Part A – Fundamentals of General Equilibrium (Q1–Q10)

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1. The general equilibrium approach was first developed by:

(A) Alfred Marshall (B) Léon Walras ✅ (C) Vilfredo Pareto (D) Adam Smith

Explanation:
Léon Walras introduced the concept of general equilibrium in his 1874 book Elements of Pure Economics. He used simultaneous equations to show how all markets in an economy reach equilibrium together.

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2. The partial equilibrium analysis assumes:

(A) Interdependence of all markets
(B) Simultaneous equilibrium of all markets
(C) Other things remain constant ✅
(D) Constant returns to scale

Explanation:
Partial equilibrium (Marshallian) isolates one market at a time, assuming ceteris paribus — all other factors such as incomes, prices of related goods, and tastes remain constant.

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3. General Equilibrium analysis considers:

(A) One market in isolation
(B) All interrelated markets simultaneously ✅
(C) Only factor markets
(D) Only goods markets

Explanation:
General equilibrium recognizes interdependence among all markets (goods and factors) and determines prices and quantities in all of them together.

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4. Equality of demand and supply in all markets simultaneously is known as:

(A) Microeconomic equilibrium
(B) General equilibrium ✅
(C) Partial equilibrium
(D) Market failure

Explanation:
General equilibrium occurs when demand equals supply in every market of an economy at the same time.

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5. The Walrasian system uses which mathematical method?

(A) Differential equations
(B) Simultaneous equations ✅
(C) Regression analysis
(D) Integral calculus

Explanation:
Walras modeled markets as a system of simultaneous equations, where all prices and quantities are determined together.

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6. In Walrasian analysis, “unknowns” represent:

(A) Quantities only
(B) Prices only
(C) Prices and quantities of all commodities and factors ✅
(D) Profits and wages only

Explanation:
The Walrasian model includes as many unknowns (prices and quantities) as independent equations for all goods and factors in the system.

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7. Walras’ Law states that:

(A) The sum of excess demands across markets equals zero ✅
(B) Total supply always exceeds demand
(C) Only one market can be in equilibrium
(D) Demand always exceeds supply

Explanation:
Walras’ Law implies that if n-1 markets are in equilibrium, the nth market must also be in equilibrium — the sum of excess demands times prices is always zero.

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8. If all but one market are in equilibrium, then according to Walras’ Law:

(A) No equilibrium exists
(B) The last market must also be in equilibrium ✅
(C) Prices will diverge
(D) Supply exceeds demand

Explanation:
Because total value of excess demand is zero, equilibrium in all but one market automatically ensures equilibrium in the remaining market.

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9. The existence of a general equilibrium solution requires:

(A) More unknowns than equations
(B) Equal number of independent equations and unknowns ✅
(C) Fewer equations than unknowns
(D) No mathematical relationship

Explanation:
A basic mathematical requirement for solvability of the Walrasian system is equality between the number of independent equations and the number of unknown variables.

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10. The Arrow–Debreu model proved:

(A) Instability of equilibrium
(B) Existence of general equilibrium ✅
(C) Monopoly equilibrium
(D) Disequilibrium in markets

Explanation:
Kenneth Arrow and Gérard Debreu (1954) gave a rigorous proof that, under convex preferences and continuous production functions, a general equilibrium always exists.

Part B – Existence, Uniqueness & Stability (Q11–Q20)

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11. The existence of equilibrium depends on:

(A) Equality of equations and unknowns
(B) Convex preferences and diminishing returns ✅
(C) Constant costs
(D) Increasing returns

Explanation:
Arrow–Debreu showed that general equilibrium exists if preferences are convex and production exhibits constant or diminishing returns.

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12. Uniqueness of equilibrium means:

(A) Multiple equilibria
(B) Only one set of prices clears all markets ✅
(C) No solution
(D) Negative prices

Explanation:
Uniqueness ensures a single consistent price–quantity combination that balances all markets; otherwise, multiple equilibria can arise.

