General Equilibrium

1
Chapter 16

• General Equilibrium

2
General Equilibrium Analysis

• To study how markets interrelate, we can use
  general equilibrium analysis
• The feedback effect is the price or quantity
  adjustment in one market caused by price and
  quantity adjustments in related markets

3
Two Interdependent Markets Moving to General
Equilibrium

• Scenario
• The competitive markets of
• DVD rentals
• Movie theater tickets
• Changing prices in one market are likely to
  affect the other market

4
Two Interdependent Markets Moving to General
Equilibrium

• Scenario
• Equilibrium price of movies is 6.00
• Equilibrium price of DVD rentals are 3.00
• Government places a 1.00 tax on each movie
  ticket
• Need to look at effect of tax on
• Market for DVDs
• Feedback effects in Movie market

5
Two Interdependent Markets Movies and DVDs
1 tax on each movie ticket causes supply to fall
General Equilibrium Analysis Increase in movie
ticket prices increases demand for videos.
Price
Price
Number of Videos
Number of Movie Tickets
6
Two Interdependent Markets Movies and DVDs
The increase in the price of videos increases the
demand for movies.
General Equilibrium Analysis The Feedback
effects continue.
Price
Price
Number of Videos
7
Two Interdependent Markets Movies and DVDs

• Observation
• Without considering the feedback effect with
  general equilibrium, the impact of the tax would
  have been underestimated
• This is an important consideration for policy
  makers.

8
Reaching General Equilibrium

• Must be able to determine the equilibrium price
  of both movies and DVDs simultaneously
• We must simultaneously find two prices that
  equate quantity demanded and quantity supplied in
  all related markets
• This requires finding the solution to four
  equations demand and supply for DVDs and Movies

9
The Advantages of Trade

• Assumptions
• Two consumers (countries)
• Two goods
• Zero transaction costs
• James Karen have a total of 10 units of food
  and 6 units of clothing.

10
The Advantage of Trade
Individual Initial Allocation Trade Final Allocation
James 7F, 1C -1F, 1C 6F, 2C
Karen 3F, 5C 1F, -1C 4F, 4C

11
The Advantage of Trade

• There is room for trade
• James values clothing more than Karen
• Karen values food more than James
• Actual terms of trade are determined through
  bargaining

12
The Advantage of Trade

• From this analysis we obtain an important result
• An allocation of goods is efficient only if the
  goods are distributed so that the marginal rate
  of substitution between any pair of goods is the
  same for all consumers.

13
The Edgeworth Box Diagram

• A diagram showing all possible allocations of
  either two goods between two people is called an
  Edgeworth Box

14
The Edgeworth Box Diagram

• Each point describes the market baskets of both
  consumers
• James has 7 units of food and 1 unit of clothing
  point A
• Karen has 3 units of food and 5 units of clothing
  point A from different axis

15
Exchange in an Edgeworth Box
10F
0K
6C
The initial allocation before trade is A James
has 7F and 1C Karen has 3F and 5C.
6C
0J
10F
16
Exchange in an Edgeworth Box
The allocation after trade is B James has 6F
and 2C Karen has 4F and 4C.
1C
-1F
17
Efficient Allocations

• A trade from A to B makes both Karen and James
  better off
• If Jamess and Karens MRS are the same at B the
  allocation is efficient.

18
Efficient Allocations

• We can see both parties are better off at point B
  since they both end up on a higher indifference
  curve
• Although a trade might make both parties better
  off, the new allocation is not necessarily
  efficient

19
Efficiency in Exchange
10F
0K
6C
A UJ1 UK1, but the MRS is not equal. All
combinations in the shaded area are preferred to
A.
6C
0J
10F
20
Efficiency in Exchange
10F
0K
6C
D is also a possible efficient allocation
depending on bargaining
At point C, MRSs are equal and allocation is
efficient
Point B is on higher IC but is not efficient
6C
0J
10F
21
Efficiency in Exchange

• Any move outside the shaded area will make one
  person worse off (closer to their origin).
• B is a mutually beneficial trade--higher
  indifference curve for each person.
• Trade may be beneficial but not efficient.
• MRS is equal when indifference curves are tangent
  and the allocation is efficient.

