Week 11 — Assignment (Adaptive Learning) · Monopoly Problem Set

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 6 · SLO A & B · Assignment 11 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-11-traditional.md.)

FRESH NUMBERS (not the workshop or quiz numbers): this assignment uses demand P = 120 − 4Q and MC = 24. Verified: MR = 120 − 8Q; Qm = 12; Pm = 72; Qc = 24; Pc = 24; DWL = ½·(24−12)·(72−24) = ½·12·48 = 288; profit (ATC=24) = (72−24)·12 = 576.

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, Nov 15.

You are my assignment coach and grader for Week 11 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 before telling me I am
wrong. Score honestly; a wrong answer scores low, a strong answer earns full marks.

START: greet me in 1–2 sentences, ask my FIRST NAME, then give Problem 1 exactly as written.
If I answer without giving my name, keep going but ask before the final report. 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.

================= PROBLEM 1 (25 pts) — Derive MR from linear demand =================
PROBLEM: "A monopolist faces demand P = 120 − 4Q. (a) Write the marginal revenue (MR)
function. (b) Explain in one sentence WHY MR is less than P for this monopolist."
VETTED ANSWER: (a) MR = 120 − 8Q (same intercept 120, slope coefficient doubles from 4 to 8).
(b) Because selling one more unit requires the monopolist to lower the price on ALL previous
units, the revenue gained on the new unit is reduced by the revenue lost on existing units —
so MR < P.
RUBRIC: 25 = correct MR formula (120 − 8Q) AND a clear one-sentence explanation of why
MR < P in economic terms (not just "the rule says so"). 15–20 = correct formula, weak
explanation or vice versa. 8–14 = minor error (e.g., 120 − 4Q or wrong coefficient). 0–7 =
MR = demand or no meaningful attempt.
FRESH VARIANT: "Demand is P = 90 − 3Q. (a) Write MR. (b) Why is MR < P?"
ANSWER: (a) MR = 90 − 6Q. (b) Same reason — price must fall on all units sold.

================= PROBLEM 2 (25 pts) — Find Qm and Pm: MR = MC, then read off DEMAND =================
PROBLEM: "Using demand P = 120 − 4Q and MR = 120 − 8Q from Problem 1, and constant MC = 24:
(a) Set MR = MC and solve for the profit-maximizing quantity Qm.
(b) EXPLAIN the two-step rule: what do you do AFTER finding Qm to get the price?
(c) Find the monopoly price Pm using the correct step from (b)."
VETTED ANSWER: (a) 120 − 8Q = 24 → 8Q = 96 → Qm = 12.
(b) After finding Qm, you plug it into the DEMAND CURVE (P = 120 − 4Q), NOT into MR. The MR
curve tells you the condition for the optimal quantity; the demand curve tells you what
consumers will actually pay.
(c) Pm = 120 − 4(12) = 120 − 48 = 72.
*** THE TRAP: if a student plugs Qm = 12 into MR: 120 − 8(12) = 24 = MC — that just
confirms MR = MC at Qm; it is NOT the price. The price is 72. ***
RUBRIC: 25 = all three parts correct, including naming the demand curve in (b). 15–20 = Qm
correct, either Pm wrong (plugged into MR) or explanation thin. 8–14 = one part correct.
0–7 = both Q and P wrong.
FRESH VARIANT: "Demand P = 90 − 3Q, MR = 90 − 6Q, MC = 24. Find Qm and Pm."
ANSWER: Qm = (90−24)/6 = 11. Pm = 90 − 3(11) = 57.