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13. A stable equilibrium is one where:

(A) Disturbances push the system away
(B) The system returns to equilibrium after disturbance ✅
(C) Output stays fixed
(D) Price never changes

Explanation:
Stability means that self-correcting forces (supply and demand) restore equilibrium when disturbed — essential for market resilience.

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14. The Cobweb theorem illustrates:

(A) Market failure
(B) Dynamic stability and instability ✅
(C) Monopoly behavior
(D) Welfare loss

Explanation:
The Cobweb theorem analyzes oscillations in price and output over time due to lagged supply responses, showing conditions for stability.

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15. In the Cobweb model, if demand is steeper than supply (|dP/dQ| < |sP/dQ|):

(A) The system is stable ✅
(B) The system diverges
(C) It is neutral
(D) Unattainable equilibrium

Explanation:
When the demand curve is flatter (less steep) than the supply curve, price and quantity adjustments converge toward equilibrium.

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16. If slopes of demand and supply are equal in Cobweb model:

(A) Stable
(B) Neutral oscillations (undamped) ✅
(C) Explosive
(D) Divergent

Explanation:
Equal slopes cause constant oscillations around equilibrium — neither converging nor diverging — known as neutral or undamped cycles.

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17. Multiple equilibria occur when:

(A) Demand curve is backward bending ✅
(B) Supply curve is linear
(C) Cost curve is flat
(D) Production is constant

Explanation:
Backward-bending demand (as for inferior goods) can intersect supply more than once, yielding multiple equilibrium points.

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18. The Arrow–Debreu model assumes:

(A) Convex preferences, no externalities ✅
(B) Increasing returns
(C) Non-convex utility
(D) Monopoly

Explanation:
For equilibrium to exist, Arrow–Debreu required convex preferences, continuous functions, and absence of externalities or joint production.

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19. A unique and stable equilibrium exists under:

(A) Perfect competition and diminishing returns ✅
(B) Monopoly power
(C) Increasing returns
(D) Oligopoly

Explanation:
Perfect competition with diminishing returns ensures no incentive for divergence — yielding stable and unique equilibrium.

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20. The automatic adjustment process in general equilibrium works best under:

(A) Government price control
(B) Perfect competition ✅
(C) Monopoly
(D) Price rigidity

Explanation:
Only under perfect competition can prices freely adjust through supply and demand, restoring equilibrium automatically.

Part C – Pareto Efficiency & Welfare (Q21–Q30)

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21. Pareto Efficiency occurs when:

(A) Total utility is maximized
(B) No one can be made better off without making someone worse off ✅
(C) Equal income distribution
(D) Government maximizes welfare

Explanation:
A Pareto efficient allocation means all possible mutual gains from trade have been exhausted.

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22. Efficiency in Exchange requires:

(A) MRTS equality
(B) MRT equality
(C) Equal MRS between individuals ✅
(D) Equal incomes

Explanation:
Exchange efficiency holds when the Marginal Rate of Substitution (MRS) between goods is the same for all consumers.

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23. Efficiency in Production requires:

(A) MRTS_X = MRTS_Y ✅
(B) MRT = MRS
(C) MU_X = MU_Y
(D) Equal factor prices only

Explanation:
Production efficiency occurs when the Marginal Rate of Technical Substitution (MRTS) between factors is equal across firms.

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24. Efficiency in Product Mix requires:

(A) MRS = MRT ✅
(B) MRTS_X = MRTS_Y
(C) MC = MR
(D) Equal profits

Explanation:
For optimal output mix, the Marginal Rate of Transformation (MRT) in production equals consumers’ MRS in consumption.

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25. Pareto Efficiency is achieved when:

(A) Exchange, production, and product-mix efficiencies all hold ✅
(B) Only exchange is efficient
(C) Factor allocation is fixed
(D) Price = average cost

Explanation:
All three efficiencies (exchange, production, and product mix) together define a Pareto optimal general equilibrium.

