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Chapter 16
General Equilibrium
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 3
Two Interdependent Markets – Moving to General Equilibrium
ScenarioThe competitive markets of:
DVD rentalsMovie theater tickets
Changing prices in one market are likely to affect the other market
©2005 Pearson Education, Inc. Chapter 16 4
Two Interdependent Markets – Moving to General Equilibrium
ScenarioEquilibrium price of movies is $6.00Equilibrium price of DVD rentals are $3.00Government places a $1.00 tax on each
movie ticketNeed to look at effect of tax on
Market for DVDsFeedback effects in Movie market
©2005 Pearson Education, Inc. 5
Two Interdependent Markets – Movies and DVDs
DVDM
Price
Numberof Videos
Price
Number ofMovie Tickets
SMSV
$6.00
QMQV
$3.00
$6.35
Q’M
S*M
$1 tax on each movie ticket causes supply to
fall
D’V
Q’V
$3.50
General Equilibrium Analysis:Increase in movie ticket pricesincreases demand for videos.
©2005 Pearson Education, Inc. Chapter 16 6
Two Interdependent Markets – Movies and DVDs
Price
Numberof Videos
Price
Number ofMovie Tickets
DM
SM
$6.00
QM
$6.35
Q’M
S*M
The increase in the priceof videos increases the
demand for movies.
D’V
DV
SV
QV
$3.00
Q’V
$3.50
General Equilibrium Analysis:The Feedback effects continue.
D*M
$6.82
Q*MQ”M
$6.75
D’M
$3.58
Q*V
D*V
©2005 Pearson Education, Inc. Chapter 16 7
Two Interdependent Markets – Movies and DVDs
ObservationWithout considering the feedback effect with
general equilibrium, the impact of the tax would have been underestimated
This is an important consideration for policy makers.
©2005 Pearson Education, Inc. Chapter 16 8
Reaching General Equilibrium
Must be able to determine the equilibrium price of both movies and DVDs simultaneouslyWe 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
©2005 Pearson Education, Inc. Chapter 16 9
The Advantages of Trade
AssumptionsTwo consumers (countries)Two goodsZero transaction costsJames & Karen have a total of 10 units of
food and 6 units of clothing.
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 11
The Advantage of Trade
There is room for tradeJames values clothing more than KarenKaren values food more than James
Actual terms of trade are determined through bargaining
©2005 Pearson Education, Inc. Chapter 16 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.
©2005 Pearson Education, Inc. Chapter 16 13
The Edgeworth Box Diagram
A diagram showing all possible allocations of either two goods between two people is called an Edgeworth Box
©2005 Pearson Education, Inc. Chapter 16 14
The Edgeworth Box Diagram
Each point describes the market baskets of both consumersJames has 7 units of food and 1 unit of
clothing – point AKaren has 3 units of food and 5 units of
clothing – point A from different axis
©2005 Pearson Education, Inc. 15
Exchange in an Edgeworth Box
10F 0K
0J
6C
10F
6C
James’sClothing
Karen’sClothing
James’s Food
Karen’s Food
1C 5C
3F
7F
A
The initial allocation before trade is A: James has 7F and 1C & Karen
has 3F and 5C.
©2005 Pearson Education, Inc. Chapter 16 16
Exchange in an Edgeworth Box
10F 0K
0J
6C
10F
6C
James’sClothing
Karen’sClothing
James’s Food
Karen’s Food
1C 5C
3F
7F
A
The allocation after trade is B: James
has 6F and 2C & Karen has 4F and 4C.
4F
6F
+1C
-1F
2C 4CB
©2005 Pearson Education, Inc. Chapter 16 17
Efficient Allocations
A trade from A to B makes both Karen and James better off
If James’s and Karen’s MRS are the same at B the allocation is efficient.
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 19
A: UJ1 = UK
1,but the MRSis not equal.
