# MST 0441 problem-writing agent

The rules for writing practice problems and solutions in MST 0441 Consumers, Trade and Business Strategy at BI, the rubrics the exam is written to, a checker for new problems and a calculator that verifies solutions.

## How to answer

- You help a student in MST 0441 Consumers, Trade and Business Strategy write practice problems with solutions.
- Before you write a problem, read the rules with mst0441_rules and the session's rubric with mst0441_rubric.
- Write problems that test the rubric criteria of one session and follow every rule. Use new names, numbers and stories. Never copy a course or textbook problem.
- Run mst0441_check_problem on every problem you write. Fix each FAIL before you show it. Read each item the tool lists as not checked by machine.
- Run mst0441_verify on every computed answer it supports, with the problem's parameters and your answer. If it reports WRONG, fix the solution and verify again.
- Where mst0441_verify says cannot check, tell the student that this part of the solution has not been verified and should be checked with Andreas Kostøl or in class.
- This agent holds no solutions to course problem sets, workshops or exams. Say so if the student asks for them.
- This agent is a practice aid. It is not the exam and does not predict it. The course page on Canvas decides where they differ.

## Where to look

- [references/01-rules.md](references/01-rules.md)
  - How to use these rules (`rules-how`, all)
  - What the exam looks like (`rules-format`, all)
  - What a good problem does (`rules-good`, all)
  - Sessions and topics (`rules-sessions`, all)
  - What is not on the exam (`rules-scope`, all)
  - Notation (`rules-notation`, all)
  - Utility and payoff functions (`rules-functions`, all)
  - Figures (`rules-figures`, all)
  - Worked economies must be consistent (`rules-consistency`, all)
  - How a solution is written (`rules-solutions`, all)
  - Do not copy course problems (`rules-new`, all)
- [references/02-rubrics.md](references/02-rubrics.md)
  - Session 1 rubric: Introduction and Decision Theory (`rubric-s01`, Part One)
  - Session 2 rubric: Budget Constraints, Preferences, Utility and Choice (`rubric-s02`, Part One)
  - Session 3 rubric: Demand, Comparative Statics and Labor Supply (`rubric-s03`, Part One)
  - Session 4 rubric: Intertemporal Choice (`rubric-s04`, Part One)
  - Session 5 rubric: Assets and Choice Under Uncertainty (`rubric-s05`, Part One)
  - Session 6 rubric: General Equilibrium and Exchange (`rubric-s06`, Part One)
  - Session 7 rubric: Market Failure and Externalities (`rubric-s07`, Part One)
  - Session 8 rubric: Firms, Tasks and Technology (`rubric-s08`, Part Two)
  - Session 9 rubric: Comparative Advantage (`rubric-s09`, Part Two)
  - Session 10 rubric: Heckscher-Ohlin and Factor Prices (`rubric-s10`, Part Two)
  - Session 11 rubric: Monopolistic Competition and Gravity (`rubric-s11`, Part Two)
  - Session 12 rubric: Static Games and Nash Equilibrium (`rubric-s12`, Part Three)
  - Session 13 rubric: Dynamic Games and Credibility (`rubric-s13`, Part Three)
  - Session 14 rubric: Incomplete Information and Signaling (`rubric-s14`, Part Three)
  - Session 15 rubric: Repeated Games and Competition Policy (`rubric-s15`, Part Three)

The same content is served as MCP tools at https://andreaskostol.no/mcp/mst0441.


---

<!-- file: references/01-rules.md -->

# Rules for writing MST 0441 problems

<!-- Authoritative source for the problem rules served at andreaskostol.no/mcp/mst0441.
     Compiled 2026-10-27 from COURSE_BIBLE.md, Decisions/DECISIONS_LOG.md and the workshop papers.
     Status: approved by Andreas 2026-10-27 ("I approve Rules/PROBLEM_RULES.md as it stands"). Students never see these comment lines.
     Format: every "## " section carries one metadata comment (id, cohort, source), as in the
     website's agents/<name>/references/ files. Tutor/export_problem_agent.py copies this file
     and the rubric store into the website repository. Edit here, never there. -->

## How to use these rules
<!-- id: rules-how | cohort: all | source: Andreas Kostøl, 27 October 2026 -->

These rules are for writing your own practice problems for MST 0441 Consumers, Trade and Business Strategy, with solutions.
Write the problem first. Then run mst0441_check_problem on it and fix every FAIL.
Then write the solution. Run mst0441_verify on every number in it that the tool can compute.
When the tool says "cannot check", the solution has not been checked by anyone. Say so to the student.
A problem is practice. It is not a prediction of the exam.
The rubric for each session is what the exam is written to. Read it with mst0441_rubric before you write.

## What the exam looks like
<!-- id: rules-format | cohort: all | source: Assessment/Workshops/W1_exam_paper.tex (5 October 2026) and Rules/Exam_workflow.md -->

The exam is a three-hour written school exam, with pen and paper, taken alone.
A paper has several problems. Each problem has a weight in percent, written as "Problem 1 (18%)".
The parts of a problem are labelled (a), (b), (c), and so on.
A problem tells a short story with named people, firms or countries, and then gives every number it needs.
Parts mix four kinds of task:

1. Draw: a figure with both axes named and every curve and point labelled.
2. Explain: in full sentences, with a cap, for example "using a maximum of 3 sentences".
3. Derive: in general notation first, one step per line.
4. Compute: with numbers, after the general derivation.

A later part may build on an earlier one, for example "Using your solution to 1(d)".
Multiple-choice questions appear in some papers. Each has one correct option out of four.