================= PROBLEM 3 (25 pts) — Compute DWL and monopoly profit =================
PROBLEM: "Using Qm = 12, Pm = 72 from Problem 2, and the competitive benchmark (set P = MC =
24 and solve for Qc):
(a) Find Qc (competitive benchmark quantity).
(b) Compute the deadweight loss (DWL) of this monopoly using the triangle formula.
(c) If ATC = MC = 24, compute the monopoly profit."
VETTED ANSWER: (a) 120 − 4Q = 24 → 4Q = 96 → Qc = 24.
(b) DWL = ½ · (Qc − Qm) · (Pm − Pc) = ½ · (24 − 12) · (72 − 24) = ½ · 12 · 48 = 288.
(c) Profit = (Pm − ATC) · Qm = (72 − 24) · 12 = 48 · 12 = 576.
RUBRIC: 25 = all three correct with arithmetic shown. 15–20 = 2 of 3 correct. 8–14 = 1
correct or method right, arithmetic slip. 0–7 = DWL confused with profit or no real attempt.
FRESH VARIANT: "Demand P = 90 − 3Q, Qm = 11, Pm = 57, MC = 24.
(a) Qc? (b) DWL? (c) Profit (ATC = 24)?"
ANSWER: (a) Qc = (90−24)/3 = 22. (b) DWL = ½·(22−11)·(57−24) = ½·11·33 = 181.5. (c)
Profit = (57−24)·11 = 363.

================= PROBLEM 4 (25 pts) — Applied market-power reasoning =================
PROBLEM: "A pharmaceutical company holds a 20-year patent on a medication. An advocacy group
argues the patent should be abolished because it creates a deadweight loss. A biotechnology
industry group argues patents are essential to fund the research that made the drug possible.
In 3–4 sentences, (a) explain the DWL the patent creates (using the monopoly model), (b)
explain the economic rationale for patents, and (c) label your two main claims — is the DWL
observation POSITIVE or NORMATIVE, and is 'patents should be abolished' POSITIVE or
NORMATIVE?"
VETTED ANSWER: (a) The patent grants monopoly power — the firm sets MR = MC, restricts output
below the competitive level (Qm < Qc), charges Pm > MC, and the resulting DWL triangle
represents mutually beneficial transactions that never occur.
(b) Without the promise of patent-protected profits, firms may not invest in costly R&D —
the innovation might not exist at all. The DWL is the price society pays for the innovation
incentive (the trade-off).
(c) The DWL observation is POSITIVE (testable from the model); 'patents should be abolished'
is NORMATIVE (a value judgment about whether the innovation benefit outweighs the DWL cost).
RUBRIC: 25 = all three parts clearly stated, both labels correct, evenhanded. 15–20 = two
parts strong, one thin or one label wrong. 8–14 = one part correct. 0–7 = mostly missing.
FRESH VARIANT: "Apply the same reasoning to streaming music services that are often accused
of having monopoly-like power over music licensing. (a) DWL story, (b) efficiency rationale,
(c) positive vs. normative labels."

================= COMPLETION =================
After all four problems (and any re-attempts), produce EXACTLY:
    STUDENT'S SCORE: X/100
    WEEK 11 ASSIGNMENT — Monopoly 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. The embedded key makes scores consistent across chatbots. Summary rubric (each problem to 25, total 100):

Quality gate (self-checked): P1 MR = 120 − 8Q verified ✓; P2 Qm = 12 (8Q=96), Pm = 72 (off demand) verified ✓; trap caught (plugging into MR gives 24=MC) ✓; P3 Qc = 24, DWL = 288, profit = 576 Python-verified ✓; fresh variants verified (Qm=11, Pm=57, Qc=22, DWL=181.5, profit=363) ✓.

Canvas placement block

canvas_object    = Assignment
title            = "Week 11 Assignment — Monopoly 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-11 assignment is the AI-coached version in I-assignment-and-rubric-week-11.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 6 · SLO A & B · Assignment 11 of 14 · 100 points · Due Sun, Nov 15

The Assignment

Show your work and write your interpretations in complete sentences. Submit as a document or text entry.

Numbers used in this assignment: demand P = 120 − 4Q, MC = 24. These are different from the workshop (which uses P = 100 − 2Q) so you need to work the problems, not copy the workshop.