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26. First Welfare Theorem states:

(A) Every Pareto efficient allocation is competitive
(B) Every competitive equilibrium is Pareto efficient ✅
(C) Equity and efficiency coincide
(D) Monopoly leads to efficiency

Explanation:
Under perfect competition and no externalities, market equilibrium automatically leads to Pareto efficiency.

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27. Second Welfare Theorem states:

(A) Equity and efficiency can’t coexist
(B) Any Pareto efficient outcome can be achieved via redistribution ✅
(C) Government must fix prices
(D) No equilibrium exists

Explanation:
The theorem separates efficiency from equity — government can redistribute initial endowments, and the market then achieves efficiency.

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28. The Kaldor–Hicks criterion allows improvement if:

(A) Everyone gains equally
(B) Gainers could compensate losers ✅
(C) No one loses
(D) Income is equal

Explanation:
Under Kaldor–Hicks, an action is welfare-improving if winners could compensate losers, even if compensation doesn’t occur.

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29. The Social Welfare Function was introduced by:

(A) Walras
(B) Bergson and Samuelson ✅
(C) Hicks
(D) Pareto

Explanation:
The Bergson–Samuelson Social Welfare Function (SWF) expresses collective welfare as a function of individual utilities.

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30. Pareto Optimum is not achieved when:

(A) MRS_A = MRS_B
(B) MRTS_X = MRTS_Y
(C) MRT ≠ MRS ✅
(D) All resources are fully employed

Explanation:
If the marginal rate of transformation (production) doesn’t equal the marginal rate of substitution (consumption), the product mix is inefficient.

Part D – Edgeworth Box, Contract Curve & Core (Q31–Q40)

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31. The Edgeworth Box represents:

(A) Two consumers and two goods ✅
(B) One good and two consumers
(C) Two producers and one good
(D) Government and consumer

Explanation:
It graphically shows allocations of two goods between two consumers (or factors between two producers).

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32. The origin for Consumer A in the Edgeworth Box is:

(A) Bottom-left ✅ (B) Top-right (C) Center (D) Bottom-right

Explanation:
Consumer A’s quantities are measured from the bottom-left corner of the box.

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33. The origin for Consumer B is:

(A) Top-right ✅ (B) Bottom-left (C) Center (D) Left edge

Explanation:
B’s origin is diagonally opposite A’s, so both measure goods in opposite directions.

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34. Every point inside the Edgeworth Box shows:

(A) One consumer’s utility
(B) An allocation of goods between A and B ✅
(C) Production level
(D) National income

Explanation:
Each point indicates how total goods X and Y are divided between the two individuals.

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35. The Contract Curve represents:

(A) All possible allocations
(B) All Pareto-efficient allocations ✅
(C) Inefficient allocations
(D) The PPF

Explanation:
The contract curve is the locus of tangency points between A’s and B’s indifference curves—Pareto efficient allocations.

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36. At every point on the Contract Curve:

(A) MRS_A ≠ MRS_B
(B) MRS_A = MRS_B ✅
(C) MRTS_X = MRTS_Y
(D) Total utility minimum

Explanation:
When the marginal rate of substitution between goods is equal for both individuals, no further mutually beneficial trade is possible.

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37. The Core of Exchange includes:

(A) Entire contract curve
(B) Efficient allocations preferred to initial endowment ✅
(C) Inefficient points
(D) Only one allocation

Explanation:
The core is the subset of Pareto-efficient points that both individuals prefer to their starting point (initial endowment).

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38. In the production version of the Edgeworth Box, indifference curves are replaced by:

(A) Isoquants ✅ (B) Iso-cost lines (C) Demand curves (D) CICs

Explanation:
In production, isoquants (equal-output curves) replace indifference curves to show combinations of inputs producing equal output.