## What a good problem does
<!-- id: rules-good | cohort: all | source: COURSE_BIBLE.md §0.1 and rules 21 and 25; Andreas, 5 October 2026 -->

A good problem tests the criteria in the session's rubric, and only those.
It states the preferences, the technology or the payoffs in full. Every number in the answer must follow from what the problem gives.
It asks for the derivation in general notation before the numbers enter.
It has one correct answer for each computed part. If a corner solution or several equilibria are possible, the problem says what the student must show.
It asks the student to draw what the algebra found, and to explain the economics in a few sentences.
It can be solved with the course material alone: the session's video, notes and the textbook chapters.
A hard problem asks for a comparative static or a special case, not for longer algebra.

## Sessions and topics
<!-- id: rules-sessions | cohort: all | source: Tutor/stores/store_A_rubrics.json, rubric titles, read 27 October 2026 -->

Part One: Consumers

- Session 1: Introduction and decision theory
- Session 2: Budget constraints, preferences, utility and choice
- Session 3: Demand, comparative statics and labor supply
- Session 4: Intertemporal choice
- Session 5: Assets and choice under uncertainty
- Session 6: General equilibrium and exchange
- Session 7: Market failure and externalities

Part Two: Trade

- Session 8: Firms, tasks and technology
- Session 9: Comparative advantage (Ricardo)
- Session 10: Heckscher-Ohlin and factor prices
- Session 11: Monopolistic competition and gravity

Part Three: Strategy

- Session 12: Static games and Nash equilibrium
- Session 13: Dynamic games and credibility
- Session 14: Incomplete information and signaling
- Session 15: Repeated games and competition policy

The word "module" is not used in this course. Say Part One, Part Two or Part Three.

## What is not on the exam
<!-- id: rules-scope | cohort: all | source: COURSE_BIBLE.md §2; Decisions/DECISIONS_LOG.md, 9 and 21 September, 25 September and 15 October 2026 -->

Do not write problems that require any of these. They are taught as context only.

- Session 1: the material on the AI tutor.
- Session 3: the Slutsky decomposition and deadweight loss.
- Session 4: inflation and nominal-to-real interest rate calculations.
- Session 5: asset pricing (bonds, perpetuities, arbitrage, market premia, Knight's distinction).
- Session 6: the planner's Lagrangian. The competitive equilibrium, the box and the contract curve from equal MRS are on the exam.
- Session 7: public goods. An externality problem may still call clean air a public good as a label.
- Sessions 9 to 11: tariffs, the small-country tariff diagram and the optimum tariff.
- Session 11: derivations and numbers. Students explain the mechanisms of monopolistic competition in words and answer multiple-choice questions on gravity.
- Session 14: whether the public-goods game with private types is on the exam is not decided. Leave it out.

## Notation
<!-- id: rules-notation | cohort: all | source: COURSE_BIBLE.md §2 rule 0 (3 September, 18 and 24 September, 8 October 2026) -->

Use the course's letters. Never use a letter for two things in one problem.

| symbol | means | never use instead |
|---|---|---|
| $V$ | non-labor income (benefits, transfers) in Part One | $m$, $I$, $A$ |
| $m$ | total money income, which may include wage income and $V$ | $I$ |
| $T$ | time endowment | $L$ |
| $L$ | leisure, and nothing else | total time, labor |
| $h$ | hours worked, $h = T - L$ | |
| $w$ | wage | |
| $C$ | consumption | |
| $W$ | wealth stock in the insurance model | |
| $E$ | the labor force in Part Two: $E$, $E^*$, $E_X + E_Y = E$ | $L$ |

The leisure-consumption budget is $C = w(T-L) + V$. The goods budget in Sessions 2 to 5 is $p_1 x_1 + p_2 x_2 = m$.
With one consumer, numbered goods are fine: $x_1, x_2$ or $c_1, c_2$.
When people or countries also carry an index, name the goods $x$ and $y$: bundles $x_A, y_A$, prices $p_x, p_y$, relative price $p = p_x/p_y$ with good $y$ the numeraire.
Point labels in a figure avoid the letters $X$ and $Y$.

## Utility and payoff functions
<!-- id: rules-functions | cohort: all | source: Andreas, 27 August 2026 (course functions); A2 to A7 problem decks -->

Use the functions the course uses. Do not invent new ones.

- Cobb-Douglas, $U = x_1^{\alpha} x_2^{1-\alpha}$, exponents summing to one, or $U = xy$.
- Leisure and consumption: $U = C \cdot L$, or Cobb-Douglas in $C$ and $L$.
- Quasilinear: $U = \ln x_1 + x_2$, or $U = C + \ln L$.
- Perfect substitutes: $U = x_1 + x_2$, or $U = ax + by$.
- Perfect complements: $U = \min\{a x_1, b x_2\}$.
- Two periods: $U = \ln c_1 + \beta \ln c_2$.
- Uncertainty: expected utility with $v(c) = \sqrt{c}$ or $v(c) = \ln c$. A risk lover has $v(c) = c^2$.

From Session 2 on, a consumer's utility function never squares its arguments. The risk lover's $v(c) = c^2$ is the one exception.
Session 1 uses payoff functions of one action, such as $u = \theta a - 4a^2$, and these are fine.
Say "β, the taste for leisure", or name what the parameter measures. Do not call a parameter a dial.
In Session 10, worked numbers use fixed input requirements (Leontief technology), with linear zero-profit and full-employment equations. Never Cobb-Douglas technology for Heckscher-Ohlin numbers.
In Part Three, payoffs are given in a matrix or a tree, or follow from linear demand and constant marginal cost.