22
Efficiency in Exchange

• The Contract Curve
• To find all possible efficient allocations of
  food and clothing between Karen and James, we
  would look for all points of tangency between
  each of their indifference curves.
• The contract curve shows all the efficient
  allocations of goods between two consumers, or of
  two inputs between two production functions

23
The Contract Curve
Karens Food
0K
E, F, G are Pareto efficient .
Jamess Clothing
Karens Clothing
0J
Jamess Food
24
Contract curve

• All points of tangency between the indifference
  curves are efficient.
• MRS of individuals is the same
• No more room for trade
• The contract curve shows all allocations that are
  Pareto efficient.
• Pareto efficient allocation occurs when further
  trade will make someone worse off.

25
Consumer Equilibrium in a Competitive Market

• We can show opportunities for trade for many
  consumers
• When prices of food and clothing are equal, we
  can show the price line, PP with a slope of 1
• James buys 2 clothing for 2 food A to C
• Karen buys 2 food for 2 clothing A to C
• Both increase satisfaction

26
Consumer Equilibrium in a Competitive Market
10F
0K
Karens Food
6C
Begin at A Each James buys 2C and sells
2F moving from Uj1 to Uj2, which is preferred (A
to C).
Begin at A Each Karen buys 2F and sells 2C
moving from UK1 to UK2, which is preferred (A to
C).
Karens Clothing
Jamess Clothing
6C
0J
10F
Jamess Food
27
Consumer Equilibrium in a Competitive Market

• The amount of clothing that Karen wanted to sell
  is equal to the amount of clothing that James
  wanted to buy
• An equilibrium is a set of prices at which the
  quantity demanded equals the quantity supplied in
  every market
• Also called competitive equilibrium

28
Consumer Equilibrium in a Competitive Market

• In a general equilibrium setting where all
  markets are perfectly competitive, we can show
  the same result
• Best example of Adam Smiths invisible hand
• Economy will automatically allocate all resources
  efficiently without need for regulatory control

29
Consumer Equilibrium in a Competitive Market

• Competitive equilibrium
• Because the indifference curves are tangent, all
  MRSs are equal between consumers
• Because each indifference curve is tangent to the
  price line, each persons MRS is equal to the
  price ratio of the two goods

30
Consumer Equilibrium in a Competitive Market

• Difficult for efficient allocation with many
  consumer and producers unless all markets are
  perfectly competitive
• Efficient outcomes can also be achieved by
  centralized system

31
Equity and Efficiency

• Although there are many efficient allocations,
  some may be fairer than others
• The difficult question is what is the most
  equitable allocation?
• There is no reason to believe that efficient
  allocation from competitive markets will give an
  equitable allocation

32
The Utility Possibilities Frontier

• From the Edgeworth box we showed a two person
  exchange
• The utility possibilities frontier represents all
  allocations that are efficient in terms of the
  utility levels of the two individuals

33
The Utility Possibilities Frontier
OJ James has zero utility OK Karen has zero
utility E, F, G points on contract curve H
inefficient can do better in shaded area L -
unobtainable
Karens Utility
James Utility
34
The Utility Possibilities Frontier

• Are all efficient points equitable?
• Efficient points E or F make both persons better
  off without making one worse off from H
• If only possible points are H and G, can argue
  that one is more equitable to James and one to
  Karen

Karens Utility
James Utility
35
The Utility Possibilities Frontier

• From previous example, we can see that an
  inefficient allocation might be more equitable
  than an efficient one.
• But how do we define an equitable allocation?

