Transcript Introduction - National Tsing Hua University

Chapter 12
General Equilibrium
and Welfare
© 2006 Thomson Learning/South-Western
An Illustration of General
Equilibrium

Figure 12-1 shows the market for
tomatoes and three of the many other
market related to it:
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The market for tomato pickers.
The market for a related product --cucumbers.
The market for cucumber pickers.
The initial equilibrium is shown by the
darker demand and supply curves.
FIGURE 12-1: The Market for Tomatoes
and Several Related Markets
Price
S
P1
S
Wages
W1
D
D
Tomatoes
0 (a) Market for Tomatoes
Tomato pickers
0 (b) Market for Tomato Pickers
Wages
Price
S
S
P2
W2
D
0
3
Cucumbers
(c) Market for Cucumbers
D
0
Cucumber pickers
(d) Market for Cucumber Pickers
An Illustration of General
Equilibrium
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The initial set of equilibrium prices are:
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P1 for tomatoes.
W1 for tomato pickers.
P2 for cucumbers.
W2 for cucumber pickers.
Since the markets are in general
equilibrium, this will persist unless
something happens to change it.
Disturbing the Equilibrium
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Assume the government announces that
tomatoes cure the common cold, resulting
in an increase in demand.
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Initially, this would shift the demand curve for
tomatoes outward to D’.
The increase in tomatoes prices brought
about by the increase in demand stimulates
the demand for more tomato pickers which
shifts outward to D’.
Disturbing the Equilibrium
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The higher wages for tomato pickers
increases the costs for tomato growers,
shifting the tomato supply curve back to S’.
If the demand for cucumbers decreased
because of the increase in demand for
tomatoes.
This decreases the price of cucumbers and
leads to less produced.
The demand for cucumber pickers falls, and
their wages also decrease.
FIGURE 12-1: The Market for Tomatoes
and Several Related Markets
Price
S’
S
S
Wages
P1
D’
W1
D’
D
D
Tomatoes
0 (a) Market for Tomatoes
Tomato pickers
0 (b) Market for Tomato Pickers
Wages
Price
S
S
P2
W2
D
D’
0
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Cucumbers
(c) Market for Cucumbers
D
D’
0
Cucumber pickers
(d) Market for Cucumber Pickers
Reestablishing Equilibrium
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Eventually we would expect each market
to eventually reach a new equilibrium.
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The new equilibrium in Figure 12-1 is shown
by the lighter colored demand and supply
curves.
There is a rise in tomato prices (to P3), an
increase in tomato picker wages (to w3), a fall
in cucumber prices (to P4), and a fall in
cucumber picker wages (to w4).
FIGURE 12-1: The Market for Tomatoes
and Several Related Markets
Price
S’
Wages
S
S
P3
P1
D’
W3
W1
D’
D
D
Tomatoes
0 (a) Market for Tomatoes
Tomato pickers
0 (b) Market for Tomato Pickers
Wages
Price
S
S
P2
W2
P4
W4
D
D’
0
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Cucumbers
(c) Market for Cucumbers
D
D’
0
Cucumber pickers
(d) Market for Cucumber Pickers
An Efficient Mix of Outputs
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A technically efficient allocation of
resources in which the output combination
also reflects people’s preferences is an
economically efficient allocation of
resources.
Figure 12-2 illustrates the requirements for
economic efficiency in the mix of outputs.
A Simple General Equilibrium Model
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The best use of resources is achieved at
point E.
This point is the utility maximizing
choice where the person’s indifference
curve is tangent to the production
possibility frontier.
Point E is defined as an economically
efficient allocation of resources.
FIGURE 12-2: Efficiency of Output Mix
Quantity
of Y
per week
P
F
E
U3
G
U2
U1
0
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P’
Quantity of
X per week
Efficiency in Output Mix
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Profit maximizing firms will equate the rate
at which they can trade X for Y in
production to the equilibrium price ratio.
Utility maximizing people will equate their
MRS to the equilibrium price ratio.
Thus, RPT equals MRS, which, when
demand equals supply, meets the
requirements for economic efficiency.
Efficiency of Perfect Competition
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With an arbitrary initial price ratio, in
Figure 12-3, profit maximizing firms will
produce the output combination X1, Y1.
Societies’ budget constraint, CC, must go
through this point since the value of
income must equal the value of output.
FIGURE 12-3: How Perfectly Competitive
Prices Bring about Efficiency
Quantity
of Y
per week
C
P
Initial prices
Y1
Y*
Y’1
U3
C
U2
0
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X1
X*
P’ X’1
Quantity of
X per week
A Graphic Demonstration
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On the budget constraint, CC, individuals
will demand X’1, Y’1.
There is an excess demand for good X1
and an excess supply of good Y1.
Firms will produce more X and less Y.
FIGURE 12-3: How Perfectly Competitive
Prices Bring about Efficiency
Quantity
of Y
per week
Efficient prices
C*
C
P
Initial prices
Y1
Y*
E
Y’1
U3
C
U2
C*
0
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X1
X*
P’ X’1
Quantity of
X per week
A Graphic Demonstration
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The market will cause prices to move toward
their equilibrium levels P*X and P*Y.
People will respond to the changes in prices by
substituting Y for X in their consumption choices.
These action will eliminate the excess demand
for X and the excess supply for Y.
Equilibrium is reached at X*, Y* with equilibrium
prices P*X and P*Y.
A Graphic Demonstration
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At this price ratio, supply and demand are
equilibrated for both goods.