## Figures
<!-- id: rules-figures | cohort: all | source: COURSE_BIBLE.md §2 rule 0 and §3 rules 14 and 22 (27 August, 24 and 25 September 2026) -->

Axes follow the textbook: Varian in Part One, Feenstra in Part Two. The Engel curve has quantity across and income up.
Every indifference curve slopes down. This holds even for a deliberately wrong curve in a figure that shows why curves cannot cross.
The MRS is the positive ratio of marginal utilities, the horizontal good over the vertical good: $MRS = U_x/U_y$. The slope of the indifference curve is $-MRS$.
A budget line's slope is minus the price of the horizontal good over the price of the vertical good.
A problem that asks for a figure names which good goes on which axis.

## Worked economies must be consistent
<!-- id: rules-consistency | cohort: all | source: COURSE_BIBLE.md §3 rule 25 (Andreas, 24 September 2026) -->

Every new economy states its preferences, endowments and technology.
Before you give the solution, derive every price, allocation and wage again with exact fractions.
Check demands, market clearing, budgets and trade balance.
A number that the stated primitives do not pin down is an error. Fix the problem, not the answer.
Two countries with the same preferences cannot need different preference parameters to give the stated world price.

## How a solution is written
<!-- id: rules-solutions | cohort: all | source: Andreas, 5 October 2026 (solution manuals); COURSE_BIBLE.md §3 rule 21; W1 exam paper instructions -->

Show every step. Never jump from a condition to a result in words.
For a constrained choice, set up the Lagrangian first: the problem, the Lagrangian, each first-order condition, then the step that divides them.
Then show the MRS route: the tangency condition with its equations.
One step per line, with the rule you use in words beside it, for example "chain rule" or "insert the budget constraint".
Draw a box around each final answer.
A figure has both axes labelled, every curve and point named, and one line under it saying what it shows.
Text answers are full sentences within the sentence cap. No arrows and no bullet fragments.

## Do not copy course problems
<!-- id: rules-new | cohort: all | source: Andreas, 27 October 2026 -->

Write new problems. Use new names, new numbers and a new story.
Do not reproduce a problem from the problem sets, the workshops, the in-class problems or the textbooks.
Textbook chapter references are fine, for example "see Varian, chapter 5".
This agent holds no solutions to course problems. Ask for them in class or on Canvas.


---

<!-- file: references/02-rubrics.md -->

# Rubrics: what the exam is written to

## Session 1 rubric: Introduction and Decision Theory
<!-- id: rubric-s01 | cohort: Part One | source: Canvas page "Rubric: Session 1", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Setting up the decision problem

**Limited.** Actions, outcomes and payoffs are mixed up or left implicit. The decision tree is missing, has no payoffs at the terminal nodes, or the branching does not match the problem described.

**Good.** Actions $A$, outcomes $X$ and a payoff function $u: X \rightarrow \mathbb{R}$ are stated correctly and a complete, correctly labeled decision tree is drawn.

**Excellent.** Setup is complete and the rationality assumptions behind it are made explicit (completeness, transitivity, knowing how actions map into outcomes), including where probabilities $p(x \mid a)$ enter under uncertainty.

### Solving for the optimal action

**Limited.** Limited understanding of how to move from a payoff function to a choice. The first-order condition is not taken, is taken incorrectly, or expected payoffs are compared without actually computing $\mathbb{E}[u(a)] = \sum_x u(a,x) p(x \mid a)$.

**Good.** The optimum is found correctly -- FOC for the continuous case (e.g.\ $a^* = \theta/8$ from $u = \theta a - 4a^2$), or the highest expected payoff across actions in the discrete case -- with the arithmetic right.

**Excellent.** The solution is derived in general form before numbers are plugged in, the second-order condition $u"<0$ or the shape of $u$ is checked, and corner or dominated actions are ruled out explicitly.

### Comparative statics and interpretation

**Limited.** The answer stops at a number. No statement about how the optimum moves with the parameter, or an economic claim that does not follow from the algebra.

**Good.** The sign of the comparative static is derived and stated in words (e.g.\ $a^*(\theta)$ is increasing in $\theta$, so larger types drink more), and the answer says what this implies for the population.

**Excellent.** Interpretation is tied back to the assumptions: what changes if utility is $\log$ rather than linear (risk aversion), or if the decision becomes sequential rather than one-shot, and which conclusions survive.

## Session 2 rubric: Budget Constraints, Preferences, Utility and Choice
<!-- id: rubric-s02 | cohort: Part One | source: Canvas page "Rubric: Session 2", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### The constrained optimization

**Limited.** Limited understanding of how the budget constraint and the utility function combine into a choice problem. The MRS is not derived, the tangency condition is asserted rather than obtained, or the budget constraint is never imposed so the solution is incomplete or has no theoretical foundation.

**Good.** The MRS is derived from the total derivative of $U$ along an indifference curve, the tangency condition $MRS = p_1/p_2$ is set up correctly for the axes in use, and it is solved jointly with the budget constraint (by substitution or Lagrange) to give the optimal bundle.

**Excellent.** The derivation is done in general notation before numbers enter, and the student checks whether the tangency condition even applies -- flagging perfect substitutes (corner), perfect complements (kink) and quasilinear cases, and solving those manually.

### Graphical representation

**Limited.** The diagram is missing, unlabelled, or inconsistent with the algebra. Axes, intercepts $m/p_1$ and $m/p_2$, or the slope are wrong; indifference curves are drawn crossing each other or sloping the wrong way.

**Good.** A correct diagram with labeled axes, correct intercepts and slope, and convex downward-sloping indifference curves. The optimum is shown at the tangency and matches the algebraic answer.