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39. In the production Edgeworth Box, efficiency occurs when:

(A) MRTS_LK^X = MRTS_LK^Y ✅
(B) MRS_A = MRS_B
(C) MRT = MRS
(D) MU_X = MU_Y

Explanation:
Factor efficiency is achieved when both industries have the same marginal rate of technical substitution between labour and capital.

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40. When MRS = MRT, the economy achieves:

(A) Efficiency in exchange
(B) Efficiency in production
(C) Efficiency in product mix ✅
(D) Market disequilibrium

Explanation:
Equality between consumer preferences (MRS) and production trade-off (MRT) ensures the right combination of goods is produced.

1. Introduction

The concept of general equilibrium represents one of the core analytical tools in microeconomics. While partial equilibrium examines individual markets in isolation, general equilibrium analysis studies the simultaneous equilibrium of all interrelated markets — goods, services, and factors — within an economy.

This framework was developed by Léon Walras, whose Elements of Pure Economics (1874) provided the mathematical foundation for modern equilibrium theory. His approach, known as the Walrasian General Equilibrium Model, remains the cornerstone of equilibrium analysis.

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2. Partial vs. General Equilibrium

Partial Equilibrium Analysis

• Introduced by Alfred Marshall, this method isolates one market or variable while assuming all others remain constant (ceteris paribus).

• It is suitable for studying specific issues like:

  • Demand and supply in a single commodity market.

  • Price determination in isolation.

• Limitations:

  • Ignores interdependence between markets.

  • Assumes other prices, incomes, and tastes remain unchanged.

General Equilibrium Analysis

• Developed by Walras, this approach considers simultaneous interaction of all markets.

• It acknowledges that a change in one market affects others (e.g., a rise in food prices affects wages, cost of production, and factor markets).

• Objective: To determine whether a set of prices exists that brings equilibrium in all markets simultaneously.

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3. Walrasian General Equilibrium Model

Assumptions

1. Perfect competition in all markets.

2. Rational consumers maximize utility; firms maximize profits.

3. Factors and goods are homogeneous and perfectly divisible.

4. All markets clear — supply equals demand.

Structure of the Model

Suppose the economy has:

• n commodities, m factors, and h households.

Each market has:

• Demand functions: $Q_i^d=D_i(P_1,P_2,\mathrm{.}\mathrm{.}\mathrm{.},P_n,M_1,M_2,\mathrm{.}\mathrm{.}\mathrm{.},M_h)$
  

• Supply functions: $Q_i^s=S_i(P_1,P_2,\mathrm{.}\mathrm{.}\mathrm{.},P_n,V_1,V_2,\mathrm{.}\mathrm{.}\mathrm{.},V_m)$
  

• Factor demand functions: $R_k^d=D_k(Q_1,\mathrm{.}\mathrm{.}\mathrm{.},Q_n,P_1,\mathrm{.}\mathrm{.}\mathrm{.},P_n,V_1,\mathrm{.}\mathrm{.}\mathrm{.},V_m)$
  

• Factor supply functions: $R_k^s=S_k(V_1,V_2,\mathrm{.}\mathrm{.}\mathrm{.},V_m;R_{k1},R_{k2},\mathrm{.}\mathrm{.}\mathrm{.},R_{kh})$
  

Walras’ Law

The sum of excess demands across all markets is zero:

$$$$

\sum (P_i Q_i^d – P_i Q_i^s) = 0
]
This means that if all but one market are in equilibrium, the last one must also be in equilibrium.

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4. Graphical Illustration (2×2×2 Model)

Consider:

• 2 goods (X and Y)

• 2 factors (Labour L and Capital K)

• 2 consumers (A and B)

When demand for one good (say X) rises:

• Price of X rises → firms in X earn supernormal profits.

• Resources (L, K) move from industry Y to X.

• Price of Y falls → firms in Y incur losses.

• Over time, this reallocation of resources restores equilibrium across both goods and factor markets.

