Consider the following conditions that may or may not apply about a market:

(1) The market structure is perfect competition.

(2) All goods are normal

(3) Demand and Supply are unit elastic.

(4) There are no externalities in the market.

The First Welfare Theorem states that the unregulated market is Pareto efficient if which of the above conditions hold?

Question

Consider the following conditions that may or may not apply about a market:

(1) The market structure is perfect competition.

(2) All goods are normal

(3) Demand and Supply are unit elastic.

(4) There are no externalities in the market.

The First Welfare Theorem states that the unregulated market is Pareto efficient if which of the above conditions hold?

BlackTom AI · Accepted Answer

Perfectly competitive markets and absence of externalities are the core requirements for the First Welfare Theorem to guarantee Pareto efficiency.

1. Relevant knowledge points and concepts
- First Welfare Theorem (FWT): any competitive equilibrium is Pareto efficient under standard assumptions. Key formal requirements include price-taking behavior (perfect competition), well-defined private property rights, no externalities, complete markets, convex preferences and production sets, and perfect information/zero transaction costs. Efficiency is characterized by equality of marginal rates of substitution (MRS) across consumers and equality of MRS to marginal rate of transformation (MRT) in production, all equated via market prices.

2. Step-by-step reasoning
- In perfect competition (condition 1), consumers maximize utility given prices and firms maximize profits given prices. Each agent takes prices as given.
- Optimality conditions imply for consumers: MRS between any two goods equals the price ratio. For firms: MRT equals the price ratio. Hence MRS = MRT across the economy, which is the necessary condition for Pareto efficiency.
- If externalities are absent (condition 4), private marginal benefits/costs equal social marginal benefits/costs. Therefore private optimization implies social optimality—no unaccounted-for third‑party effects distort allocations.
- Conversely, if externalities exist, private decisions do not reflect social costs/benefits, breaking the equality between private MRS and social MRT and thus breaking efficiency.

3. Intermediate logical steps (no numerical calculation)
- Consumer optimum: maximize u(x) s.t. p·x = income ⇒ MRS = p1/p2.
- Producer optimum: minimize cost or maximize profit ⇒ MRT = p1/p2.
- With no externalities, private MRS = MRT ⇒ allocation is Pareto efficient.

4. Why the correct answer is correct
- Conditions (1) and (4) together ensure the price mechanism aligns private choices with social welfare, which is precisely what FWT asserts.

5. Why other options are incorrect
- (2) “All goods are normal”: normality concerns income effects and demand responses, not efficiency conditions—irrelevant to FWT.
- (3) “Demand and Supply are unit elastic”: elasticity values affect quantities and price responsiveness but do not determine whether equilibria are Pareto efficient.

6. Conclusion
Given the theorem’s assumptions, the unregulated market is Pareto efficient when (1) perfect competition and (4) no externalities hold. This matches the provided answer "(1) and (4)".

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