**Excellent.** The diagram carries the argument on its own: the shift or rotation of the budget line under a change in $p$, $m$, $w$ or $V$ is drawn correctly, and the special-case indifference curve shapes are drawn to justify why a corner or kink solution obtains.

### Economic interpretation

**Limited.** Terms are used loosely. The slope is not interpreted as an opportunity cost, and the preference axioms are recited rather than used to justify the shape of the indifference curves.

**Good.** The slope is interpreted as the rate at which the market lets you trade goods, the MRS as the rate at which the consumer is willing to trade, and the optimum as the point where the two coincide. Convexity and monotonicity are linked to the curve's shape.

**Excellent.** The interpretation extends to the leisure--consumption case: the student explains why a wage change moves both the relative price of leisure and full income $wT + V$, and uses heterogeneous preference parameters to explain why different people, or countries, choose differently.

## Session 3 rubric: Demand, Comparative Statics and Labor Supply
<!-- id: rubric-s03 | cohort: Part One | source: Canvas page "Rubric: Session 3", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Deriving demand functions

**Limited.** Limited understanding of how the optimal choice from consumer theory (Lagrange, $MRS$ or the substitution method) delivers a demand function. The answer stops at the first-order conditions, never imposes the budget constraint, or reports a bundle of numbers instead of $x_i(p_1,p_2,m)$. The solution is incomplete, incorrect, or lacks a fundamental theoretical foundation.

**Good.** The Marshallian demand functions are derived correctly in general form from the FOCs and the budget constraint, and the student can state what changes if utility rather than income is held fixed (compensated demand).

**Excellent.** The derivation is clean and general, corner and kink cases are checked rather than assumed away, and the expenditure share structure of the solution (e.g.\ $p_1 x_1^* / m = \alpha/(\alpha+\beta)$ under Cobb--Douglas) is recognized and used.

### Graphical analysis of price and income changes

**Limited.** Curves are asserted, not constructed. The income offer, Engel, price offer and demand curves are confused with one another, axes are unlabelled or reversed, and the budget line is shifted when it should rotate (or vice versa).

**Good.** The relevant curve is drawn correctly from the underlying optimization, with correct axes, and the rotation of the budget line under a price or tariff change is shown together with the movement of the optimal bundle.

**Excellent.** The diagram does analytical work: the substitution effect is shown as a pivot along the initial indifference curve and the income effect as the parallel shift, the two are separated cleanly, and the graph is used to justify a claim the algebra alone would not make obvious.

### Interpretation and comparative statics

**Limited.** The sign of the response is stated without derivation, or the good is classified as normal, inferior or Giffen with no reference to the income and substitution effects. Policy conclusions do not follow from the model.

**Good.** The comparative static is signed from the demand function, the good is classified correctly, and the tariff experiment is interpreted -- the new bundle and the revenue raised.

**Excellent.** The interpretation is carried through to the labor supply case: which of the two effects dominates is argued rather than asserted, the backward-bending supply curve and the Giffen case are explained as the same mechanism, and the conclusions are tied to the observed trends in hours and expenditure shares shown in the data.

## Session 4 rubric: Intertemporal Choice
<!-- id: rubric-s04 | cohort: Part One | source: Canvas page "Rubric: Session 4", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Deriving and solving the intertemporal problem

**Limited.** The two period constraints are not combined into a single NPV constraint, or $b_1$ is never eliminated. The Lagrangean is set up incorrectly or abandoned, and no first-order conditions are produced.

**Good.** The intertemporal budget constraint is derived correctly and the Lagrangean gives the condition $u'(c_1)=(1+r)\beta u'(c_2)$. The log case is solved for $c_1^*$, but algebra slips or the second consumption function is left unfinished.

**Excellent.** Both Marshallian consumption functions are derived cleanly and checked against the budget constraint. The role of $\beta$ and $r$ in the solution is stated explicitly, and the method is shown to extend to $N$ periods.

### Graphical representation in $(c_1,c_2)$ space

**Limited.** The budget line is drawn without an endowment point, the axes are unlabelled, or the slope is not $-(1+r)$. Indifference curves, if drawn, do not touch the budget line at a tangency.

**Good.** A correct budget line through the endowment with both intercepts labeled and a tangency at the optimum. The rotation of the line when $r$ changes is drawn, but the pivot point or its direction is imprecise.

**Excellent.** The diagram is fully labeled and used as an argument, not a decoration: the rotation around $e$ is exact, borrower and lender are placed on opposite sides of the endowment, and the graph carries the conclusion of the algebra.

### Economic interpretation and comparative statics

**Limited.** Answers restate that "lower $r$ means less saving" without reference to the model. The endowment position is ignored, so the answer is given as if it were the same for everyone.

**Good.** Correctly signs the welfare effect of a change in $r$ for a borrower and for a lender, and distinguishes the two by where consumption lies relative to the endowment.

**Excellent.** Signs the effect of a change in $r$ conditional on the endowment position, explains why a lender and a borrower are affected in opposite directions, and applies this to the deck's questions -- why savings rates differ across countries (patience vs.\ demography).

## Session 5 rubric: Assets and Choice Under Uncertainty
<!-- id: rubric-s05 | cohort: Part One | source: Canvas page "Rubric: Session 5", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Expected utility and the insurance problem

**Limited.** Expected utility is confused with the utility of the expected value, or probabilities are not used as weights. The maximization over coverage $K$ is not set up, or the first-order condition is written without differentiating the state-contingent utilities.

**Good.** Expected utility is computed correctly and the first-order condition in $K$ is derived. The actuarially fair substitution $q=\pi$ is made, but the step from $v'_g=v'_b$ to $K=D$ is asserted rather than shown.

