Module M17 Quiz: Exchange Economy and General Equilibrium

25 questions · Intermediate · Multiple choice, calculation, and short answer

How to use

Attempt each question before clicking Show Answer.

Question 1

Lesson L01 · Welfare

In an Edgeworth box the total endowment of good 1 equals:

Type: Multiple Choice

A) Consumer A's endowment only
B) Consumer B's endowment only
C) The sum of both consumers' endowments
D) The equilibrium quantity traded

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Answer: C) The sum of both consumers' endowments

The box dimensions are fixed by total endowments: x1_total = ω_A1 + ω_B1 and x2_total = ω_A2 + ω_B2.

Question 2

Lesson L01 · Welfare

Consumer A has endowment (6,2) and consumer B has endowment (4,6). Total endowments are:

Type: Calculation

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Answer: (10,8)

x1_total=6+4=10; x2_total=2+6=8.

Question 3

Lesson L01 · Welfare

A trade from the endowment point that makes consumer A better off and consumer B no worse off is called:

Type: Multiple Choice

A) A Pareto efficient allocation
B) A Pareto improvement
C) A competitive equilibrium
D) A core allocation

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Answer: B) A Pareto improvement

A Pareto improvement makes at least one person better off without making anyone worse off.

Question 4

Lesson L01 · Welfare

Explain why the 'lens' region in an Edgeworth box represents mutually beneficial trades.

Type: Short Answer

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Answer: The lens is the set of allocations where both consumers' indifference curves through the endowment are satisfied — both consumers are at least as well off as at the endowment. Any allocation in the lens interior is a Pareto improvement over the endowment.

Both ICs through the endowment bound the lens — trades inside make both better off.

Question 5

Lesson L01 · Welfare

At the endowment MRS_A = 3 and MRS_B = 1 (both = -dx2/dx1). Can both consumers gain from trade?

Type: Multiple Choice

A) No — MRS are already equal
B) Yes — they value goods differently so trade can make both better off
C) Only consumer A gains
D) Only if prices are set by an auctioneer

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Answer: B) Yes — they value goods differently so trade can make both better off

When MRS_A ≠ MRS_B there are unexploited gains from trade. They can rearrange consumption to both be better off until MRS_A = MRS_B.

Question 6

Lesson L02 · Welfare

An allocation is Pareto efficient if:

Type: Multiple Choice

A) Total utility is maximised
B) No one can be made better off without making someone else worse off
C) Both consumers have equal utility
D) The allocation is on the budget line

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Answer: B) No one can be made better off without making someone else worse off

Pareto efficiency: no Pareto improvements are possible. The contract curve traces all such allocations.

Question 7

Lesson L02 · Welfare

The contract curve in an Edgeworth box is the locus of allocations where:

Type: Multiple Choice

A) Both consumers have the same endowment
B) Indifference curves of both consumers are tangent (MRS_A = MRS_B)
C) Prices are competitive
D) Total surplus is maximised

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Answer: B) Indifference curves of both consumers are tangent (MRS_A = MRS_B)

Tangency of ICs means MRS_A = MRS_B — any deviation creates unexploited gains, so these are Pareto-efficient allocations.

Question 8

Lesson L02 · Welfare

For Cobb-Douglas preferences U_A = x1^0.5 × x2^0.5 and U_B = x1^0.5 × x2^0.5 with totals (10,8): write the contract curve condition.

Type: Calculation

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Answer: x2_A/x1_A = x2_B/x1_B → allocations on the diagonal

MRS_A = x2_A/x1_A; MRS_B = x2_B/x1_B. Setting equal: x2_A/x1_A = (8-x2_A)/(10-x1_A) → contract curve is the main diagonal x2_A = 0.8 × x1_A.

Question 9

Lesson L02 · Welfare

Why does the core of an exchange economy lie on the contract curve?

Type: Short Answer

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Answer: The core is the set of allocations that no coalition can block. Any allocation off the contract curve can be improved for at least one person — the 2-person coalition can block it. Hence only Pareto-efficient allocations (on the contract curve) in the lens can be in the core.

