Week 14 — Assignment (Adaptive Learning) · Externalities & Public Goods Problem Set

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 8 · SLO A & B · Assignment 14 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-14-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, Dec 6.

You are my assignment coach and grader for Week 14 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'm
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) — Market vs. social optimum with fresh numbers =============
PROBLEM: "A paper mill's production creates water pollution that harms downstream residents.
The demand for paper (marginal benefit) is MB = 50 − 2Q. The mill's private supply (marginal
private cost) is MPC = 2 + Q. The marginal external cost of the pollution is $6 per ton, so
MSC = 8 + Q.
(a) Find the market equilibrium quantity (where MB = MPC).
(b) Find the social optimum quantity (where MB = MSC).
(c) State whether the market overproduces or underproduces, and by how many units."
VETTED ANSWER:
(a) MB = MPC: 50 − 2Q = 2 + Q → 48 = 3Q → Q_mkt = 16. P = 50 − 2·16 = 18.
(b) MB = MSC: 50 − 2Q = 8 + Q → 42 = 3Q → Q_soc = 14. P = 50 − 2·14 = 22.
(c) Market OVERproduces: 16 − 14 = 2 extra units relative to the social optimum.
(Note: external cost shifts supply UP by $6, so MSC intercept goes from 2 to 8.)
RUBRIC: 25 = all three parts correct with algebra shown. 15–20 = two correct, one slip.
8–14 = one correct, or right method with arithmetic error. 0–7 = wrong direction (says
underproduce) or no algebra.
FRESH VARIANT: "MB = 60 − 2Q, MPC = 4 + Q, marginal external cost = 8 (MSC = 12 + Q).
(a) Q_mkt; (b) Q_soc; (c) over- or underproduces, by how much?"
VARIANT ANSWER: (a) 60−2Q=4+Q → 56=3Q → Q_mkt≈18.67 (not clean).
USE INSTEAD: MB=60−Q, MPC=4+2Q, EMC=6, MSC=10+2Q. MB=MPC: 60−Q=4+2Q → 56=3Q → Q_mkt≈18.67 still messy.
CLEAN VARIANT: MB=50−Q, MPC=5+2Q, EMC=6, MSC=11+2Q. MB=MPC: 50−Q=5+2Q → 45=3Q → Q_mkt=15, P=35.
MB=MSC: 50−Q=11+2Q → 39=3Q → Q_soc=13, P=37. Overproduces by 2 units.
(Use this clean variant: MB=50−Q, MPC=5+2Q, EMC=6, MSC=11+2Q.)

============= PROBLEM 2 (25 pts) — Pigouvian tax and DWL =============
PROBLEM: "Using the paper mill market from Problem 1 (MB = 50 − 2Q, MPC = 2 + Q, MSC = 8 + Q):
(a) What is the correct Pigouvian tax per ton of paper?
(b) Calculate the deadweight loss (DWL) caused by the negative externality (before any tax).
(c) If the Pigouvian tax is imposed, what happens to the DWL?"
VETTED ANSWER:
(a) Pigouvian tax = marginal external cost = $6 per ton.
(b) DWL = ½ × (Q_mkt − Q_soc) × EMC = ½ × (16 − 14) × 6 = ½ × 2 × 6 = $6.
(c) A correctly set Pigouvian tax (= $6) shifts MPC up to MSC, moves market to Q_soc = 14.
The DWL is eliminated (falls to zero). The externality is fully internalized.
RUBRIC: 25 = all three parts correct; (a) = 6; (b) uses ΔQ = 2 (not Q_mkt = 16); (c) says
DWL = 0 with brief explanation. 15–20 = two correct or (b) uses wrong base. 8–14 = (a)
correct but (b) wrong formula. 0–7 = Pigouvian tax wrong.
FRESH VARIANT: "Same structure: MB=50−Q, MPC=5+2Q, EMC=6, MSC=11+2Q. Q_mkt=15, Q_soc=13.
(a) Pigouvian tax? (b) DWL? (c) After tax?"
VARIANT ANSWER: (a) $6. (b) ½×(15−13)×6 = ½×2×6 = $6. (c) DWL = 0 after tax.

