Unit 5 — General Equilibrium & Welfare Economics

Walras's Vision of the Economic System

Walras saw the economy as a network of interconnected markets. Every commodity price depends not only on its own demand and supply, but also on prices in all other markets. The entire system is like a spider's web — pull one thread and everything moves.

His key insight: In a perfectly competitive economy, if all consumers maximise utility and all producers maximise profit, and if prices are flexible, then the economy will automatically find a point where every single market clears at once.

Key Assumptions

Tâtonnement Process (Trial-and-Error Adjustment)

"Tâtonnement" is a French word meaning groping or trial and error. Walras proposed that an imaginary auctioneer calls out prices, and the market adjusts until equilibrium is found.

Criticism of Walrasian System

• Assumptions (perfect competition, perfect info) are unrealistic
• No real-world "auctioneer" exists — prices don't adjust so smoothly
• Government intervention and market failures are ignored
• Static model — doesn't account for changes over time

Three Conditions for Pareto Optimality 5 Marks

For an economy to be fully Pareto Efficient, three marginal conditions must hold simultaneously:

Explanation of Product Mix Efficiency

MRT (Marginal Rate of Transformation) = the rate at which the economy can convert production of Good Y into Good X. It is the slope (absolute value) of the Production Possibility Frontier (PPF). Mathematically, MRT = MC_X / MC_Y.

MRS (Marginal Rate of Substitution) = the rate at which a consumer is willing to give up Good Y for Good X while staying equally happy.

If MRT > MRS: society is producing more of Good X than consumers want → produce less X, more Y. If MRT < MRS: consumers want more X than being produced → produce more X. Efficiency only when MRT = MRS.

Limitations of Pareto Optimality

• Ignores income distribution — an unequal economy can still be "Pareto optimal"
• Most real policies have winners and losers → strict Pareto rarely applies
• Focuses only on efficiency, not fairness or social justice
• Very difficult to achieve in reality due to market failures

What Does the Contract Curve Tell Us?

• Every point on the contract curve is Pareto Optimal (MRS_A = MRS_B holds)
• Points off the curve are inefficient — moving toward the curve is a Pareto Improvement
• Once on the curve, improving A requires harming B, and vice versa
• The curve shows the range of efficient "deals" consumers can agree to through exchange

Why Was It Needed?

Pareto Optimality is too strict — it only approves changes where nobody loses. But almost every real-world policy (building roads, tax reform, trade deals) benefits some people and harms others. Kaldor-Hicks provides a practical way to evaluate such policies.

Simple Example

Government builds a highway: Benefits = ₹500 crore (travellers, businesses), Losses = ₹100 crore (displaced residents). Since 500 > 100, gainers could compensate losers (pay ₹100 cr) and still enjoy ₹400 cr net gain → Project should proceed per Kaldor-Hicks.

Criticism of Kaldor-Hicks

• Compensation is potential, not actual — losers may never receive anything
• Ignores income distribution — large gains for the rich can outweigh small losses for the poor
• Not all welfare effects can be measured in money (e.g., cultural loss)
• Does not address social justice or fairness

Slope of the Transformation Curve = MRT 2 Marks — Q2j

The slope of the PPF at any point = the Marginal Rate of Transformation (MRT). It tells us how many units of Good Y must be sacrificed to produce one more unit of Good X. Because resources are not perfectly adaptable, this opportunity cost increases as you produce more of one good — hence the PPF is concave.

PPF for a Multi-Product Firm 10 Marks — Q4b

A multi-product firm produces two goods (X and Y) using the same set of resources (labour, capital, raw materials). The firm faces a trade-off: producing more X means using resources that could have produced Y.

How is the PPF Derived?

1. Fixed resources: The firm has a fixed amount of inputs (say, L units of labour and K units of capital) which can be shared between producing X and Y.
2. Production functions: X = f₁(L₁, K₁) and Y = f₂(L₂, K₂), where L₁+L₂ = L and K₁+K₂ = K.
3. Maximum output combinations: By shifting resources from Y to X (or vice versa), we get different output combinations. Plotting all maximum combinations traces out the PPF.
4. Shape (concave): As the firm produces more and more X, it must use progressively less-suitable resources for X production (resources better suited for Y are pulled away), causing the opportunity cost to increase → concave PPF.

Product Mix Efficiency Condition on PPF

For Pareto optimal product mix, the economy should produce at the point on the PPF where: MRT = MRS. This is the point where the PPF is tangent to the highest possible social indifference curve (see Welfare Theorems chapter).

As individual utilities increase, W increases. As they fall, W falls. The function tells society which allocation of resources is best — it is a normative (value-based) tool.

Types of SWF

Importance of SWF

• Provides a method to compare different economic situations/policies
• Goes beyond Pareto Efficiency — can choose among Pareto optimal allocations
• Bridges economics and ethics by incorporating value judgments
• Used in policy evaluation: taxation, subsidies, welfare programs

Limitations

• Utility cannot be precisely measured
• Interpersonal utility comparisons are philosophically controversial
• The function depends on subjective value judgments — different people may disagree
• Arrow's Impossibility Theorem later showed that constructing a consistent SWF from individual preferences is impossible (see Chapter 9)

First Welfare Theorem — Detailed 5 Marks

In a perfectly competitive economy, when every consumer maximises utility and every firm maximises profit, the resulting equilibrium is Pareto Efficient. The invisible hand coordinates all individual decisions to achieve social efficiency without any central planner.

Assumptions

• Perfect competition (many buyers & sellers)
• Perfect information (all prices known)
• No externalities (no pollution, no side-effects)
• Complete markets (markets exist for all goods)
• Rational behaviour

Second Welfare Theorem — Detailed 5 Marks — Q3h 2025

The Second Theorem separates efficiency from equity (fairness). A perfectly efficient allocation might still be socially undesirable if it's very unequal (e.g., one person gets almost everything). The Second Theorem says:

"The government can first redistribute initial endowments (through lump-sum taxes or transfers), and then let competitive markets operate. The result will still be a Pareto Efficient allocation — but now one that is also more equitable."

Limitations of Both Theorems

• Perfect competition rarely exists in reality
• Externalities (pollution) violate the "no externalities" assumption
• Public goods and monopolies cause market failures
• Redistribution in practice is politically difficult and may cause distortions

Simple idea: In a democracy, everyone votes → we try to combine votes into a single social decision. Arrow proved there is no "perfect" rule for doing this. Every voting system will have some flaw.

Arrow's Five Conditions (The "Desirable" Properties)

For a fair social decision-making rule, Arrow said it should satisfy all 5 of these conditions. He then proved no rule can satisfy ALL of them at once:

The Voting Paradox (Why It's Impossible)

Arrow's Main Conclusion

No social welfare function that converts individual preferences into a social ordering can satisfy all five conditions simultaneously when there are 3 or more alternatives. Every voting system must violate at least one condition → "There is no perfect democratic decision-making rule."

Importance

• Founded modern Social Choice Theory
• Showed major limitation of welfare economics — a consistent SWF from individual preferences is impossible
• Influenced the design of voting systems and policy-making frameworks
• Won Arrow the Nobel Prize in 1972

Criticism

• Conditions may be too strict — relaxing IIA allows some consistent systems
• Real-world voting systems work "well enough" even if not perfectly consistent

1-Mark Definitions (Copy These Exactly)

All Key Formulas at a Glance

Who Did What? (Developer Table)

Arrow's 5 Conditions — Quick Memory

The Big 3 Pareto Conditions — Diagram Summary