This automatic adjustment mechanism demonstrates how the market tends toward general equilibrium.

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5. Existence, Uniqueness, and Stability of General Equilibrium

1️⃣ Existence

A general equilibrium exists if a set of prices makes aggregate demand = aggregate supply in all markets.

• Walras proved existence mathematically using simultaneous equations.

• Modern proofs (Arrow–Debreu, 1954) showed equilibrium exists under:

  • Convex preferences,

  • Continuous, decreasing returns to scale,

  • No externalities.

2️⃣ Uniqueness

Equilibrium is unique if there is only one set of prices that clears all markets.

• Uniqueness requires:

  • Strict convexity of preferences,

  • Non-intersecting excess demand curves.

• If demand curves are backward-bending (as in Giffen goods), multiple equilibria can exist.

3️⃣ Stability

An equilibrium is stable if deviations from it trigger market forces that restore equilibrium.

• Stable Equilibrium: When market adjustment brings the system back (demand < supply → prices fall → equilibrium restored).

• Unstable Equilibrium: Divergence from equilibrium continues.

• Stability depends on relative slopes of demand and supply curves and adjustment mechanisms.

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6. Pareto Efficiency and General Equilibrium

A general equilibrium is Pareto efficient when no reallocation of resources can make someone better off without making someone else worse off.

Conditions for Pareto Optimality:

1. Efficiency in Consumption:

   • MRS (A) = MRS (B)

2. Efficiency in Production:

   • MRTS (X) = MRTS (Y)

3. Efficiency in Product Mix:

   • MRT (production) = MRS (consumption)

When these three conditions are met, the economy achieves Pareto optimality.

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7. Extensions of General Equilibrium

• Kaldor–Hicks Efficiency: Improvement is efficient if gainers could compensate losers.

• Social Welfare Function (Bergson–Samuelson): Aggregates individual preferences into a measure of societal welfare.

• Second Welfare Theorem: Any Pareto optimal allocation can be achieved through appropriate redistribution and competitive equilibrium.

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8. Limitations of General Equilibrium Analysis

1. Assumes perfect competition, rarely observed in reality.

2. Neglects time-lags and dynamic processes.

3. Requires complete information and rationality.

4. Ignores externalities and public goods.

5. Complex mathematical modeling limits empirical application.

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9. Key Terms

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10. Summary for UGC NET Preparation

• Distinguish between Partial and General Equilibrium.

• Understand Walrasian Model and Walras’ Law.

• Learn the conditions of existence, uniqueness, and stability.

• Relate General Equilibrium to Welfare Economics (Pareto, Kaldor–Hicks).

• Review the Arrow–Debreu model for modern proofs.

• Remember diagrams for 2×2×2 model, Edgeworth Box, and Production Possibility Frontier.

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Suggested Readings

• D.N. Dwivedi, Microeconomics: Theory and Applications.

• Hal R. Varian, Microeconomic Analysis.

• Koutsoyiannis, Modern Microeconomics.

• Mas-Colell, Whinston, Green, Microeconomic Theory.

 

General Equilibrium Analysis (Extended Notes with Edgeworth Box & Pareto Efficiency)

(UGC NET Economics – Unit 1: Microeconomics)

1. Introduction to the Edgeworth Box

The Edgeworth Box Diagram is one of the most important tools for understanding General Equilibrium and Pareto Efficiency in both exchange and production.

It was developed by Francis Ysidro Edgeworth (1881) and later refined by Vilfredo Pareto (1906).

The Edgeworth Box provides a graphical representation of a two-person, two-good economy, showing how resources or goods can be distributed between two individuals (or firms) to achieve efficient allocations.

2. Structure of the Edgeworth Box

Assumptions:

1. Two consumers (A and B)

2. Two goods (X and Y)

3. Fixed total quantities of X and Y

   $$X_A+X_B=\bar{X},Y_A+Y_B=\bar{Y}$$

4. Preferences of both consumers are convex, continuous, and represented by indifference curves.

5. There is no production — only exchange.

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Diagram Description

Imagine a rectangle (the box):

• The width of the box represents the total quantity of good X available.

