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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

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P2

Market 2Market 2

Equilibrium in Two Markets

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Q1

P1 = Q1s - 2

P1 = 4 + P2/3 – Q1D/3•3

e1

5

P1

Market 1Market 1

Equilibrium in Two Markets

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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

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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…

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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.

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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.