Profit maximizing firms will produce X* and Y*.
With the income generated, individuals will
maximize utility by choosing X* and Y*.
Competitive market have generated an
efficient allocation of resources.
Why Markets Fail to Achieve
Economic Efficiency
Imperfect competition
 Externalities
 Public goods
 Imperfect information
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Imperfect Competition
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Imperfect competition is a market
situation in which buyers or sellers have
some influence on the prices of goods or
services.
In this case, the firm is not a price taker so
marginal revenue does not equal price.
Relative prices do not reflect relative
marginal costs, and inefficiency can result
(for example, monopoly dead-weight loss).
Externalities
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Externalities represent additional costs-those that arise from the external damage.
The firm, however, only responds to
private input costs, it disregards the social
costs of pollution.
This results in a gap between market price
and social marginal cost, which leads to a
misallocation of resources.
Public Goods
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Price cannot equal marginal cost (which is
zero), since the fixed cost of providing the
good would not be covered.
The incentive is for people to refuse to pay
for the good hoping others will purchase,
and thus provide the good.
This causes society to not allocate enough
resources to public goods.
Imperfect Information
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It has been assumed that economic actors
are fully informed, especially about
equilibrium market prices.
Without this information, the “invisible hand”
results do not hold.
Without perfect information, a consumer
would have problems (costs) finding quality
and the prices charged by different firms.
Efficiency and Equity
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Equity is the fairness of the distribution of
goods or utility.
A primary problem with this concept is
developing an accepted definition of “fair”
or “unfair” allocations of resources.
Opinions vary from, an allocation is fair if
no laws are broken in obtaining it to a fair
allocation requires all people share
equally.
The Edgeworth Box Diagram
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The Edgeworth box diagram is a graphic
device for illustrating all of the possible
allocations of two goods (or two inputs)
that are in fixed supply.
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It can be used to show how the production
possibility frontier is constructed.
It can also be adapted to illustrate voluntary
exchange between two individuals.
FIGURE 12-4: Edgeworth Box Diagram
OJ
Total Y
OS
Total X
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The Edgeworth Box Diagram for
Exchange
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For consumer Smith, quantities of X are
measured along the horizontal axis rightward
from her axis OS, and quantities of Y are
shown along the vertical axis above OS.
Consumption for the other consumer, Jones, is
shown starting from the origin OJ.
At point E, for example, Smith gets XES, YES
and Jones gets XEJ, YEJ.
FIGURE 12-4: Edgeworth Box Diagram
E
XJ
E
Total Y
YJ
E
E
YS
OS
E
XS
Total X
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OJ
Mutually Beneficial Trades
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All possible allocations of the goods
between Smith and Jones are shown
within the box.
To identify those which provide mutually
beneficial trades, indifference curves
representing the preferences of Smith and
Jones are shown in Figure 12-5.
Mutually Beneficial Trades
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Smith’s indifference curve map is drawn
with origin OS.
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Jones’s indifference curve map is drawn
with origin OJ.
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Movements in the northeasterly direction
represent higher levels of utility for Smith.
Movements in a southwesterly direction
represent higher levels of utility for Jones.
FIGURE 12-5: Edgeworth Box diagram of
Pareto Efficiency in Exchange
Jones’s X
OJ
U1J
Jones’s Y
U2J
M4
US4
3
Total Y
UJ
M3
4
UJ
3
M2
F
US
2
US
M1
1
E
Smith’s Y
OS
Total X
Smith’s X
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US
Mutually Beneficial Trades
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Any point for which the MRS for Smith is
unequal to that for Jones represents an
allocation where mutually beneficial trades
can take place.
Such a point, E, is shown where the
indifference curves intersect.
Any point inside the oval-shaped area
represent mutually beneficial trades.
Efficiency in Exchange
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When the marginal rates of substitution
are equal, such as points M1 through M4,
mutually beneficial trades are no longer
possible.
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Movements away from these tangency positions
result in at least one person being made worse off.
The movement from M2 to E, for example, makes
Smith worse off and Jones no better off.
Contract Curve
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The contract curve is the set of efficient
allocations of the existing goods in an
exchange situation. Points off that curve
are necessarily inefficient, since
individuals can be made unambiguously
better-off by moving to the curve.
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In Figure 12-5, this curve is the set of points,
such as M2, on the line connecting OS to OJ.
Contract Curve
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A movement to the curve from off the
curve represents mutually beneficial
trades, but a movement along the curve
does not since one of the parties is always
worse off.
If the contract curve is interior to the
Edgeworth box, the individuals’ MRS will
be equal along the curve.
Efficiency and Equity
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Suppose, for example, that everyone
agreed that the only fair allocation is one
of equal utilities.
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Point E in Figure 12-6 might be such a point.
Assume point A is the initial
endowments; the initial holdings of good
from which trading begins.
FIGURE 12-6: Voluntary Transactions
May Not Result in Equitable Allocations
Jones’s X OJ
Jones’s Y
1
UJ
M4
Total Y
U2J
U3J
U4S
M3
4
E
UJ
U3S
M2
A
M1
Smith’s Y
OS
Smith’s X
38
1
US
Total X
U2S
Efficiency and Equity
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Point E lies outside of the region on the
contract curve, between M2 and M3, which
is mutually preferable to point A.
Smith would not voluntarily agree to point
E since she would be made worse off.
With unbalanced initial endowment, a
equal allocation is not possible through
mutually beneficial trade.