• The height represents the total quantity of good Y.

• The origin for consumer A is at the bottom-left corner (Oₐ).

• The origin for consumer B is at the top-right corner (Oᵦ).

Each point inside the box represents one possible distribution of goods X and Y between A and B.

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Indifference Curves

• ICₐ = Indifference curves of consumer A (convex to Oₐ).

• ICᵦ = Indifference curves of consumer B (convex to Oᵦ).

• The point of tangency between ICₐ and ICᵦ shows a state where both consumers cannot be made better off without hurting the other — a Pareto efficient allocation.

3. The Contract Curve

Definition:

The Contract Curve is the locus of all tangency points between the indifference curves of A and B inside the Edgeworth Box.

It represents all Pareto Efficient (optimal) allocations of the two goods between the two individuals.

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Mathematical Condition:

At Pareto Efficiency, the Marginal Rate of Substitution (MRS) of both individuals must be equal:

$$MR{S}_{XY}^A=MR{S}_{XY}^B$$

That is,

$$\frac{M{U}_X^A}{M{U}_Y^A}=\frac{M{U}_X^B}{M{U}_Y^B}$$

When this condition holds, neither A nor B can be made better off without making the other worse off.

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Interpretation:

• Every point on the Contract Curve is Pareto Efficient, but not all points are socially desirable.

• The final outcome depends on initial endowments and bargaining power (see the core of exchange below).

4. The Core of Exchange

• The Core is the subset of Pareto-efficient points on the contract curve that both individuals prefer over their initial endowment.

• It represents the possible range of mutually beneficial trades.

Thus:

$$\text{Core}\subset \text{Contract Curve}$$

At any point outside the core, one or both individuals would reject the trade.

5. Edgeworth Box for Production

In the production version of the Edgeworth Box:

• Consumers are replaced by firms.

• Goods X and Y are replaced by two factors of production (Labour L and Capital K).

• Isoquants represent combinations of inputs (L, K) producing the same output.

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Production Efficiency Condition:

For efficiency in production,

$$MRT{S}_{LK}^X=MRT{S}_{LK}^Y$$

That is, the Marginal Rate of Technical Substitution between labour and capital must be equal for both industries.

This ensures that no reallocation of resources can increase total output of one good without reducing that of another.

6. Combining Exchange and Production: The General Equilibrium

Once efficiency in production and efficiency in exchange are achieved, we combine both through the Production Possibility Frontier (PPF) and the Community Indifference Curve (CIC).

Efficiency in Product Mix:

$$MR{T}_{XY}=MR{S}_{XY}$$

Where:

• MRT = Marginal Rate of Transformation (slope of PPF)

• MRS = Marginal Rate of Substitution (slope of CIC)

This ensures the optimal combination of goods produced matches the pattern of consumers’ preferences.

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🧮 7. Three Conditions for Pareto Efficiency

When all three hold simultaneously, the economy is in general equilibrium and Pareto efficient.

8. Graphical Summary

• The Edgeworth Box (Exchange) shows efficient distribution of goods between consumers.

• The Edgeworth Box (Production) shows efficient allocation of factors among firms.

• The PPF–CIC Framework shows efficient combination of goods matching social preferences.

These three layers together form the General Equilibrium Model of the economy.

9. Welfare Theorems and General Equilibrium

First Fundamental Theorem of Welfare Economics

Under perfect competition, every general equilibrium allocation is Pareto Efficient.

Second Fundamental Theorem of Welfare Economics

Any Pareto Efficient allocation can be achieved by suitable redistribution of initial endowments and then allowing competitive equilibrium.

This implies that equity and efficiency can be separated — government can redistribute endowments without distorting market efficiency.

10. Key Takeaways for UGC NET