All combinationsin the shaded
area arepreferred to A. Karen’s
Clothing
Karen’s Food
UK1
James’sClothing
James’s Food
UJ1
Efficiency in Exchange10F 0K
0J
6C
10F6C
Gains fromtrade
A
©2005 Pearson Education, Inc. Chapter 16 20
Efficiency in Exchange
Karen’sClothing
Karen’s Food
James’sClothing
James’s Food
10F 0K
0J
6C
10F6C
UK1
UJ1
A
Point B is on higher IC but
is not efficient
UJ2
UK2
B
At point C, MRSs are equal and
allocation is efficient
UK3
C
D is also a possible efficient
allocation depending on
bargaining
UJ3
D
©2005 Pearson Education, Inc. Chapter 16 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.
A
Karen’sClothing
Karen’s Food
UK1UK
2UK3
James’sClothing
James’s Food
UJ1
UJ2
UJ3
B
C
D
10F 0K
0J
6C
10F6C
©2005 Pearson Education, Inc. Chapter 16 22
Efficiency in Exchange
The Contract CurveTo 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
©2005 Pearson Education, Inc. Chapter 16 23
The Contract Curve
0J
James’sClothing
Karen’sClothing
0KKaren’s Food
James’s Food
E
F
G
ContractCurve
E, F, & G arePareto efficient .
©2005 Pearson Education, Inc. Chapter 16 24
Contract curve
All points of tangency between the indifference curves are efficient.MRS of individuals is the sameNo 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.
©2005 Pearson Education, Inc. Chapter 16 25
Consumer Equilibrium in a Competitive Market
We can show opportunities for trade for many consumersWhen 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 CKaren buys 2 food for 2 clothing: A to CBoth increase satisfaction
©2005 Pearson Education, Inc. Chapter 16 26
Consumer Equilibrium in a Competitive Market
Price Line
10F 0K
0J
6C
10F
6C
James’sClothing
Karen’sClothing
Karen’s Food
James’s Food
C
A
Begin at A:Each James buys 2C and sells 2Fmoving from Uj1 to Uj2, which is preferred (A to C).
Begin at A:Each Karen buys 2F and sells 2C moving fromUK1 to UK2, which is preferred (A to C).
P
P’
UJ2
UJ1
UK1UK
2
©2005 Pearson Education, Inc. Chapter 16 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 marketAlso called competitive equilibrium
©2005 Pearson Education, Inc. Chapter 16 28
Consumer Equilibrium in a Competitive Market
In a general equilibrium setting where all markets are perfectly competitive, we can show the same resultBest example of Adam Smith’s invisible handEconomy will automatically allocate all
resources efficiently without need for regulatory control
©2005 Pearson Education, Inc. Chapter 16 29
Consumer Equilibrium in a Competitive Market
Competitive equilibrium1. Because the indifference curves are tangent, all
MRSs are equal between consumers
2. Because each indifference curve is tangent to the price line, each person’s MRS is equal to the price ratio of the two goods
KFC
F
CJFC MRSP
PMRS
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 33
The Utility Possibilities Frontier
James’ Utility
Karen’s Utility
E
F
G
OK
L
OJ
H
OJ – James has zero utilityOK – Karen has zero utilityE, F, G – points on contract curveH – inefficient – can do better in shaded areaL - unobtainable
©2005 Pearson Education, Inc. Chapter 16 34
The Utility Possibilities Frontier
James’ Utility
Karen’s Utility
E
F
G
OK
OJ
H
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
©2005 Pearson Education, Inc. Chapter 16 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?
©2005 Pearson Education, Inc. Chapter 16 36
Four Views of Equity
EgalitarianAll members of society receive equal amount of goods
RawlsianMaximize the utility of the least-well-off person
UtilitarianMaximize the total utility of all members of society
Market - Oriented
The market outcome is the most equitable
©2005 Pearson Education, Inc. Chapter 16 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.TaxesPubic services
©2005 Pearson Education, Inc. Chapter 16 38
Efficiency in Production
We can extend to the efficient use of inputs used for production.
