Factor markets -- Labor markets Dr. D. Foster – ECO 284 & General Equilibrium.
1 Chapter 16 General Equilibrium Theory 16.1 General Equilibrium Analysis: Two Markets 16.2 General...
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Transcript of 1 Chapter 16 General Equilibrium Theory 16.1 General Equilibrium Analysis: Two Markets 16.2 General...
1
Chapter 16General 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
2Chapter Sixteen
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).
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).
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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:
4Chapter Thirteen
GE: Two Markets
1) Find Reaction Functions (S=D in each market)
2) Use reaction functions to solve for P’s3) Use P’s to solve for Q`s 4) Summarize
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GE: Two MarketsQ1
D = 12 – 3p1 + p2 Q1s = 2 + p1
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2
1) Find Reaction Functions
Market 1 equilibrium: Q1D = Q1
s
12 – 3p1 + p2 = 2 + p1
p1 = 10/4 + p2/4
Market 2 equilibrium: Q2D = Q2
s
4 – 2p2 + p1 = 1 + p2
p2 = 1 + p1/3
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GE: Two MarketsQ1
D = 12 – 3p1 + p2 Q1s = 2 + p1 p1 = 10/4 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3
2) Find Prices
p1 = 10/4 + p2/4p1 = 10/4 + [1 + p1/3 ]/4p1 = 11/4 + p1/12(11/12)p1 = 11/4p1 = 3
p2 = 1 + p1/3p2 = 1 + 3/3p2 = 2
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GE: Two MarketsQ1
D = 12 – 3p1 + p2 Q1s = 2 + p1 p1 = 10/4 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3p1 = 3 p2 = 2
3) Find Quantities
Q1* = 2 + p1 Q1* = 2 + 3 Q1* = 5
Q2* = 1 + p2
Q2* = 1 + 2Q2* = 3
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GE: Two MarketsQ1
D = 12 – 3p1 + p2 Q1s = 2 + p1 p1 = 10/4 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3
p1 = 3 p2 = 2Q1* = 5 Q2* = 3
In general equilibrium, market 1 sells 5 goods for $3 each, and market 2 sells 3 goods for $2 each.
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Q2
P2 = Q2s - 1
P2 = 4 + P1/2 - Q2D/2
•2e2
3
P2
Market 2Market 2
Equilibrium in Two Markets
10
Q1
P1 = Q1s - 2
P1 = 4 + P2/3 – Q1D/3•3
e1
5
P1
Market 1Market 1
Equilibrium in Two Markets
11
Shifts in Two Markets
Suppose an exogenous shock increases demand in market 1 to: Q1
D = 22 – 3p1 + p2 What is the new general equilibrium?
If either market faces a shift in demand or supply, the ENTIRE PROCESS must be redone:
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GE: Two Markets ShiftsQ1
D = 22 – 3p1 + p2 Q1s = 2 + p1
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2
1) Find Reaction Functions
Market 1 equilibrium: Q1D = Q1
s
22 – 3p1 + p2 = 2 + p1
p1 = 5 + p2/4
Market 2 equilibrium: Q2D = Q2
s
4 – 2p2 + p1 = 1 + p2
p2 = 1 + p1/3
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GE: Two Markets ShiftsQ1
D = 22 – 3p1 + p2 Q1s = 2 + p1 p1 = 5 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3
2) Find Prices
p1 = 5 + p2/4 p1 = 5 + [1 + p1/3 ] /4p1 = 5.25 + p1/12(11/12)p1 = 5.25p1 = 5.73
p2 = 1 + p1/3p2 = 1 + 5.73 /3p2 = 2.91
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GE: Two Markets ShiftsQ1
D = 22 – 3p1 + p2 Q1s = 2 + p1 p1 = 5 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3p1 = 5.73 p2 = 2.91
3) Find Quantities
Q1* = 2 + p1 Q1* = 2 + 5.73Q1* = 7.73
Q2* = 1 + p2
Q2* = 1 + 2.91Q2* = 3.91
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GE: Two Markets ShiftsQ1
D = 22 – 3p1 + p2 Q1s = 2 + p1 p1 = 5 + p2/4
Q2D = 4 – 2p2 + p1 Q2
s = 1 + p2 p2 = 1 + p1/3p1 = 5.73 p2 = 2.91
Q1* = 7.73 Q2* = 3.91
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.
