Pure Exchange Economy Flashcards
Consumer i’s budget set
Consumer i’s demand
Offer curve
also known as price-consumption-curve
Represents the set of optimal consumption choices (bundles of goods) for an individual consumer for different price levels, holding wealth or income constant.
Here’s what the offer curve stands for:
1. Optimal Choices Over Prices:
It traces out the consumer’s preferred combination of goods as prices change. For each price vector, the consumer’s budget constraint rotates around their level of wealth, and the offer curve marks the point of tangency between the budget line and the highest attainable indifference curve.
- **Revealing Preferences: **
The curve reveals how a consumer’s demand for goods changes with prices. - **Illustrating Substitution: **
The offer curve illustrates the substitution effect of changing prices since it holds income constant and shows how the consumer substitutes between goods as their relative prices change.
Excess Demand
The consumer demand more of a good than the total supply in the economy.
Walras Law
(2)
The total value of the excess demands for all goods is always zero at any prices.
Walrasian Equibilibrium
A price vector p star and an allocation x star are in a Walrasian equilibrium, when two conditions are met:
1. Utility Maximization:
Each consumer i chooses an allocation x star (a bundle of goods) that maximizes their utility given the market prices p star and their initial endowment (wealth).
2. Market Clearing
The sum of the allocations of all goods equals the sum of the initial endowments for those goods across all consumers.
Graphically: where two indifferent curves are tangent
Properties of Walrasian Equilibrium
- where two indifferent curves are tangent since utility max requires each consumer’s MRS to be equal to common price ratio (exceptions on edge)
- at intersection of two offer curves (except ω) is equilibrium
- equilibrium determines relative prices for p1/p2
* equilibrium determines relative prices by establishing the rate at which goods can be exchanged in the market such that both consumers maximize their utility
* Relative price is the price of one good in terms of another good, rather than in absolute monetary terms
* includes homogeneity of degree 0 in p
Cases in which no equilibrium exists
1. Non-Convex Preferences
* for an equilibrium to exist, consumer preferences need to be convex = Convex preferences indicate that consumers are willing to substitute between goods = prefer mixtures of goods over extremes
* If preferences are non-convex, consumers might prefer extreme bundles of goods (all or nothing of a certain good), leading to no tangency between indifference curves and thus no intersection of offer curves.
2. No intersection of offer curves
Signifying that there’s no mutually agreeable trade between the two consumers that would equilibrate the market.
Why is it important?
Because it means that market forces alone may not lead to a distribution of goods that all consumers agree upon, suggesting the need for external intervention or the development of more complex market mechanisms to reach a satisfactory allocation of resources.
Pareto Efficiency
An allocation is pareto efficient if there is NO alternative allocation x’ with
1) There is no other allocation x’ where for all consumers, the allocation x’ is at least as good as allocation x
2) and any consumer would be strictly better off without at least one other consumer being worse off.
Pareto Efficiency in the Edgeworth Box
Graphically
If Optimum is an Interior Point:
When the optimum is at an interior point of the Edgeworth box (not on the boundaries), the indifference curves of the two consumers are tangent. This means that their marginal rates of substitution are equal, and there is no way to reallocate goods between them to make one consumer better off without making the other worse off. This point of tangency represents a state of allocative efficiency in the economy.
Pareto Set
or Pareto Frontier
Set of all pareto optimal allocations
The entire set encompasses all these tangent points between the indifference curves of the two consumers
Contract Curve
Part of the Pareto Set where both consumers do at least as well as at the initial endowment.
Each point on the contract curve suggests a potential agreement point between the two consumers if they were to trade goods with each other starting from their initial endowment. It’s the “contract” part of the curve because these are the allocations that the two consumers might agree upon if they were to make a contract for trading the goods between them.
First Fundamental Theorem of Welfare
Any Walrasian or competitive equilibrium is Pareto efficient
No Lens Between Indifference Curves: There’s no “lens” (shaded area between the indifference curves of the two consumers) at the equilibrium, meaning there are no allocations that would make both consumers better off simultaneously. Each consumer is at their highest possible indifference curve given their budget constraints, implying they cannot improve their situation without harming the other.
Adam Smith: The theorem underpins the classical liberal economic theory proposed by Adam Smith, where he suggested that individuals pursuing their self-interest would, through the mechanism of the market, produce an outcome beneficial to society as a whole. In modern terms, this means that competitive markets tend to lead to resource allocations that are efficient.
Policy Intervention Justification: While the First Fundamental Theorem justifies the efficiency of free markets, it does not account for equity or fairness. As a result, policy interventions may still be justified on distributional grounds
Second Fundamental Theorem of Welfare
Any Pareto optimal allocation is supportable as an
equilibrium with transfers (fulfills distributional objectives!)
What does this mean?
Any Pareto optimal allocation can be achieved as a competitive (Walrasian) equilibrium provided that we redistribute wealth or endowments appropriately.
Suggests that while free markets can lead to efficient outcomes, they don’t inherently lead to equitable outcomes.
– relates to the allocation of resources and distributional equity.
Can be achieved through direct transfer of wealth or transfers of the actual goods, taxes, subsidies etc.
Non-Convexity
Non-Convexities:
In the context of consumer preferences, convexity means that a consumer always prefers average or mixed bundles of goods to extreme bundles. If preferences are non-convex, this means the consumer may have a “satiation point” or prefer extreme combinations of goods, which leads to indifference curves that are not bowed inward as typically depicted but could instead exhibit flat spots or even outward bulges.
Second Welfare Theorem and Non-Convexities:
The Second Fundamental Theorem of Welfare Economics states that any Pareto efficient allocation can be supported as a competitive equilibrium with the appropriate transfers. However, this theorem assumes that preferences are convex. When preferences are non-convex, as shown for consumer 1 in the illustration, the theorem doesn’t necessarily hold.
Non-convexities present a challenge to achieving a Pareto optimal allocation through market mechanisms because they can result in multiple, potentially inefficient equilibria or no equilibrium at all. This situation might require additional market design considerations or policy interventions to reach a desirable outcome.