============= PROBLEM 3 (25 pts) — Positive externality and subsidy direction =============
PROBLEM: "A tutoring service creates a positive externality: the students tutored pass their
classes at higher rates, which benefits their study groups and future employers (who get
better-prepared workers). The private marginal benefit (demand) is MPB = 20 − Q; the
marginal social benefit is MSB = 24 − Q (external benefit = $4 per session); private supply
(MPC) = 4 + Q.
(a) Find the market equilibrium quantity (where MPB = MPC).
(b) Find the social optimum quantity (where MSB = MPC).
(c) Does the market over- or underproduce? What is the appropriate policy correction, and
what should be its size?"
VETTED ANSWER:
(a) MPB=MPC: 20−Q=4+Q → 16=2Q → Q_mkt=8. P=12.
(b) MSB=MPC: 24−Q=4+Q → 20=2Q → Q_soc=10. P=14.
(c) Market UNDERPRODUCES by 2 units (8 < 10). Correction: a SUBSIDY of $4 per session
(= the marginal external benefit). A tax would make the under-provision WORSE.
RUBRIC: 25 = all three correct; (c) must say SUBSIDY (not tax) and give the $4 size.
15–20 = two correct, or correct that it's underproduction but says tax. 8–14 = one correct
or direction right but no policy stated. 0–7 = says overproduction.
FRESH VARIANT: "MPB=30−Q, MSB=35−Q (external benefit=$5), MPC=5+Q.
(a) Q_mkt; (b) Q_soc; (c) over/under + correction?"
VARIANT ANSWER: (a) 30−Q=5+Q → 25=2Q → Q_mkt=12.5 (not clean).
CLEAN VARIANT: MPB=20−Q, MSB=26−Q (EMB=6), MPC=2+Q.
(a) 20−Q=2+Q → 18=2Q → Q_mkt=9, P=11.
(b) 26−Q=2+Q → 24=2Q → Q_soc=12, P=14.
(c) Underproduces by 3; subsidy = $6.

============= PROBLEM 4 (25 pts) — Public goods, free-rider, and applied reasoning =============
PROBLEM: "A neighborhood group is considering hiring a private security patrol that would
reduce crime in the entire neighborhood — every resident would benefit, whether or not they
paid for the patrol, and one resident benefiting does not reduce the protection for others.
(a) Is neighborhood security a public good, a private good, a club good, or a common
resource? Use the rival/excludable criteria.
(b) Explain in 2–3 sentences why a private market would likely underprovide neighborhood
security.
(c) A city councilmember proposes funding the patrol with a neighborhood property-tax levy
(mandatory). A neighbor argues this is unfair because 'I can handle my own security.'
Identify the positive economic concept underlying both the problem AND the solution, and
explain (in 1–2 sentences) why the normative objection, while understandable, doesn't change
the positive economics."
VETTED ANSWER:
(a) A public good: NON-RIVAL (one resident's protection does not reduce others') and
NON-EXCLUDABLE (once the patrol is running, you cannot practically stop a resident from
benefiting). So: non-rival + non-excludable = public good.
(b) The free-rider problem: each resident has an incentive to not pay, hoping others will
fund the patrol and they'll benefit anyway. Because no one can be excluded from the
protection, private providers cannot recover their costs only from willing payers — so the
patrol would be underprovided or not provided at all, even if total willingness to pay
exceeds the cost.
(c) The positive concept is the FREE-RIDER PROBLEM: when a good is non-excludable, rational
individuals under-contribute to its provision. The mandatory levy solves the free-rider
problem by forcing contributions from all beneficiaries. The neighbor's objection ("I'll
handle my own security") is a normative value judgment (a preference for individual
autonomy over collective provision) — it is a legitimate value, but the positive economics
of free-riding remains true regardless of whether one finds the levy fair.
RUBRIC: 25 = all three parts complete. (a) non-rival + non-excludable = public good (both
properties named). (b) free-rider clearly explained. (c) names free-rider; positive vs.
normative split explicit. 15–20 = two strong, one thin. 8–14 = one strong. 0–7 = bad
classification or no economic reasoning.
FRESH VARIANT: "A city proposes a fireworks display on July 4. It would be visible from all
parts of the city; you cannot stop anyone from watching. (a) Good type? (b) Why would the
private market underprovide it? (c) The city funds it with a hotel tax (non-residents pay).
A business owner says it's unfair. Positive vs. normative analysis."
VARIANT ANSWER: (a) Non-rival + non-excludable = public good. (b) Free-rider — can't charge
viewers, so private provider can't recover cost. (c) Free-rider problem solved by mandatory
hotel tax; business owner's fairness objection is normative (a value judgment about who
should pay), which doesn't change the positive economics of public-goods provision.

============= COMPLETION =============
After all four problems (and any re-attempts), produce EXACTLY:
    STUDENT'S SCORE: X/100
    WEEK 14 ASSIGNMENT — Externalities & Public Goods
    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): all numbers pre-computed in Python:
- P1: MB=MPC → 50−2Q=2+Q → Q_mkt=16; MB=MSC → 50−2Q=8+Q → Q_soc=14; overproduces by 2. ✓
- P2: Pigouvian tax = $6 = EMC; DWL = ½×2×6 = 6; DWL=0 after tax. ✓
- P3: MPB=MPC → Q_mkt=8; MSB=MPC → Q_soc=10; underproduces by 2; subsidy = $4. ✓
- P4: non-rival + non-excludable → public good; free-rider; positive/normative split. ✓
All curve-shift directions verified: tax shifts MPC up (negative externality); subsidy raises effective demand (positive externality); both move market toward social optimum.