**Excellent.** The full chain is derived: first-order condition, $q=\pi$, $v'_g=v'_b$, and $W-qK = W-D-qK+K \Rightarrow K=D$. The linear-utility case is handled separately: all feasible coverage levels tie at $q=\pi$, while $q>\pi$ gives the corner $K=0$. The price condition is explained, not just stated.

### Graphical work in contingent-consumption space

**Limited.** Axes are not states of the world, or the endowment with uneven resources across states is missing. No certainty line, and indifference curves are drawn without regard to the direction of increasing utility.

**Good.** Correct $(c_{bad},c_{good})$ diagram with the endowment, the certainty line $c_{good}=c_{bad}$ and a budget line of slope $-\frac{\pi}{1-\pi}$. Indifference curves are drawn, but the tangency is not clearly located at full insurance.

**Excellent.** The diagram proves the result: convex indifference curves, tangency on the certainty line under fair pricing, and a demonstration that moving off the endowment towards the certainty line reaches a higher indifference curve. Unfair pricing $q>\pi$ is shown to move the tangency off the certainty line.

## Session 6 rubric: General Equilibrium and Exchange
<!-- id: rubric-s06 | cohort: Part One | source: Canvas page "Rubric: Session 6", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### 1. The Edgeworth Box as a Tool

**Limited.** The box is drawn without endowments, or one agent's origin is missing so the
 allocations cannot be read. Indifference curves are drawn for one agent only,
 or cross in ways that contradict monotonicity.

**Good.** Both origins, the endowment point and both sets of indifference curves are
 drawn correctly, and the region of mutually beneficial trade is identified.

**Excellent.** The box is used as an argument, not a picture: the lens of mutual gains is
 derived from the endowment, the tangency locus is traced out as the contract
 curve, and the diagram carries the efficiency conclusion on its own, with the core
 identified as the contract curve inside the lens.

### 2. Edgeworth Box and the Contract Curve

**Limited.** Box is drawn but B's origin is not rotated to the north-east corner, or the
 endowment point is missing, or the axes are unlabelled. The contract curve is
 drawn without reference to tangency.

**Good.** Box is correctly constructed with both origins, both indifference maps and the
 endowment $\omega$. The contract curve is drawn through the tangency points and
 the lens of mutually improving trades is identified.

**Excellent.** Box is precise: the contract curve is derived from $MRS_A=MRS_B$
 together with the resource constraints, and the budget line through $\omega$ is
 used to distinguish a clearing from a non-clearing price ratio, naming which
 good is in excess demand and which in excess supply. The candidate also solves for
 $p = p_x/p_y$ using endogenous income $m_i = p\,\omega^x_i + \omega^y_i$ (good $y$ the numeraire) and Walras' Law.

### 3. Welfare Interpretation

**Limited.** Treats "equilibrium" and "efficient" as the same word. No statement of what
 Pareto efficiency rules out, and the general-equilibrium discussion is
 descriptive rather than analytical.

**Good.** States the first fundamental welfare theorem and shows that the competitive
 equilibrium lies on the contract curve: at the equilibrium price ratio,
 $MRS_A = MRS_B$. The planner's Lagrangian is not required.
 States the second welfare theorem in the correct direction, after a lump-sum
 redistribution of endowments.

**Excellent.** Explains why every point on the contract curve is Pareto efficient, states
 the assumptions the welfare theorem needs (no externalities, no market power,
 an equilibrium exists), and separates the efficiency claim from the
 distributional one -- efficiency says nothing about which point is fair. Distinguishes
 the two theorems by direction and conditions the Second on convex preferences.

## Session 7 rubric: Market Failure and Externalities
<!-- id: rubric-s07 | cohort: Part One | source: Canvas page "Rubric: Session 7", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### 1. Modeling the Externality

**Limited.** Describes pollution in words but never writes $S$ into a utility function.
 Signs of the partial derivatives are missing or wrong, so $S$ is not shown to be
 a good for $A$ and a bad for $B$. The efficiency condition is never stated.

**Good.** Sets up $u_A(x_A,S)$ and $u_B(x_B,1-S)$ with correct signs and states the
 efficiency condition: the two MRS between good $x$ and smoke are equal. The
 planner's Lagrangian is not required.
 The quasi-linear case is solved, though a step may be asserted rather than shown.

**Excellent.** States the Pareto condition, explains why unequal marginal values leave a gain,
 and computes $S^*$ for the functional forms given, then re-solves the decentralized problem with a price $p_S$ and shows the
 conditions coincide. The exercise-level rubric on the competitive-equilibrium
 slide is the same standard applied to the no-externality benchmark.

### 2. Graphical Argument in the Edgeworth Box

**Limited.** Box is drawn with unlabelled or mismatched axes -- pollution and clean air not
 read from opposite origins -- and the endowment is placed arbitrarily. The
 inefficiency of the market outcome is stated but never shown on the diagram.

**Good.** Box is correctly oriented with pollution measured from $A$'s origin and clean air
 from $B$'s, both endowments marked, and the over-pollution outcome located away
 from the contract curve. Indifference curves are present if not precise.

**Excellent.** Diagram carries the argument on its own: the contract curve is horizontal under
 quasi-linear preferences, the two property-rights endowments are at different
 points on the same vertical line, and the budget line through each endowment
 lands on the same $S^*$. Meets the precision demanded by the exercise rubric
 earlier in the deck, now applied to the polluted economy.

### 3. Policy and Welfare Conclusion

**Limited.** Concludes only that "the government should intervene" with no mechanism, or
 confuses the efficient level of pollution with zero pollution. No conditions
 attached to the Coase result.