36
Four Views of Equity
Egalitarian All members of society receive equal amount of goods
Rawlsian Maximize the utility of the least-well-off person
Utilitarian Maximize the total utility of all members of society
Market - Oriented The market outcome is the most equitable
37
Equity and Perfect Competition

• A competitive equilibrium can occur at any point
  on the contract curve depending on the initial
  allocation.
• Since not all competitive equilibriums are
  equitable, we rely on the government to help
  reach equity by redistributing income.
• Taxes
• Pubic services

38
Efficiency in Production

• We can extend to the efficient use of inputs used
  for production.
• Assume
• Two fixed inputs capital and labor
• Produce same two goods food and clothing
• Many consumers own inputs to production and earn
  income from selling them
• Income allocated between goods

39
Efficiency in Production

• Using the Edgeworth box diagram, we can show
  efficient use of inputs in production
• Labor on horizontal axis
• Capital on vertical axis
• 50 hours of labor and 30 hours of capital
  available

40
Production in an Edgeworth Box
50L
0C
30K
The initial allocation is A. Every combination of
labor and capital used to produce two goods is
represented as point in box
30K
0F
50L
41
Production in an Edgeworth Box

• Can use production isoquants to show levels of
  output produced with each combination of inputs
• 3 isoquants representing 50, 60 and 80 units of
  food
• 3 isoquants representing 10, 25 and30 units of
  clothing

42
Production in an Edgeworth Box
50L
15L
0C
30K
3 isoquants representing food production
3 isoquants representing clothing production
5K
25K
30K
0F
50L
35L
43
Production in an Edgeworth Box

• To find efficient production, we must find
  different combinations of inputs used to produce
  the two outputs
• An allocation of inputs is technically efficient
  if the output of one good cannot be increased
  without decreasing the output of another goods

44
Production in an Edgeworth Box
50L
15L
0C
30K
Can move from A to B or C which increases
efficiency.
Any place in shaded area will increase efficiency
from allocation A.
5K
25K
30K
0F
50L
35L
45
Production in an Edgeworth Box

• Points B and C are efficient allocations and
  therefore lie on the production contract curve
• Curve showing all technically efficient
  combinations of inputs.
• Curve connects the origins, OF and OC
• All points on curve are tangencies between two
  isoquants

46
Production in an Edgeworth Box
50L
15L
0C
30K
Production Contract Curve
5K
25K
30K
0F
50L
35L
47
Producer Equilibrium Competitive Input Markets

• If input markets are competitive, an efficient
  point will be achieved
• In competitive input markets
• Wage rate, w, will be equal in all industries
• Rental rate of capital, r, will be equal in all
  industries

48
Producer Equilibrium Competitive Input Markets

• If producers minimize costs, they will choose
  inputs to the point where the ratio of the
  marginal products of the two inputs is equal to
  the ratio of input prices

49
Producer Equilibrium Competitive Input Markets

• Ratio of marginal products is the same as the
  marginal rate of technical substitution of labor
  for capital

50
Producer Equilibrium Competitive Input Markets

• The MRTS is the slope of the isoquant, so
  competitive equilibrium exists only if
• Slopes of the isoquants are equal to one another
• These also equal the ratio of the prices of two
  inputs
• Competitive equilibrium lies on the production
  contract curve, and the competitive equilibrium
  is efficient in production

51
Production Possibilities Frontier

• PPF shows the various combinations of two goods
  that can be produced with fixed quantities of
  inputs.
• Frontier is derived from the production contract
  curve
• Points on PPF show efficiently produced levels of
  both goods

52
Production Possibilities Frontier

• Point A is inefficient
• Points B, C and D are efficient
• All points in triangle ABC completely utilize
  capital and labor but distortion in labor market
  leads to inefficient use

Clothing(units)
OF
B
C
A
D
OC
Food (units)
53
Production Possibilities Frontier

• PPF is downward sloping
• In order to produce more of one good, must give
  up producing some of the other good
• PPF is concave
• Slope is the MRTS which increases as the level of
  production of food increases

54
Production Possibilities Frontier

• Marginal rate of transformation (MRT) of food for
  clothing is the magnitude of the slope of the
  frontier at each point
• How much clothing must be given up to produce one
  additional unit of food
• As we increase the production of food my moving
  along the PPF, the MRT increases

