Week 4 term 1

Question 1

What is the equation for competitive equilibirum?

Answer 1

Question 2

What is Competitive Equilibrium?

Answer 2

A state where the markets for commodities clear at a price vector p* and allocation x*

Also known as Walrasian Equilibrium
- each consumer maximizes utility given their budget constraint
- markets clear - total deman equals total supply
- consumers solve:

In this state, the allocation x* is such that all consumers’ preferences are satisfied given their budget sets.

Question 3

What is the Walras Law?

Answer 3

The sum of the aggregate excess demands is identically 0

This holds true for all possible prices, not just equilibrium prices.

Question 4

What does the budget set B(p) represent?

Answer 4

B(p) = {x ∈ R : px ≤ pω}

It indicates the set of all consumption bundles x that a consumer can afford given their wealth and the prices.

Question 5

What is the formula for consumer i’s wealth?

Answer 5

p.ω = p1iω1 + p2iω2

This represents the market value of the consumer’s endowments.

Question 6

In the Edgeworth Box, what does it mean if Person A is a net supplier of Good 1?

Answer 6

e < 0

This indicates that Person A has more of Good 1 than they demand.

Question 7

In the Edgeworth Box, what does it mean if Person B is a net demander of Good 2?

Answer 7

e > 0

This implies that Person B wants more of Good 2 than they currently have.

Question 8

What condition must be met for an equilibrium to occur?

Answer 8

Prices p1 and p2 must cause both markets for commodities 1 and 2 to clear

This means that the total demand equals total supply in both markets.

Question 9

What does it mean if the aggregate excess demand for Good 1 is less than zero?

Answer 9

p ↓

This indicates that the price of Good 1 will fall to reach equilibrium.

Question 10

Define Individual Utility Maximisation.

Answer 10

The process by which a consumer chooses a consumption bundle that maximizes their utility given their budget constraint

This involves comparing the marginal utility per price of goods.

Question 11

What is the implication of Walras’ Law regarding market equilibrium?

Answer 11

If one market is in equilibrium, then the other market must also be in equilibrium

This means excess demand in one market will lead to excess supply in another.

Question 12

Fill in the blank: A Walrasian (competitive) Equilibrium for a pure exchange economy is a price vector p* and an allocation x* such that for i = A, B, x*i ≿ x’i ∀ x ∈ B(p)’i.

Answer 12

[Competitive Equilibrium Definition]

Question 13

What does eA represent for consumer A?

Answer 13

A’s net demand (or excess demand) for good 1

It is calculated as eA = (x*A - ωA).

Question 14

What does eB represent for consumer B?

Answer 14

B’s net demand (or excess demand) for good 1

It is calculated as eB = (x*B - ωB).

Question 15

What happens to the budget constraint when the price changes?

Answer 15

The budget constraint will pivot about the endowment point and become less steep

This reflects changes in relative prices affecting the consumption choices.

Question 16

What is the condition for aggregate excess demand for Good 1 in the Edgeworth Box?

Answer 16

A1 + B1 = e + e < 0

This indicates that the overall demand for Good 1 is less than the supply.

Question 17

What is the condition for aggregate excess demand for Good 2 in the Edgeworth Box?

Answer 17

A2 + B2 = e + e > 0

This indicates that the overall demand for Good 2 is greater than the supply.

Question 18

What does the utility function u_i(x_i1, x_i2) = x_i1 * x_i2 represent?

Answer 18

The utility derived from consuming goods 1 and 2

This function illustrates the preferences of consumers A and B.

Question 19

What does Walras’ Law state in the context of competitive equilibrium?

Answer 19

Markets clear in equilibrium

This implies that the total demand equals total supply.

Question 20

What does the First Welfare Theorem state?

Answer 20

A competitive equilibrium is always Pareto efficient.
- gurantees that a competitve market will exhaust all gains from trade
- the contract curve and price lines instersect at equilibrium points

This means that resources are allocated in a way that no individual can be made better off without making someone else worse off.

Question 21

Does the First Welfare Theorem address equity or redistribution?

Answer 21

No

It only focuses on efficiency, not fairness in distribution.

Question 22

What assumption does the First Welfare Theorem make about consumer preferences?

Answer 22

Consumers only care about their own consumption

This assumption implies a lack of concern for others’ consumption.

Question 23

What is a necessary condition for a competitive market according to the First Welfare Theorem?

Answer 23

Consumers behave competitively

This assumption may not hold true in real-world scenarios.

Question 24

What is implied if an allocation x* is not Pareto efficient?

Answer 24

There exists another allocation x that is strictly preferred by at least one consumer

This indicates room for improvement in resource allocation.

Question 25

What does the Second Welfare Theorem state?

Answer 25

Any Pareto optimal allocation can be achieved as a competitive equilibrium ## Footnote This theorem allows for the implementation of efficiency through market mechanisms.

Question 26

Under what conditions can preferences lead to a Pareto efficient allocation?

Answer 26

Preferences must be well behaved and convex ## Footnote Convex preferences help ensure that consumers can reach efficient allocations.

Question 27

What can be said about allocations that cannot be achieved by competitive equilibrium?

Answer 27

They may exist under non-convex preferences ## Footnote Non-convex preferences can result in inefficient allocations.

Question 28

True or False: Redistribution of endowments can determine how much wealth consumers have.

Answer 28

True ## Footnote This is a key aspect of implementing the Second Welfare Theorem.

Question 29

What happens if both consumers have convex preferences?

Answer 29

A straight line can be drawn between their preferred bundles ## Footnote This line helps determine relative prices for equilibrium.

Question 30

Fill in the blank: The First Welfare Theorem guarantees that a competitive market will exhaust all ______.

Answer 30

gains from trade ## Footnote This reflects the efficiency of resource allocation in competitive markets.

Question 31

What does it mean for an allocation to be Pareto efficient?

Answer 31

It means no reallocation can make one individual better off without making another worse off ## Footnote This is a key concept in welfare economics.

Question 32

What is the significance of prices in the Second Welfare Theorem?

Answer 32

Prices indicate relative scarcity and can implement Pareto optimal allocations ## Footnote This facilitates market transactions based on consumer preferences.

Question 33

What are price lines in an exchnage economy?

Answer 33

- they represent all combinations of goods that a consumer can afford given initial endowment and relative price of goods. - slope of the budget line is the relative price - this line shows all affordable bundles - every line goes through the initial endowment point - each consumer can trade along that lin and selling at market prices - slope = -p1/p2