Chapter 16
General Equilibrium Theory
16.1 General Equilibrium Analysis: Two
Markets
16.2 General Equilibrium Analysis: Many
Markets
16.3 General Equilibrium Analysis:
Comparative Statics
16.4 The Efficiency of Competitive Markets
16.5 Gains from Free Trade
1
16.1 Partial vs. General Equilibrium
Definition: General Equilibrium analysis
is the study of how equilibrium is
determined in all markets simultaneously
(e.g. product markets and labor markets).
Definition:
Partial Equilibrium analysis
is the study of how equilibrium is
determined in only a single market (e.g. a
single product market).
2
Chapter Sixteen
16.1 GE: Two Markets
In two RELATED markets, the outcomes in
one market are influence by the outcomes
in the other market
ie: CD’s and music downloads
ie: Health food and gym memberships
Original equilibrium is calculated similar to a
BETRAND MODEL WITH
DIFFERENTIATED PRODUCTS:
3
GE: Two Markets
1) Find Reaction Functions
(S=D in each market)
2) Use reaction functions to solve for P’s
3) Use P’s to solve for Q`s
4) Summarize
4
Chapter Thirteen
GE: Two Markets
Q1D = 12 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p1
Q2s = 1 + p2
1) Find Reaction Functions
Market 1 equilibrium:
Q1D = Q1s
12 – 3p1 + p2 = 2 + p1
p1 = 10/4 + p2/4
Market 2 equilibrium:
Q2D = Q2s
4 – 2p2 + p1 = 1 + p2
p2 = 1 + p1/3
5
GE: Two Markets
Q1D = 12 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p 1
Q2s = 1 + p2
p1 = 10/4 + p2/4
p2 = 1 + p1/3
2) Find Prices
p1 = 10/4 + p2/4
p1 = 10/4 + [1 + p1/3 ]/4
p1 = 11/4 + p1/12
(11/12)p1 = 11/4
p1 = 3
p2 = 1 + p1/3
p2 = 1 + 3/3
p2 = 2
6
GE: Two Markets
Q1D = 12 – 3p1 + p2
Q2D = 4 – 2p2 + p1
p1 = 3
p2 = 2
Q1s = 2 + p 1
Q2s = 1 + p2
p1 = 10/4 + p2/4
p2 = 1 + p1/3
3) Find Quantities
Q1* = 2 + p1
Q1* = 2 + 3
Q1* = 5
Q2* = 1 + p2
Q2* = 1 + 2
Q2* = 3
7
GE: Two Markets
Q1D = 12 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p 1
Q2s = 1 + p2
p1 = 3 p2 = 2
Q1* = 5 Q2* = 3
p1 = 10/4 + p2/4
p2 = 1 + p1/3
In general equilibrium, market 1 sells
5 goods for $3 each, and market 2
sells 3 goods for $2 each.
8
Equilibrium in Two Markets
P2
P2 = Q2s - 1
Market 2
2
e2
•
3
P2 = 4 + P1/2 - Q2D/2
Q2
9
Equilibrium in Two Markets
P1
Market 1
P1 = Q1s - 2
e1
3
•
P1 = 4 + P2/3 – Q1D/3
5
Q1
10
Shifts in Two Markets
If either market faces a shift in demand or
supply, the ENTIRE PROCESS must be
redone:
Suppose an exogenous shock increases
demand in market 1 to:
Q1D = 22 – 3p1 + p2
What is the new general equilibrium?
11
GE: Two Markets Shifts
Q1D = 22 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p1
Q2s = 1 + p2
1) Find Reaction Functions
Market 1 equilibrium:
Q1D = Q1s
22 – 3p1 + p2 = 2 + p1
p1 = 5 + p2/4
Market 2 equilibrium:
Q2D = Q2s
4 – 2p2 + p1 = 1 + p2
p2 = 1 + p1/3
12
GE: Two Markets Shifts
Q1D = 22 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p 1
Q2s = 1 + p2
p1 = 5 + p2/4
p2 = 1 + p1/3
2) Find Prices
p1 = 5 + p2/4
p1 = 5 + [1 + p1/3 ] /4
p1 = 5.25 + p1/12
(11/12)p1 = 5.25
p1 = 5.73
p2 = 1 + p1/3
p2 = 1 + 5.73 /3
p2 = 2.91
13
GE: Two Markets Shifts
Q1D = 22 – 3p1 + p2
Q1s = 2 + p 1
Q2D = 4 – 2p2 + p1
Q2s = 1 + p2
p1 = 5.73
p2 = 2.91
p1 = 5 + p2/4
p2 = 1 + p1/3
3) Find Quantities
Q1* = 2 + p1
Q1* = 2 + 5.73
Q1* = 7.73
Q2* = 1 + p2
Q2* = 1 + 2.91
Q2* = 3.91
14
GE: Two Markets Shifts
Q1D = 22 – 3p1 + p2
Q1s = 2 + p 1
Q2D = 4 – 2p2 + p1
Q2s = 1 + p2
p1 = 5.73
p2 = 2.91
Q1* = 7.73
Q2* = 3.91
p1 = 5 + p2/4
p2 = 1 + p1/3
After the shift in market 1’s demand, market
1 sells 7.73 goods for $5.73 each, and
market 2 sells 2.91 goods for $3.91 each.
