CHAPTER 30 EXCHANGE - PowerPoint PPT Presentation

1 / 29
About This Presentation
Title:

CHAPTER 30 EXCHANGE

Description:

CHAPTER 30 EXCHANGE Partial equilibrium analysis: The equilibrium conditions of ONE particular market, leaving other markets untreated. General equilibrium analysis ... – PowerPoint PPT presentation

Number of Views:105
Avg rating:3.0/5.0
Slides: 30
Provided by: hnu9
Category:

less

Transcript and Presenter's Notes

Title: CHAPTER 30 EXCHANGE


1
CHAPTER 30EXCHANGE
2
  • Partial equilibrium analysis The equilibrium
    conditions of ONE particular market, leaving
    other markets untreated.
  • General equilibrium analysis The equilibrium
    conditions of ALL markets, allowing interactions
    between different markets.

3
30.1 The Edgeworth Box
  • Two consumers A and B.
  • Two goods 1 and 2.
  • Initial endowment
  • Allocation
  • Feasible allocation total consumption does not
    exceed total endowment for both goods.

4
30.1 The Edgeworth Box
5
30.1 The Edgeworth Box
  • Each point in the Edgeworth box represents a
    feasible allocation.
  • From W to M
  • Person A trades units of good 1
    for units of good 2
  • Person B trades units of good 2
    for units of good 1.

6
30.2 Trade
7
30.2 Trade
  • Trade happens whenever both consumers are better
    off.
  • Starting from W, M is a possible outcome of the
    exchange economy because
  • Person A is strictly better off with
    than with
  • Person B is strictly better off with
    than with .

8
30.3 Pareto Efficient Allocations
  • An allocation is Pareto efficient whenever
  • There is no way to make everyone strictly better
    off
  • There is no way to make some strictly better off
    without making someone else worse off
  • All of the gains from trade have been exhausted
  • There are no (further) mutually advantageous
    trades to be made.

9
30.3 Pareto Efficient Allocations
10
30.3 Pareto Efficient Allocations
  • Pareto efficiency is given by the tangency of the
    indifference curves.
  • Contract curve the locus of all Pareto efficient
    allocations.
  • Any allocation off the contract curve is Pareto
    inefficient.

11
30.4 Market Trade
  • Gross demand Quantity demanded for a good by a
    particular consumer at the market price.
  • Excess demand The difference between the gross
    demand and the initial endowment of a good by a
    particular consumer.
  • Disequilibrium Excess demands by both consumers
    do not sum up to zero.

12
30.4 Market Trade
13
30.4 Market Trade
  • Competitive equilibrium A relative price
    and an allocation ,
    such that
  • The allocation matches the gross demands by both
    consumers, given the relative price and initial
    endowments
  • The allocation is feasible.

14
30.4 Market Trade
15
30.5 The Algebra of Equilibrium
  • Consumer As demands
  • Consumer Bs demands
  • The equilibrium condition
  • Re-arrangement

16
30.5 The Algebra of Equilibrium
  • Net demand
  • Aggregate excess demand
  • Another expression

17
30.6 Walras Law
  • Budget constraints
  • Re-arrange the terms
  • Adding up

18
30.6 Walras Law
  • Walras Law The value of aggregate excess demand
    is always zero.
  • Applications of the Walras law
  • implies
  • Market clearing for one good implies that of the
    other good
  • With k goods, we only need to find a set of
    prices where k-1 of the markets are cleared.

19
30.7 Relative Prices
  • Walras law implies k-1 independent equations for
    k unknown prices.
  • Only k-1 independent prices.
  • Numeraire prices the price which can be used to
    measure all other prices.
  • If we choose p1 as the numeraire price, then it
    is just like multiplying all prices by the
    constant t1/p1.

20
EXAMPLE An Algebraic Example of Equilibrium
  • The Cobb-Douglas utility function
  • The demand functions

21
EXAMPLE An Algebraic Example of Equilibrium
  • Income from endowments
  • Aggregate excess demand for good 1

22
EXAMPLE An Algebraic Example of Equilibrium
  • Equilibrium condition
  • Equilibrium price

23
30.8 The Existence of Equilibrium
  • The existence of a competitive equilibrium can be
    proved rigorously.
  • A formal proof is quite complicated and far
    beyond the scope of this course.

24
30.9 Equilibrium and Efficiency
  • Both indifference curves are tangent to the
    budget line at the equilibrium allocation.
  • The equilibrium allocation lies upon the contract
    curve.
  • The First Theorem of Welfare Economics Any
    competitive equilibrium is Pareto efficient.

25
EXAMPLE Monopoly in the Edgeworth Box
  • A regular monopolist

26
EXAMPLE Monopoly in the Edgeworth Box
  • First degree price discrimination

27
30.11 Efficiency and Equilibrium
  • Reverse engineering
  • Starting from any Pareto efficient allocation
  • Use the common tangent line as the budget line
  • Use any allocation on the budget line as the
    initial endowment.
  • The Second Theorem of Welfare Economics For
    convex preferences, any Pareto efficient
    allocation is a competitive equilibrium for some
    set of prices and some initial endowments.

28
30.11 Efficiency and Equilibrium
  • The Second Theorem of Welfare Economics

29
30.11 Efficiency and Equilibrium
  • A Pareto efficient allocation that is not a
    competitive equilibrium.
Write a Comment
User Comments (0)
About PowerShow.com