**Good.** States that creating a price for pollution restores the efficiency condition and
 that either assignment of property rights can work, provided rights are
 well defined. Notes that efficient pollution is strictly positive.

**Excellent.** States the efficiency claim with its assumptions (well-defined rights, low
 transaction costs) and the invariance claim with the extra one (quasi-linear
 preferences, no income effects),
 separates the efficiency conclusion from the distributional one, and says where
 the assumptions plausibly fail in real climate policy (many parties, no
 enforceable rights across borders).

### 4. AI Where There Is No Price

**Limited.** Asserts that AI or better data will solve environmental coordination, with no
 mechanism; or dismisses the tools without an argument.

**Good.** Separates what better measurement can do -- making an externality observable and
 hence excludable, so a market can exist -- from what it cannot, and gives
 sustainability as the leading case of a market with no price signal.

**Excellent.** Maps the claim onto the model: says which of measurement, aggregation and matching
 a tool actually addresses, argues that preference revelation is a strategic and not
 a computational problem, and raises the concentration of control over measurement
 as a cost to weigh against the gain.

## Session 8 rubric: Firms, Tasks and Technology
<!-- id: rubric-s08 | cohort: Part Two | source: Canvas page "Rubric: Session 8", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### The elasticity of substitution

**Limited.** Treats $\sigma$ as a slope or a price, or says what cheaper AI does to labor's cost share without using $\sigma$.

**Good.** Defines $\sigma$ as the percentage change in $K/E$ per percentage change in $w/r$, and places straight and L-shaped isoquants at $\sigma=\infty$ and $\sigma=0$.

**Excellent.** Shows that a fall in $r/w$ moves spending on AI relative to labor by $(\sigma-1)$ percent per percent, so labor's cost share falls if $\sigma>1$ and rises if $\sigma<1$, and explains why two inputs alone cannot make the wage fall.

### Substitutes, complements and the task cutoff

**Limited.** Confuses input prices with costs per task-unit, or assigns automation from a job title.

**Good.** Explains why human and AI output within a task are perfect substitutes and applies the task cutoff with stated units.

**Excellent.** Derives the cutoff from unit costs, handles ties and explains cheaper AI, higher wages and task-specific productivity changes with other inputs fixed.

### Aggregating to the productivity gain

**Limited.** Adds task savings without weights or calls every finite saving an exact TFP change.

**Good.** Computes the fixed-weight index and distinguishes it from the automated set.

**Excellent.** States baseline-share and fixed-recipe assumptions, explains continuity and kinks, and distinguishes the index from a local log-TFP approximation.

### Productivity, wages and exposure

**Limited.** Infers wages or adoption directly from technical exposure or productivity.

**Good.** Distinguishes displacement from output expansion and exposure from adoption.

**Excellent.** Explains why the given-wage firm model needs labor-market and demand assumptions for wage predictions, and identifies quality or adoption costs as limits.

### From tasks to the frontier

**Limited.** Infers an unconditional price change or names losers from the PPF alone.

**Good.** Draws the PPF after a specified sectoral labor-efficiency change and computes the new productivity factor.

**Excellent.** States when relative price equals opportunity cost, separates allocation from the frontier and gives conditional distribution examples with explicit assumptions.

## Session 9 rubric: Comparative Advantage
<!-- id: rubric-s09 | cohort: Part Two | source: Canvas page "Rubric: Session 9", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Analytical derivation

**Limited.** States comparative advantage as a comparison of $a_x$ with $a_x^*$, i.e.\ confuses it
 with absolute advantage. Does not compute autarky relative prices, or computes them
 without connecting them to $a_x/a_y$.

**Good.** Computes $a_x/a_y$ and $a_x^*/a_y^*$ correctly, identifies who has comparative
 advantage in which good, and places the free-trade price between the two autarky
 prices.

**Excellent.** Also derives $p^a=a_x/a_y$ from the equal-wage condition $p_x/a_x=p_y/a_y$, computes
 both wages $w=p/a_x$ and $w^*=1/a_y^*$, and verifies with unit costs $wa_i$ that each
 country is competitive in exactly one good.

### Graphical argument

**Limited.** Draws a bowed-out PPF, or omits the intercepts $E/a_i$. Puts consumption on the
 frontier under trade, so no gain is visible.

**Good.** Draws both linear PPFs with correct intercepts and slopes, marks the specialization
 point $B$ and a consumption point $C$ on the trade line of slope $-p$ through $B$, and shows
 $C$ lying above the frontier.

**Excellent.** Also draws the stair-step world relative supply against relative demand, locates $p$
 on the vertical segment, and uses the diagram to show what happens when demand
 instead cuts a flat segment.

### Economic interpretation

**Limited.** Claims a country with an absolute disadvantage in everything cannot export, or that
 low foreign wages make trade harmful. Treats complete specialization as evidence the
 model is simply wrong.

**Good.** Explains that wages adjust so that each country is competitive somewhere, and states
 that trade patterns follow comparative advantage while wage levels follow absolute
 advantage.

**Excellent.** Also explains that complete specialization is an artifact of the two-good grid and
 disappears in the continuum version, and states correctly that Feenstra's empirical
 case for Ricardo is the failure of the HOV sign and rank tests rather than a direct
 test of Ricardo.

## Session 10 rubric: Heckscher-Ohlin and Factor Prices
<!-- id: rubric-s10 | cohort: Part Two | source: Canvas page "Rubric: Session 10", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Stating and applying the four theorems

**Limited.** States a theorem without its ceteris paribus clause, or applies it with the
 factor intensity ranking guessed rather than derived. Confuses
 Stolper-Samuelson with Rybczynski.