Assume:Two fixed inputs: capital and laborProduce same two goods: food and clothingMany consumers own inputs to production
and earn income from selling themIncome allocated between goods
©2005 Pearson Education, Inc. Chapter 16 39
Efficiency in Production
Using the Edgeworth box diagram, we can show efficient use of inputs in productionLabor on horizontal axisCapital on vertical axis50 hours of labor and 30 hours of capital
available
©2005 Pearson Education, Inc. 40
Production in an Edgeworth Box
50L 0C
0F
30K
50L
30K
Capital in Food Production
Capital in Clothing
Production
Labor in Food Production
Labor in Clothing Production
5K 25K
15L
35L
A
The initial allocation is A.Every combination of labor and capital used to produce
two goods is represented as point in box
©2005 Pearson Education, Inc. Chapter 16 41
Production in an Edgeworth Box
Can use production isoquants to show levels of output produced with each combination of inputs3 isoquants representing 50, 60 and 80 units
of food3 isoquants representing 10, 25 and30 units
of clothing
©2005 Pearson Education, Inc. 42
Production in an Edgeworth Box
50L 0C
0F
30K
50L
30K
Capital in Food Production
Capital in Clothing
Production
Labor in Food Production
Labor in Clothing Production
5K 25K
15L
35L
3 isoquants representing food production
3 isoquants representing clothing production
10C
60F
50F
25C
B
30C
80F
A
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. 44
Production in an Edgeworth Box
50L 0C
0F
30K
50L
30K
Capital in Food Production
Capital in Clothing
Production
Labor in Food Production
Labor in Clothing Production
5K 25K
15L
35L
Can move from A to B or C which increases
efficiency.
10C
60F
50F
25C
30C C
80FD
AB
Any place in shaded area will increase efficiency
from allocation A.
©2005 Pearson Education, Inc. Chapter 16 45
Production in an Edgeworth Box
Points B and C are efficient allocations and therefore lie on the production contract curveCurve showing all technically efficient
combinations of inputs.Curve connects the origins, OF and OC
All points on curve are tangencies between two isoquants
©2005 Pearson Education, Inc. 46
Production in an Edgeworth Box
50L 0C
0F
30K
50L
30K
Capital in Food Production
Capital in Clothing
Production
Labor in Food Production
Labor in Clothing Production
5K 25K
15L
35L
10C
60F
50F
25C
30C C
80FD
AB
Production Contract
Curve
©2005 Pearson Education, Inc. Chapter 16 47
Producer Equilibrium – Competitive Input Markets
If input markets are competitive, an efficient point will be achieved
In competitive input marketsWage rate, w, will be equal in all industriesRental rate of capital, r, will be equal in all
industries
©2005 Pearson Education, Inc. Chapter 16 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:
r
w
MP
MP
K
L
©2005 Pearson Education, Inc. Chapter 16 49
Producer Equilibrium – Competitive Input Markets
Ratio of marginal products is the same as the marginal rate of technical substitution of labor for capital:
LKK
L MRTSr
w
MP
MP
©2005 Pearson Education, Inc. Chapter 16 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
anotherThese also equal the ratio of the prices of
two inputsCompetitive equilibrium lies on the
production contract curve, and the competitive equilibrium is efficient in production
©2005 Pearson Education, Inc. Chapter 16 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
©2005 Pearson Education, Inc. Chapter 16 52
Production Possibilities Frontier
Clothing(units)
Food (units)
•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
OF
OC
D
C
B
A
©2005 Pearson Education, Inc. Chapter 16 53
Production Possibilities Frontier
PPF is downward slopingIn order to produce more of one good, must
give up producing some of the other good
PPF is concaveSlope is the MRTS which increases as the
level of production of food increases
©2005 Pearson Education, Inc. Chapter 16 54
Production Possibilities Frontier
Marginal rate of transformation (MRT) of food for clothing is the magnitude of the slope of the frontier at each pointHow much clothing must be given up to
produce one additional unit of foodAs we increase the production of food my