Canvas placement block

canvas_object    = Assignment
title            = "Week 14 Assignment — Externalities & Public Goods (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-14 assignment is the AI-coached version in I-assignment-and-rubric-week-14.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 8 · SLO A & B · Assignment 14 of 14 · 100 points · Due Sun, Dec 6

The Assignment

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

Problem 1 — Market vs. social optimum (25 pts). A paper mill creates water pollution that harms downstream residents. The demand for paper (marginal benefit) is MB = 50 − 2Q. The mill's private supply is MPC = 2 + Q. The marginal external cost of the pollution is $6 per ton, so MSC = 8 + Q.
(a) Find the market equilibrium quantity (where MB = MPC). Show the algebra.
(b) Find the social optimum quantity (where MB = MSC). Show the algebra.
(c) Does the market overproduce or underproduce? By how many units?

Problem 2 — Pigouvian tax and DWL (25 pts). Using the paper mill market from Problem 1 (MB = 50 − 2Q, MPC = 2 + Q, MSC = 8 + Q, Q_mkt = 16, Q_soc = 14):
(a) What is the correct Pigouvian tax per ton of paper?
(b) Calculate the deadweight loss (DWL) caused by the negative externality (before any tax). Show the formula.
(c) If the Pigouvian tax is imposed, what happens to the DWL? Explain in one sentence.

Problem 3 — Positive externality and the direction of correction (25 pts). A tutoring service creates a positive externality (it improves outcomes for study groups and future employers). The private demand is MPB = 20 − Q, the marginal social benefit is MSB = 24 − Q (external benefit = $4/session), and private supply is MPC = 4 + Q.
(a) Find the market equilibrium quantity (where MPB = MPC).
(b) Find the social optimum quantity (where MSB = MPC).
(c) Does the market over- or underproduce? What is the appropriate policy correction and its size? (A common error: choosing a tax when a subsidy is correct — think carefully about the direction.)

Problem 4 — Public goods, free-rider, and positive vs. normative (25 pts). A neighborhood group considers hiring a private security patrol that would reduce crime for all residents; once the patrol is running, no resident can be excluded from the protection, and one resident's protection doesn't reduce another's.
(a) Is neighborhood security a public good, private good, club good, or common resource? Identify both the rival/excludable properties and the good type.
(b) In 2–3 sentences, explain why a private market would likely underprovide this security patrol.
(c) A city councilmember proposes mandatory funding via a property-tax levy. A neighbor objects: "I can handle my own security — this is unfair." In 2–3 sentences, identify the positive economic concept behind both the problem and the solution, and explain why the neighbor's objection is a normative judgment that doesn't change the positive economics.

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 (verified in Python):
- (a) MB = MPC: 50 − 2Q = 2 + Q → 48 = 3Q → Q_mkt = 16; P = 50 − 32 = 18.
- (b) MB = MSC: 50 − 2Q = 8 + Q → 42 = 3Q → Q_soc = 14; P = 50 − 28 = 22.
- (c) Overproduces by 16 − 14 = 2 units. The market ignores $6/unit of external cost.

P2 (verified):
- (a) Pigouvian tax = marginal external cost = $6/ton. Shifts MPC up by $6 → new effective supply = MSC. ✓
- (b) DWL = ½ × (Q_mkt − Q_soc) × EMC = ½ × (16 − 14) × 6 = ½ × 2 × 6 = $6. (Base = ΔQ = 2, NOT Q_mkt = 16 — the most common error.)
- (c) DWL falls to zero: the Pigouvian tax fully internalizes the externality, eliminating the triangle.

P3 (verified):
- (a) MPB = MPC: 20 − Q = 4 + Q → 16 = 2Q → Q_mkt = 8; P = 12.
- (b) MSB = MPC: 24 − Q = 4 + Q → 20 = 2Q → Q_soc = 10; P = 14.
- (c) Underproduces by 2. Correction: SUBSIDY = $4/session (= marginal external benefit). A tax would make underproduction worse — this is the most common direction error. ✓

P4:
- (a) Public good: NON-RIVAL (one resident's protection does not reduce others') + NON-EXCLUDABLE (cannot exclude any resident once patrol is operating). ✓
- (b) Free-rider problem: each resident can benefit from the patrol without paying. Private providers cannot recover costs only from willing payers → underprovision, even if total willingness to pay exceeds cost.
- (c) Free-rider problem (positive concept). Mandatory levy solves it by compelling all beneficiaries to contribute. The neighbor's "I can handle my own security" is a normative judgment (valuing individual autonomy over collective provision) — legitimate as a value, but it doesn't change the positive economics of free-riding.

Quality gate (self-checked): all numbers computed in Python ✓: P1 (3Q=48→Q=16; 3Q=42→Q=14); P2 (DWL=½×2×6=6); P3 (2Q=16→Q=8; 2Q=20→Q=10; subsidy direction verified). Curve-shift directions: negative externality → tax shifts MPC up (verified); positive externality → subsidy shifts demand/supply toward social optimum (verified). Free-rider/non-excludable logic: confirmed against rival/excludable grid. ✓

Canvas placement block

canvas_object    = Assignment
title            = "Week 14 Assignment — Externalities & Public Goods (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
submission_types = [online_upload, online_text_entry]
due_offset_days  = 6
rubric_ref       = "w14-assignment-rubric"
published        = true
provenance       = "~ Prof. Kessler's edition · Fall 2026 · built with thecoursemaker.com"