Core ⊆ contract curve: Pareto improvements would be blocked by the improving party.

Question 10

Lesson L02 · Welfare

Moving along the contract curve from consumer A's corner to B's corner generally:

Type: Multiple Choice

A) Keeps both consumers' utility constant
B) Transfers utility from A to B (A gets less as we move toward B's corner)
C) Has no effect on welfare
D) Increases total utility

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Answer: B) Transfers utility from A to B (A gets less as we move toward B's corner)

The contract curve traces Pareto-efficient allocations — as we move toward B's corner B gets more of both goods and A gets less.

Question 11

Lesson L03 · Welfare

In a Walrasian equilibrium both consumers are price takers and markets clear. Market clearing requires:

Type: Multiple Choice

A) Prices are equal for both consumers
B) Aggregate demand equals aggregate supply for each good
C) All consumers have equal income
D) Both consumers have the same MRS

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Answer: B) Aggregate demand equals aggregate supply for each good

Walras equilibrium: p*(x_A*(p*)+x_B*(p*)) = p*(ω_A+ω_B) — at equilibrium prices excess demand is zero.

Question 12

Lesson L03 · Welfare

For U_A = x1^0.5 × x2^0.5 with ω_A=(6,2) and total endowment (10,8): Consumer A's demand is x1_A = 0.5(p1×6+p2×2)/p1. Setting p2=1 find A's demand for good 1 in terms of p1.

Type: Calculation

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Answer: x1_A = (3p1+1)/p1 = 3 + 1/p1

A's income: m_A = 6p1 + 2×1 = 6p1+2. Demand: x1_A = 0.5×(6p1+2)/p1 = 3 + 1/p1.

Question 13

Lesson L03 · Welfare

Walras' Law states that:

Type: Multiple Choice

A) All prices sum to one
B) The value of excess demands across all markets sums to zero — if n-1 markets clear the nth must also clear
C) Each consumer's budget balances
D) All markets clear simultaneously

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Answer: B) The value of excess demands across all markets sums to zero — if n-1 markets clear the nth must also clear

Walras' Law: Σ pᵢ zᵢ = 0 where zᵢ is excess demand for good i. This follows from budget constraints — allows us to normalise one price.

Question 14

Lesson L03 · Welfare

Explain why the numeraire convention is used in general equilibrium analysis.

Type: Short Answer

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Answer: Only relative prices matter for allocation decisions (demand is homogeneous degree 0). Setting one price equal to 1 (the numeraire) removes the indeterminacy of the price level without changing any allocation.

Absolute price levels are irrelevant; only price ratios determine optimal choices.

Question 15

Lesson L03 · Welfare

If at prices (p1,p2)=(2,1) excess demand for good 1 is +3 units and there are only two goods, what is excess demand for good 2?

Type: Calculation

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Answer: −6 units (excess supply)

Walras' Law: p1×z1 + p2×z2 = 0 → 2×3 + 1×z2 = 0 → z2 = −6.

Question 16

Lesson L04 · Welfare

The First Welfare Theorem states that:

Type: Multiple Choice

A) Government should redistribute income
B) Every competitive equilibrium allocation is Pareto efficient
C) Markets always produce equal outcomes
D) The equilibrium maximises total utility

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Answer: B) Every competitive equilibrium allocation is Pareto efficient

First Welfare Theorem: under conditions (no externalities, complete markets, price-taking), competitive equilibria are Pareto efficient — the 'invisible hand' result.

Question 17

Lesson L04 · Welfare

The Second Welfare Theorem states that:

Type: Multiple Choice

A) Any efficient allocation can be decentralised as a competitive equilibrium with appropriate lump-sum transfers
B) Markets are always efficient
C) Government cannot improve on market outcomes
D) Redistribution always reduces efficiency

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Answer: A) Any efficient allocation can be decentralised as a competitive equilibrium with appropriate lump-sum transfers

Second Welfare Theorem: separates efficiency from distribution — any Pareto-efficient allocation is achievable via competitive markets if we redistribute endowments appropriately.

