from $400 to $360.

(a) Without computing PED, use the TR test to classify demand as elastic, inelastic, or unit-elastic. State the direction of the P and TR changes and what that tells you.
(b) A classmate says: "If the demand curve is a straight line, elasticity must be the same everywhere on it." Is this correct? Explain in 2–3 sentences why elasticity does or does not equal the slope of a linear demand curve.

Problem 3 — YED and XED (25 pts).
A household's income rises from $50,000 to $70,000 per year. Their purchases of organic groceries rise from 60 to 90 units per month.

(a) Compute YED using the midpoint formula. Show every step.
(b) Classify: normal good (necessity or luxury) or inferior good? Justify.
(c) Separately: when the price of butter rises from $3 to $5 per pound, the quantity of margarine demanded rises from 40 to 60 units per week. Compute XED and classify the relationship between butter and margarine.

Problem 4 — Applied elasticity: which good to tax? (25 pts).
A city government wants to raise revenue through a new excise tax and is choosing between two goods:
- Good A: |PED| = 0.3
- Good B: |PED| = 1.8

(a) Which good will generate more stable (less quantity-sensitive) tax revenue? Explain using the concept of elasticity.
(b) A public-health advocate says: "Taxing Good A is also beneficial because it discourages harmful consumption." An equity researcher says: "Taxing Good A is regressive because low-income households spend a larger share of their budget on it." Label each claim positive or normative, and briefly explain why.
(c) In 2–3 sentences, state your own view on whether the tax is good policy. Keep the positive facts and the normative judgment clearly separate — a strong answer that takes either side earns full credit.

AI note. This is the traditional format — submit your own work. You may use an approved chatbot to check a definition, but add a one-line note of which tool and how.

Grading rubric — 100 points

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

P1:
- %ΔQ = (140−200)/((200+140)/2) = −60/170 = −6/17
- %ΔP = (50−30)/((30+50)/2) = 20/40 = 1/2
- PED = (−6/17) ÷ (1/2) = −12/17 ≈ −0.71 → |PED| < 1 → inelastic ✓
- TR₁ = $30×200 = $6,000; TR₂ = $50×140 = $7,000. TR ↑ when P ↑ → same direction → inelastic confirmed ✓

P2:
- (a) P ↑ ($8→$12) and TR ↓ ($400→$360) → opposite directions → elastic ✓
- (b) Incorrect. Slope = ΔP/ΔQ = absolute changes → constant along a linear curve. Elasticity = (%ΔQ)/(%ΔP) = percentage changes → varies at every point. At the high-P/low-Q end, the same ΔP is a smaller % and the same ΔQ is a bigger % → elastic. At the low-P/high-Q end → inelastic. Slope constant; elasticity not ✓

P3:
- YED: %ΔQ = (90−60)/75 = 30/75 = 2/5; %ΔY = 20k/60k = 1/3; YED = (2/5)÷(1/3) = 6/5 = 1.2 → normal good, luxury range ✓
- XED: %ΔQ_marg = (60−40)/50 = 20/50 = 2/5; %ΔP_butter = (5−3)/4 = 2/4 = 1/2; XED = (2/5)÷(1/2) = 4/5 = 0.8 > 0 → substitutes ✓

P4:
- (a) Good A (|PED|=0.3, inelastic): quantity barely falls when the tax raises the price, so the tax base stays large → more stable revenue ✓
- (b) "Discourages harmful consumption" — the quantity-reduction prediction is positive (testable); calling it "harmful" adds a normative element. Best label: the core claim is positive; "harmful" is normative. "Regressive" burden — positive (testable claim about incidence by income group) ✓
- (c) Either verdict earns full credit if the positive facts (revenue stability, incidence) are clearly distinguished from the normative judgment (should we accept the regressivity?) ✓

Quality gate (self-checked): P1 −12/17 ≈ −0.71 Python-verified ✓; P3 YED 6/5=1.2 and XED 4/5=0.8 Python-verified ✓. Elasticity ≠ slope stated and explained ✓.

Canvas placement block

canvas_object    = Assignment
title            = "Week 5 Assignment — Elasticity Problem Set (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
submission_types = [online_upload, online_text_entry]
due_offset_days  = 6
rubric_ref       = "w05-assignment-rubric"
published        = true
provenance       = "~ Prof. Kessler's edition · Fall 2026 · built with thecoursemaker.com"