What does it mean for all markets to 'clear' in a Walrasian equilibrium?
AAll goods sell at the same price across markets
BQuantity supplied equals quantity demanded in every market simultaneously
CEvery firm earns zero economic profit
DConsumers spend their entire income on a single good
Market clearing means excess demand is zero in every market at the equilibrium price vector. This must hold simultaneously across all markets — not just one — which is what distinguishes general equilibrium from partial equilibrium analysis.
Question 2 True / False
A Walrasian equilibrium requires a central planner to compute and announce prices so that most markets clear simultaneously.
TTrue
FFalse
Answer: False
The key insight of Walrasian theory is that competitive price adjustment — not central coordination — can achieve general equilibrium. The 'Walrasian auctioneer' is a thought experiment, not a policy prescription. Each agent responds to prices as given; equilibrium emerges from decentralized optimization.
Question 3 Short Answer
Why is proving the existence of a Walrasian equilibrium mathematically non-trivial, and what tool is typically used?
Think about your answer, then reveal below.
Model answer: Existence is non-trivial because it requires showing that a single price vector can simultaneously satisfy excess-demand-equals-zero conditions across all markets at once. The standard proof uses a fixed-point theorem (Brouwer's or Kakutani's): the excess demand function can be mapped to a price-adjustment rule, and a fixed point of that map is an equilibrium price vector.
The difficulty is not finding equilibrium in one market — that follows from basic supply and demand. The challenge is that adjusting prices in one market changes demand in all others (via income and substitution effects), so equilibrium must be a simultaneous solution to a system of conditions. Fixed-point theorems guarantee such a solution exists under continuity and convexity conditions.