Note: The following graphs show one shift, where there could be a
series of shrinking shifts as markets adjust.
15
Shifts in Two Markets
P1
Market 1
P1 = Q1s - 2
5.73
3
•
2
5
P2‘= 7.33 + P1/2 - Q2D/2
P1 = 4 + P2/3 – Q1D/3
7.73
Q1
16
Shifts in Two Markets
P2
P2 = Q2s - 1
Market 2
3.91
2
•
2.91 3
P2 = 4 + P1/2 - Q2D/2
Q2
17
In Depth Shifts in Two Markets
1) Coffee supply down =>Coffee price up…..
2) Tea demand up=>Tea price up…..
3) Coffee demand up=>Coffee price up….. 18
16.2 Equilibrium in Many Markets
Consider an
economy with:
1) 2 goods –
energy
and food
2) 2 input
services –
labor and
capital
19
Chapter Sixteen
16.2 Equilibrium in 4 Markets
20
Chapter Sixteen
16.2 GE: Many Markets
To solve a general equilibrium in many
markets, systems of equations are solved.
Example:
SupplyGood A = DemandGood A
SupplyGood B = DemandGood B
SupplyInput A = DemandInput A
SupplyInput B = DemandInput B
21
16.3 Comparative Statics
Once we have calculated a General
Equilibrium, we can calculate the effect of
a change (ie: tax or policy change) on ALL
related markets
Often, the end results are not as ideal as
politicians would claim…
22
Fast Food and Healthy Food
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
QFs = pF
QHs = 10 + pH
1) Find Reaction Functions
Fast Food equilibrium:
QFD = QFs
20 –3pF + pH = pF
pF = 5 + pH/4
Health Food equilibrium:
QHD = QHs
40 – pH + 2pF = 10 + pH
pH = 15 + pF
23
Fast Food and Healthy Food
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
QFs = pF
QHs = 10 + pH
pF = 5 + pH/4
pH = 15 + pF
2) Find Prices
pF = 5 + pH/4
pF = 5 + (15 + pF )/4
pF = 8.75+ pF/4
pF = $11.67
pH = 15 + pF
pH = 15 + $11.67
pH = $26.67
24
Fast Food and Healthy Food
QFD = 20 –3pF + pH
QFs = pF
QHD = 40 – pH + 2pF
QHs = 10 + pH
pF = $11.67
pH = $26.67
pF = 5 + pH/4
pH = 15 + pF
3) Find Quantities
QF* = pF
QF* = 11.67
QH* = 10 + pH
QH* = 10 + $26.67
QH* = 36.67
25
Fast Food and Healthy Food
QFD = 20 –3pF + pH
QFs = pF
QHD = 40 – pH + 2pF
QHs = 10 + pH
pF = $11.67
pH = $26.67
QF* = 11.67
QH* = 36.67
pF = 5 + pH/4
pH = 15 + pF
In general equilibrium:
11.67 people buy fast food for $11.67,
and
36.67 people buy healthy food for $26.67.
26
Comparative Statics - Tax
PF
PF = QF+2
PF = QF
Assume a $2 tax imposed
on sellers of fast food.
2
QF
27
Comparative Statics - Tax
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
QFs = pF-2
QHs = 10 + pH
1) Find Reaction Functions
Fast Food equilibrium:
QFD = QFs
20 –3pF + pH = pF-2
pF = 5.5 + pH/4
Health Food equilibrium:
QHD = QHs
40 – pH + 2pF = 10 + pH
pH = 15 + pF
28
Comparative Statics - Tax
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
QFs = pF-2
QHs = 10 + pH
pF = 5.5 + pH/4
pH = 15 + pF
2) Find Prices
pF = 5.5 + pH/4
pF = 5.5 + (15 + pF )/4
pF = 9.25+ pF/4
pF = $12.33
pH = 15 + pF
pH = 15 + $12.33
pH = $27.33
29
Comparative Statics - Tax
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
pF = $12.33
QFs = pF-2
QHs = 10 + pH
pH = $27.33
pF = 5.5 + pH/4
pH = 15 + pF
3) Find Quantities
QF* = pF -2
QF* = 12.33-2
QF* = 10.33
QH* = 10 + pH
QH* = 10 + $27.33
QH* = 37.33
30
Comparative Statics - Tax
QFD = 20 –3pF + pH
QHD = 40 – pH + 2pF
pF = $12.33
QF* = 10.33
QFs = pF-2
QHs = 10 + pH
pH = $27.33
QH* = 37.33
pF = 5.5 + pH/4
pH = 15 + pF
After the tax:
∆QF*= 10.33-11.67= -1.34
∆pF = $12.33 -$11.67= $0.66
∆QH*= 37.33 - 36.67 = 0.66
∆pH = $27.33 -$26.67 = $0.66
31
Comparative Statics - Tax
The tax had the goal of:
1) Increasing fast food prices to decrease
fast food consumption
2) Increasing healthy food consumption
But also had the negative result of:
3) Increasing the price of healthy foods
32
C. Statics – More Markets
Effect of
an
energy
tax on
energy,
food,
and
labor
markets.
33
C. Statics – More Markets
Effect of an
energy tax on
energy, food, and
labor markets.
34
C. Statics – More Markets
Effect of an
energy tax on
energy, food, and
labor markets.
35