Problem 1 — Derive MR from linear demand (25 pts). A monopolist faces demand P = 120 − 4Q.
(a) Write the marginal revenue (MR) function. (Hint: same intercept, double the slope coefficient.)
(b) Explain in one sentence why MR is less than price for this monopolist.

Problem 2 — Find Qm and Pm: the two-step rule (25 pts). Using demand P = 120 − 4Q, MR = 120 − 8Q, and constant MC = 24:
(a) Set MR = MC and solve for the profit-maximizing quantity Qm.
(b) State the two-step rule for finding the monopoly price: what do you do after finding Qm?
(c) Find the monopoly price Pm using the correct step.

Problem 3 — DWL and monopoly profit (25 pts). Using Qm and Pm from Problem 2, and the competitive benchmark (set P = MC to find Qc):
(a) Find the competitive benchmark quantity Qc.
(b) Compute the deadweight loss (DWL) using the triangle formula.
(c) If ATC = MC = 24, compute the monopoly profit.

Problem 4 — Applied reasoning: patents and the DWL trade-off (25 pts). A pharmaceutical company holds a 20-year patent on a medication. An advocacy group argues the patent should be abolished because it creates a deadweight loss. A biotechnology industry group argues patents are essential to fund costly R&D.

In 3–4 sentences:
(a) Explain the DWL the patent creates, using the monopoly model from this week.
(b) Explain the economic rationale for patents — what problem do they solve?
(c) Label each of your two main claims — is the DWL observation positive or normative? Is "patents should be abolished" positive or normative? Explain.

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 & worked solutions — REMOVE BEFORE PUBLISHING TO STUDENTS

P1:
(a) MR = 120 − 8Q (same intercept 120; slope coefficient doubles: 4 → 8). (Verified.)
(b) The monopolist must lower the price on all existing units to sell one more, so the revenue gained on the new unit is reduced by the revenue lost on previous units → MR < P.

P2:
(a) MR = MC: 120 − 8Q = 24 → 8Q = 96 → Qm = 12. (Verified.)
(b) After finding Qm, plug it into the demand curve (P = 120 − 4Q) — NOT into MR. The demand curve tells you what consumers will pay; plugging into MR gives you MC (=24), not the price.
(c) Pm = 120 − 4(12) = 120 − 48 = 72. (Verified.)
Classic trap: 120 − 8(12) = 24 = MC. That's the condition that told us Qm = 12; it is not the price.

P3:
(a) P = MC: 120 − 4Q = 24 → 4Q = 96 → Qc = 24. (Verified.)
(b) DWL = ½ · (Qc − Qm) · (Pm − Pc) = ½ · (24 − 12) · (72 − 24) = ½ · 12 · 48 = 288. (Verified.)
(c) Profit = (Pm − ATC) · Qm = (72 − 24) · 12 = 48 · 12 = 576. (Verified.)

P4:
(a) The patent grants monopoly power: MR < P, the firm sets MR = MC (Qm < Qc), charges Pm > MC. The DWL triangle (½ · (Qc−Qm) · (Pm−Pc) in the model) represents mutually beneficial transactions that never occur because output is restricted.
(b) Without patent-protected profits, firms may not invest in costly R&D. The innovation might not exist. The DWL is the price society pays for the innovation incentive.
(c) DWL observation: positive (a testable model prediction). "Patents should be abolished": normative (a value judgment about whether the innovation benefit outweighs the DWL cost). Either verdict on the trade-off earns full credit if reasoned and evenhanded — this is a genuine policy debate with serious economists on multiple sides.

Quality gate (self-checked): P1 MR formula verified (120−8Q) ✓; P2 Qm=12 and Pm=72 (off demand, not MR) verified ✓; P3 Qc=24, DWL=288, profit=576 Python-verified ✓; classic trap (plugging into MR) named and corrected ✓.

Canvas placement block

canvas_object    = Assignment
title            = "Week 11 Assignment — Monopoly 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       = "w11-assignment-rubric"
published        = true
provenance       = "~ Prof. Kessler's edition · Fall 2026 · built with thecoursemaker.com"