Question 18

Lesson L04 · Welfare

The First Welfare Theorem fails when there are externalities because:

Type: Calculation

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Answer: Private prices don't reflect social costs/benefits so MRS ≠ MSB/MSC at equilibrium

Externalities mean the competitive equilibrium is not Pareto efficient — someone could be made better off without making others worse off by internalising the externality.

Question 19

Lesson L04 · Welfare

Why does the Second Welfare Theorem justify redistribution via lump-sum transfers rather than distortionary taxes?

Type: Short Answer

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Answer: The Second Welfare Theorem shows any Pareto-efficient allocation is achievable by redistributing endowments and then letting markets operate. Lump-sum transfers don't distort relative prices; distortionary taxes do — they move the equilibrium away from Pareto efficiency.

Redistribute endowments (lump-sum) to achieve equity; use markets for efficiency.

Question 20

Lesson L04 · Welfare

Which condition is NOT required for the First Welfare Theorem to hold?

Type: Multiple Choice

A) No externalities
B) Complete markets
C) Equal income distribution
D) Price-taking behaviour

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Answer: C) Equal income distribution

The First Welfare Theorem requires no externalities, complete markets, and price-taking. Equal income is NOT required — markets can be efficient even with unequal incomes.

Question 21

Lesson L05 · Information

Information asymmetry causes market failure because:

Type: Multiple Choice

A) People have different preferences
B) One party knows more than the other — prices cannot efficiently aggregate private information leading to adverse selection or moral hazard
C) Markets have too many participants
D) Government regulation is absent

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Answer: B) One party knows more than the other — prices cannot efficiently aggregate private information leading to adverse selection or moral hazard

Information asymmetries create adverse selection (hidden information) and moral hazard (hidden action) — both prevent competitive markets from achieving efficient outcomes.

Question 22

Lesson L05 · Welfare

Which is an example of missing markets causing inefficiency?

Type: Multiple Choice

A) A tariff on imports
B) Future markets for climate-related risks that don't exist — so private agents cannot efficiently hedge or price these risks
C) A monopoly setting price above MC
D) Income inequality

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Answer: B) Future markets for climate-related risks that don't exist — so private agents cannot efficiently hedge or price these risks

Missing markets (like complete state-contingent insurance) prevent optimal risk sharing — a source of market failure beyond the standard five.

Question 23

Lesson L05 · Welfare

Australia's emissions trading scheme attempts to create a market for carbon rights. This is an application of which economic principle?

Type: Calculation

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Answer: Creating missing markets (property rights in emissions) to achieve the Pareto-efficient allocation that internalises the externality

Carbon markets create property rights in emissions, allowing the market to price the externality and achieve efficiency — a direct application of the Second Welfare Theorem approach.

Question 24

Lesson L05 · Welfare

Public goods cause market failure because the First Welfare Theorem assumes:

Type: Short Answer

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Answer: Complete markets — but public goods cannot be efficiently provided by markets due to non-excludability (free-rider problem) and non-rivalry. These violate the completeness assumption required for the First Welfare Theorem.

Non-excludability means the market for the public good is effectively missing.

Question 25

Lesson L05 · Welfare

Market power (monopoly) violates the First Welfare Theorem because:

Type: Multiple Choice

A) Monopolists earn too much profit
B) A monopolist is not a price taker — it sets P>MC creating a wedge between MRS and the price ratio and producing below the efficient output level
C) Government hasn't regulated the monopolist
D) Consumers don't optimise

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Answer: B) A monopolist is not a price taker — it sets P>MC creating a wedge between MRS and the price ratio and producing below the efficient output level

The First Welfare Theorem requires price-taking behaviour. A monopolist's P>MC means consumers' MRS ≠ marginal cost of production — the allocation is not Pareto efficient.