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Q12 7.73
P1 = Q1s - 2
P1 = 4 + P2/3 – Q1D/3•3
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P1
Market 1Market 1
Shifts in Two Markets
P2‘= 7.33 + P1/2 - Q2
D/25.73
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Q2
P2 = Q2s - 1
P2 = 4 + P1/2 - Q2D/2
•2
2.91 3
P2
Market 2Market 2
Shifts in Two Markets
3.91
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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…..
19Chapter Sixteen
Consider an economy with:1)2 goods – energy and food
2) 2 input services – labor and capital
Consider an economy with:1)2 goods – energy and food
2) 2 input services – labor and capital
16.2 Equilibrium in Many Markets
20Chapter Sixteen
16.2 Equilibrium in 4 Markets
21
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
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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…
23
Fast Food and Healthy FoodQF
D = 20 –3pF + pH QFs = pF
QHD = 40 – pH + 2pF QH
s = 10 + pH
1) Find Reaction Functions
Fast Food equilibrium: QFD = QF
s
20 –3pF + pH = pF
pF = 5 + pH/4
Health Food equilibrium: QHD = QH
s
40 – pH + 2pF = 10 + pH
pH = 15 + pF
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Fast Food and Healthy FoodQF
D = 20 –3pF + pH QFs = pF pF = 5 + pH/4
QHD = 40 – pH + 2pF QH
s = 10 + pH pH = 15 + pF
2) Find Prices
pF = 5 + pH/4 pF = 5 + (15 + pF )/4 pF = 8.75+ pF/4pF = $11.67
pH = 15 + pF
pH = 15 + $11.67 pH = $26.67
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Fast Food and Healthy FoodQF
D = 20 –3pF + pH QFs = pF pF = 5 + pH/4
QHD = 40 – pH + 2pF QH
s = 10 + pH pH = 15 + pF
pF = $11.67 pH = $26.67
3) Find Quantities
QF* = pF
QF* = 11.67
QH* = 10 + pH
QH* = 10 + $26.67
QH* = 36.67
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Fast Food and Healthy FoodQF
D = 20 –3pF + pH QFs = pF pF = 5 + pH/4
QHD = 40 – pH + 2pF QH
s = 10 + pH pH = 15 + pF
pF = $11.67 pH = $26.67
QF* = 11.67 QH
* = 36.67
In general equilibrium:
11.67 people buy fast food for $11.67,
and
36.67 people buy healthy food for $26.67.
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QF
PF = QF
Assume a $2 tax imposed on sellers of fast food.
PF
Comparative Statics - Tax
PF = QF+2
2
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Comparative Statics - TaxQF
D = 20 –3pF + pH QFs = pF-2
QHD = 40 – pH + 2pF QH
s = 10 + pH
1) Find Reaction Functions
Fast Food equilibrium: QFD = QF
s
20 –3pF + pH = pF-2pF = 5.5 +
pH/4
Health Food equilibrium: QHD = QH
s
40 – pH + 2pF = 10 + pH
pH = 15 + pF
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Comparative Statics - TaxQF
D = 20 –3pF + pH QFs = pF-2 pF = 5.5 +
pH/4QH
D = 40 – pH + 2pF QHs = 10 + pH pH = 15 + pF
2) Find Prices
pF = 5.5 + pH/4 pF = 5.5 + (15 + pF )/4 pF = 9.25+ pF/4pF = $12.33
pH = 15 + pF
pH = 15 + $12.33pH = $27.33
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Comparative Statics - TaxQF
D = 20 –3pF + pH QFs = pF-2 pF = 5.5 +
pH/4QH
D = 40 – pH + 2pF QHs = 10 + pH pH = 15 + pF
pF = $12.33 pH = $27.33
3) Find Quantities
QF* = pF -2
QF* = 12.33-2
QF* = 10.33
QH* = 10 + pH
QH* = 10 + $27.33
QH* = 37.33
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Comparative Statics - TaxQF
D = 20 –3pF + pH QFs = pF-2 pF = 5.5 +
pH/4QH
D = 40 – pH + 2pF QHs = 10 + pH pH = 15 + pF
pF = $12.33 pH = $27.33
QF* = 10.33 QH
* = 37.33 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
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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
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C. Statics – More MarketsEffect of an energy tax on energy, food, and labor markets.
34
C. Statics – More MarketsEffect of an energy tax on energy, food, and labor markets.
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C. Statics – More MarketsEffect of an energy tax on energy, food, and labor markets.