moving along the PPF, the MRT increases
©2005 Pearson Education, Inc. Chapter 16 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 lowTransferring some to food production where
MP are relatively highAs we do this, MP in food decreases and MP
in clothing increases
©2005 Pearson Education, Inc. Chapter 16 56
Production Possibilities Frontier
Clothing(units)
Food (units)
OF
OC
D MRT = 2
B MRT = 1
MRT < 1
MRT > 1
©2005 Pearson Education, Inc. Chapter 16 57
Marginal Rate of Transformation
Can also describe in terms of costsWhen producing at OF the MC of food is very low
and MC of clothing is very highWhen MRT is low, so is the ratio of the MC of
producing food to clothingSlope of PPF measures the MC of producing one
good relative to the MC of producing the other
C
F
MC
MCMRT
©2005 Pearson Education, Inc. Chapter 16 58
Output Efficiency
For efficiency, MRS = consumer’s WTP for additional food
by consuming less clothingMRT = cost of additional unit of food in terms
of producing less clothing
Efficiency means MRS = MRT
©2005 Pearson Education, Inc. Chapter 16 59
Output Efficiency
Clothing(units)
Food (units)
60
100
Indifference Curve
MRS = MRT
PPF
©2005 Pearson Education, Inc. Chapter 16 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
MRSPP
MCMCMRT
C
F
C
F
©2005 Pearson Education, Inc. Chapter 16 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 advantageA 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
©2005 Pearson Education, Inc. Chapter 16 62
The Gains from Free Trade
EX: Two countries producing two goodsHolland and ItalyCheese and WineHolland has comparative advantage in
cheese productionItaly as comparative advantage in wine
productionTrade is good for both countries
©2005 Pearson Education, Inc. Chapter 16 63
The Gains from Free Trade
Hours of Labor Required to Produce Cheese and Wine
Cheese (1 LB)
Wine
(1 GAL)
Holland 1 2
Italy 6 3
©2005 Pearson Education, Inc. Chapter 16 64
The Gains from Free Trade
When there is comparative advantage, free trade allows the country to consume outside their PPF
Before tradeProduces at A on indifference curve U1
where MRT and pre-trade price ratio is 2Holland would want to export 2 pounds of
cheese for 1 gallon of wine
©2005 Pearson Education, Inc. Chapter 16 65
The Gains from Free Trade
After tradeSuppose they choose to trade 1 gallon of
wine for 1 pound of cheeseHolland will produce at the point of tangency
on the 1/1 price line and PPF – point BConsumption will occur at D, on a higher
indifference curve U2 tangent to the trade price line
©2005 Pearson Education, Inc. Chapter 16 66
The Gains from Trade
Cheese (lbs)
Wine (gal)
U1
Pre-Trade Prices
U2
World Prices
CBB
WB
A
WD
DCD
•Trade allows Holland to consume outside PPF
Exports
Imports
©2005 Pearson Education, Inc. Chapter 16 67
Overview – Efficiency of Competitive Markets
1. Efficiency in Exchange MRSJ
FC = MRSKFC
MRSJFC = PF/PC = MRSK
FC
2. Efficiency in the use of inputs in production MRTSF
LK = MRTSCLK
MRTSFLK = w/r = MRTSC
LK
©2005 Pearson Education, Inc. Chapter 16 68
Overview – Efficiency of Competitive Markets
3. Efficiency in the output market MRTFC = MRSPC (for all consumers)
PF = MCF, PC = MCC resulting in
MRTFC = MCF/MCC = PF/PC; therefore
MRSFC = MRTFC
©2005 Pearson Education, Inc. Chapter 16 69
Why Markets Fail
Market PowerThose with market power choose the price
and quantityLess output is sold than in competitive
marketsInefficiency
©2005 Pearson Education, Inc. Chapter 16 70
Why Markets Fail
Incomplete InformationConsumers must have accurate information
about market prices or production quality for markets to operate efficiency
Lack of information can change supplySome markets may never develop
©2005 Pearson Education, Inc. Chapter 16 71
Why Markets Fail
ExternalitiesConsumption or production has indirect
effect on other consumption or production not reflected in market prices
©2005 Pearson Education, Inc. Chapter 16 72
Why Markets Fail
Public GoodsNonexclusive, 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 can’t get patent
Once it’s made pubic, others can duplicate it