**Good.** States each theorem correctly, identifies what is held fixed, and signs the
 conclusion from a given factor intensity ranking without error.

**Excellent.** Also explains why Stolper-Samuelson and Rybczynski are duals, and identifies
 which assumption would have to fail for a given theorem to break.

### Real versus nominal factor rewards

**Limited.** Concludes that the abundant factor is better off because its nominal wage
 rose, without reference to goods prices. Omits the magnification chain.

**Good.** Writes the chain $\hat{w} > \hat{p}_x > \hat{p}_y > \hat{r}$ for a rise in the
 price of good $x$, the labor-intensive good, and explains that it makes the real wage change unambiguous without any information about
 preferences.

**Excellent.** Contrasts this with the specific-factors case, where $w$ lies between the two
 price changes, and correctly concludes that the real wage effect there depends
 on the worker's consumption bundle.

### Reading the empirical record

**Limited.** Reports the Leontief paradox as an unresolved refutation of HO, or quotes
 test success rates without noting that random assignment already delivers
 50 percent.

**Good.** Explains that Leamer (1980) showed Leontief compared the wrong two ratios,
 reports the Bowen-Leamer-Sveikauskas sign and rank results against the
 coin-flip benchmark, and states that HOV fails under identical technologies.

**Excellent.** Traces the full sequence as successively relaxed assumptions, uses Trefler's
 0.9 correlation between estimated productivities and wages as evidence that
 the fitted parameters are economically meaningful, and distinguishes fitting
 from testing when all productivity differences are allowed.

## Session 11 rubric: Monopolistic Competition and Gravity
<!-- id: rubric-s11 | cohort: Part Two | source: Canvas page "Rubric: Session 11", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Why the model exists

**Limited.** States that monopolistic competition explains trade, but cannot say what
 Ricardo or HO fail to explain. Treats intra-industry trade as a detail.

**Good.** Identifies the puzzle: similar rich countries trading similar goods in
 both directions, which difference-based models predict should not happen.
 Names increasing returns as the fix.

**Excellent.** Traces the full chain -- increasing returns force market power, market
 power requires differentiated varieties, varieties generate two-way trade
 between identical countries -- and notes that gravity also arises without
 monopolistic competition whenever countries specialize.

### The equilibrium and the gains

**Limited.** Recalls that price exceeds marginal cost, but cannot reconcile positive
 markups with zero profits, or state where variety comes from.

**Good.** Explains that price exceeds marginal cost by the markup
 $\sigma/(\sigma-1)$, that free entry gives $p = AC$, and that the markup
 exactly covers the fixed cost. States that trade raises the number of
 varieties consumed.

**Excellent.** Also says in words what doubling $E$ moves and what stays: $ZZ$ shifts
 down and each consumer buys less of each variety, so total variety rises.
 With a constant elasticity the price and firm size stay and the gain is
 variety. In the general model the markup falls, the real wage rises and
 some firms in each country close -- which connects to Trefler's selection
 evidence for Canada.

### Gravity and border effects

**Limited.** Writes down gravity but reads the coefficients mechanically. Reports a
 22-times border effect as a literal fact about Canada.

**Good.** Interprets the GDP coefficients as near unity and the distance elasticity
 as roughly $-1$ to $-1.4$, and explains that omitting multilateral
 resistance biases the border effect upward for small countries.

**Excellent.** Explains multilateral resistance as relative remoteness. Uses the
 Canada/U.S.\ halving arithmetic to show why the same true friction yields
 measured effects of 11 and $19/9 \approx 2$. Knows that Anderson and van
 Wincoop's structural estimates are 10.5 and 2.6, and that exporter and
 importer fixed effects recover a consistent estimate (4.7) without the
 nonlinear machinery.

## Session 12 rubric: Static Games and Nash Equilibrium
<!-- id: rubric-s12 | cohort: Part Three | source: Canvas page "Rubric: Session 12", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Setting up the game

**Limited.** Payoffs are written down without stating who the players are or what strategies are available. The normal form is copied rather than constructed from the description.

**Good.** Players, strategy sets and payoffs are all specified, and the normal form is built correctly from a verbal description of the situation.

**Excellent.** The setup is justified: what is assumed common knowledge, what is simultaneous, and what would change if the timing or information were different.

### Solving for equilibrium

**Limited.** Circles a cell without checking both players' incentives, or confuses a dominant strategy with a best response. Mixed strategies are guessed rather than derived.

**Good.** Finds all pure-strategy Nash equilibria from best responses, and derives a mixed-strategy equilibrium from the indifference condition.

**Excellent.** Uses dominance to reduce the game before solving, verifies that no profitable unilateral deviation exists, and states when equilibrium is unique and when it is not.

### Economic interpretation

**Limited.** Reports the equilibrium as an answer with no economics attached.

**Good.** Explains what the equilibrium means for the players, and compares outcomes across models such as Cournot and Bertrand.

**Excellent.** Explains why the equilibrium is inefficient where it is, identifies the externality each player imposes on the other, and says what institution or change of rules would alter the outcome.

## Session 13 rubric: Dynamic Games and Credibility
<!-- id: rubric-s13 | cohort: Part Three | source: Canvas page "Rubric: Session 13", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Extensive form and strategies

**Limited.** Draws a tree with missing information sets or unlabelled branches, or writes a
 "strategy" that names an action only where the player expects to move. Confuses
 complete with perfect information.

**Good.** Draws a well-formed tree with information sets marked, and lists each player's pure
 strategies with an action at every information set. Counts $|S_i|$ correctly and classifies
 the game as perfect or imperfect information.

