Competitive equilibrium (also called: Walrasian equilibrium) is the traditional concept of economic equilibrium, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated.
A competitive equilibrium consists of two elements:
- A vector of prices - a price for each different type of commodity;
- For each agent, an allocation vector - the quantity of each commodity allocated to this agent.
These vectors should satisfy the following requirements:
- Feasibility - the total demand of each good equals the total supply of that good (i.e. the market is cleared);
- Rationality - every agent weakly prefers their allocation to any other possible allocation they might receive given their budget. In other words, if an agent strongly prefers another combination of goods, the agent can't afford it.
Indivisible item assignment
A. Alice has a car which she values as 10. Bob has no car, and he values Alice's car as 20. A possible competitive equilibrium is: the price of the car is 15, Bob gets the car and pays 15 to Alice. This is an equilibrium because the market is cleared and both agents prefer their final bundle to their initial bundle. In fact, every price between 10 and 20 will be a competitive equilibrium price. The same situation holds when the car is not initially held by Alice but rather sold by an external auctioneer: the car will go to Bob and the price will be anywhere between 10 and 20.
On the other hand, any price below 10 is not an equilibrium price because there is an excess demand (both Alice and Bob want the car at that price), and any price above 20 is not an equilibrium price because there is an excess supply (neither Alice nor Bob want the car at that price).
B. A horse and a carriage are sold in an auction. Alice wants only the horse and the carriage together - she receives a utility of 100 from holding both of them but a utility of 0 for holding only one of them. Bob wants either the horse or the carriage but doesn't need both - he receives a utility of 60 from holding one of them and the same utility of 60 for holding both of them. Here there is no competitive equilibrium, i.e. no price will clear the market. To see this, consider the following options for the sum of the prices (horse-price + carriage-price):
- The sum is less than 100. Then Alice wants both items. Since the price of at least one item is smaller than 60, Bob wants that item, so there is an excess demand.
- The sum is exactly 100. Then Alice is indifferent between buying both items and not buying any item. But Bob still wants exactly one item, so there is either an excess demand or excess supply.
- The sum is more than 100. Then Alice wants no item and Bob still wants at most a single item, so there is an excess supply.
There are two kinds of products: bananas and apples, and 2 individuals: Jane and Kelvin. The price of bananas is Pb, and the price of apples is Pa.
Suppose that the initial allocation is at point X, where Jane has more apples than Kelvin does and Kelvin has more bananas than Jane does.
By looking at their indifference curves J1 of Jane and K1 of Kelvin, we can see that this is not an equilibrium - both agents are willing to trade with each other at the prices Pb and Pa. After trading, both Jane and Kelvin move to an indifference curve which depicts a higher level of utility, J2 and K2. The new indifference curves intersect at point E. The slope of the tangent of both curves equals -Pb/Pa.
And the MRSJane=Pb/Pa; MRSKelvin=Pb/Pa. The marginal rate of substitution of Jane equals that of Kelvin. Therefore the 2 individuals society reaches Pareto efficiency, where there is no way to make Jane or Kelvin better off without making the other worse off.
The competitive equilibrium and allocative efficiency
At the competitive equilibrium, the value society places on a good is equivalent to the value of the resources given up to produce it (marginal benefit equals marginal cost). By definition, this ensures allocative efficiency (the additional value society places on another unit of the good is equal to what society must give up in resources to produce it).
Note that microeconomic analysis does NOT assume additive utility nor does it assume any interpersonal utility tradeoffs. Efficiency therefore refers to the absence of Pareto improvements. It does not in any way opine on the fairness of the allocation (in the sense of distributive justice or equity). An 'efficient' equilibrium could be one where one player has all the goods and other players have none (in an extreme example). This is efficient in the sense that one may not be able to find a Pareto improvement - which makes all players (including the one with everything in this case) better off (for a strict Pareto improvement), or not worse off.
- About.com dictionary
- Callan, S.J & Thomas, J.M. (2007). 'Modelling the Market Process: A Review of the Basics', Chapter 2 in Environmental Economics and Management: Theory, Politics and Applications, 4th ed., Thompson Southwestern, Mason, OH, USA
- Competitive equilibrium, Walrasian equilibrium and Walrasian auction in Economics Stack Exchange.