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