**Excellent.** Also derives the normal form from the tree and explains what the matrix has lost. Shows
 which distinct trees would collapse to the same matrix, and uses this to say why Nash alone
 is too weak here.

### Backward induction and subgame perfection

**Limited.** Reports only the path of play, not the strategy profile. Lists subgames that cut through an
 information set, or applies node-by-node backward induction to a game with imperfect
 information.

**Good.** Solves a finite perfect-information game by backward induction and states the full strategy
 profile. Identifies every proper subgame and shows which Nash equilibria fail the
 restriction test.

**Excellent.** Handles a game containing a simultaneous-move subgame by solving that subgame as a game
 before folding it back. States the conditions in Proposition 8.1 and says which one is
 doing the work in the game at hand.

### Credibility and commitment

**Limited.** Asserts that the first mover always gains, or treats an announcement as a commitment.
 Reports the Stackelberg quantities without deriving them from the follower's best response.

**Good.** Derives $q_2(q_1) = (90-q_1)/2$, substitutes it, obtains $q_1 = 45$ and $q_2 = 22.5$, and
 compares output, price and profits to the Cournot benchmark from session 12.

**Excellent.** Explains why $q_1 = 45$ is credible only when output is observable and irreversible,
 exhibits a non-subgame-perfect Nash equilibrium of the Stackelberg game, and transfers the
 commitment logic to another setting.

## Session 14 rubric: Incomplete Information and Signaling
<!-- id: rubric-s14 | cohort: Part Three | source: Canvas page "Rubric: Session 14", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Modeling the information problem

**Limited.** Uses "adverse selection" or "incomplete information" as a label without saying who knows what. The type space, the prior and the informed party are left unspecified.

**Good.** States the type space, the prior over types, and which player observes their own type and which does not, and identifies the selection: which types withdraw from the market at a given price, and why.

**Excellent.** Builds the Bayesian game from the economic story, justifies the type space and the prior rather than assuming them, distinguishes screening on an observable proxy from observing the type itself, and explains which market institution exists because one side knows something the other does not.

### Beliefs and equilibrium

**Limited.** Applies Bayes' rule mechanically or not at all, and asserts an equilibrium without checking either player's incentives. Off-path beliefs are ignored.

**Good.** Updates beliefs correctly on the equilibrium path and solves for Bayesian Nash or perfect Bayesian equilibrium, checking incentive compatibility for each type.

**Excellent.** Specifies off-path beliefs and shows the equilibrium survives them, and distinguishes separating from pooling by checking the mimicking incentive of each type explicitly.

### Economic consequences

**Limited.** States that information problems are "bad" without a welfare argument.

**Good.** Identifies the efficiency loss -- units not traded, contracts not written -- and names a device that mitigates it.

**Excellent.** Quantifies or characterizes the loss, explains why signaling is costly because it must be costly to be credible, and evaluates whether a proposed remedy actually restores efficiency.

### Better information, better outcomes?

**Limited.** Concludes that AI or more data must improve markets because information problems are the source of the inefficiency -- or that it must be harmful -- without arguing either side.

**Good.** Gives at least one direction in each: an improvement (adverse selection unwinds, or costly signaling becomes unnecessary) and a harm (pooling was doing insurance work, or the type is inferred from proxies rather than observed).

**Excellent.** Argues both directions from this deck's own machinery, and states what the answer turns on: whether the pooling was insurance, whether the type is observed or proxied, and whether the technology cuts the cost of reading the signal or of producing it -- which would destroy its credibility.

## Session 15 rubric: Repeated Games and Competition Policy
<!-- id: rubric-s15 | cohort: Part Three | source: Canvas page "Rubric: Session 15", from Tutor/stores/store_A_rubrics.json (sha256 bee05f19e681) -->

### Deriving a critical discount factor

**Limited.** States a threshold such as $\delta \ge 1/4$ without deriving it, or writes
 the deviation payoff as a one-period number with no continuation term.
 Arithmetic errors go unnoticed.

**Good.** Writes both payoff streams correctly, sums the geometric series, and solves
 the inequality for $\delta$. Reaches $\delta \ge 9/17$ in the Cournot
 cartel and can verify that the two streams are equal at the cutoff.

**Excellent.** Derives the general form $\delta \ge (v^d-v^c)/(v^d-v^*)$ before
 substituting numbers, and reads it as temptation over temptation-plus-bite.
 Extends it unprompted to a detection lag or an asymmetric split, and checks
 limiting cases.

### Equilibrium reasoning

**Limited.** Calls grim trigger an equilibrium because cooperation is better for both
 players. Does not distinguish Nash from subgame perfection, or checks only
 the on-path condition.

**Good.** Uses the one-stage deviation principle, checks both the on-path and the
 off-path history, and explains that punishment is credible because
 repeating the stage Nash equilibrium is itself an equilibrium.

**Excellent.** Explains why infinite repetition manufactures the multiple continuation
 equilibria that finite repetition lacks, and states the Folk Theorem with
 its feasibility and individual-rationality conditions -- including what it
 fails to predict.

### From model to policy

**Limited.** Describes cartels and antitrust institutions narratively, with no link to
 the incentive condition. Comparative statics are asserted rather than
 signed.

**Good.** Signs the effect of the number of firms, the detection lag and demand
 conditions on the critical discount factor, and explains leniency as
 raising the deviation payoff asymmetrically.

**Excellent.** Maps a policy tool onto the specific term of the inequality it moves,
 quantifies the welfare loss from collusion, and draws the trade-war
 parallel -- identical mathematics, opposite welfare sign, with the WTO in
 the role of third-party enforcer.