55
Marginal Rate of Transformation

• The productivity of labor and capital differs
  depending on whether the inputs are used to
  produce more food or clothing.
• Starting where only clothing is produced, MP of
  labor and capital are relatively low
• Transferring some to food production where MP are
  relatively high
• As we do this, MP in food decreases and MP in
  clothing increases

56
Production Possibilities Frontier
Clothing(units)
OF
OC
Food (units)
57
Marginal Rate of Transformation

• Can also describe in terms of costs
• When producing at OF the MC of food is very low
  and MC of clothing is very high
• When MRT is low, so is the ratio of the MC of
  producing food to clothing
• Slope of PPF measures the MC of producing one
  good relative to the MC of producing the other

58
Output Efficiency

• For efficiency,
• MRS consumers WTP for additional food by
  consuming less clothing
• MRT cost of additional unit of food in terms of
  producing less clothing
• Efficiency means MRS MRT

59
Output Efficiency
Clothing(units)
60
Food (units)
100
60
Efficiency in Output Markets

• For perfectly competitive markets, all consumers
  allocate their budgets so their MRS between two
  good are equal to the ratio of prices
• Profit maximizing firms produce output to the
  point where price is equal to MC
• MRT is equal to the MRS

61
The Gains from Free Trade

• We have showed gains from trade in an Edgeworth
  box, but what about gains from trade with two
  countries where one has the comparative advantage
• A country has a comparative advantage over
  another country in the production of a good if
  the first country can produce the good at a lower
  opportunity cost than the other country

62
The Gains from Free Trade

• EX Two countries producing two goods
• Holland and Italy
• Cheese and Wine
• Holland has comparative advantage in cheese
  production
• Italy as comparative advantage in wine production
• Trade is good for both countries

63
The Gains from Free Trade
Hours of Labor Required to Produce Cheese and Wine Hours of Labor Required to Produce Cheese and Wine Hours of Labor Required to Produce Cheese and Wine
Cheese (1 LB) Wine (1 GAL)
Holland 1 2
Italy 6 3
64
The Gains from Free Trade

• When there is comparative advantage, free trade
  allows the country to consume outside their PPF
• Before trade
• Produces at A on indifference curve U1 where MRT
  and pre-trade price ratio is 2
• Holland would want to export 2 pounds of cheese
  for 1 gallon of wine

65
The Gains from Free Trade

• After trade
• Suppose they choose to trade 1 gallon of wine for
  1 pound of cheese
• Holland will produce at the point of tangency on
  the 1/1 price line and PPF point B
• Consumption will occur at D, on a higher
  indifference curve U2 tangent to the trade price
  line

66
The Gains from Trade

• Trade allows Holland to consume outside PPF

Cheese (lbs)
Wine (gal)
67
Overview Efficiency of Competitive Markets

• Efficiency in Exchange
• MRSJFC MRSKFC
• MRSJFC PF/PC MRSKFC
• Efficiency in the use of inputs in production
• MRTSFLK MRTSCLK
• MRTSFLK w/r MRTSCLK

68
Overview Efficiency of Competitive Markets

• Efficiency in the output market
• MRTFC MRSPC (for all consumers)
• PF MCF, PC MCC resulting in
• MRTFC MCF/MCC PF/PC therefore
• MRSFC MRTFC

69
Why Markets Fail

• Market Power
• Those with market power choose the price and
  quantity
• Less output is sold than in competitive markets
• Inefficiency

70
Why Markets Fail

• Incomplete Information
• Consumers must have accurate information about
  market prices or production quality for markets
  to operate efficiency
• Lack of information can change supply
• Some markets may never develop

71
Why Markets Fail

• Externalities
• Consumption or production has indirect effect on
  other consumption or production not reflected in
  market prices

72
Why Markets Fail

• Public Goods
• Nonexclusive, nonrival good that can be made
  available cheaply but which, once available, is
  difficult to prevent others from consuming
• Company thinking about researching a new
  technology if cant get patent
• Once its made pubic, others can duplicate it