# 1 Chapter 16 General Equilibrium Theory 16.1 General Equilibrium Analysis: Two Markets 16.2 General Equilibrium Analysis: Many Markets 16.3 General Equilibrium.

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1 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

2 Chapter 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).

3 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:

4 Chapter Thirteen 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

5 GE: Two Markets Q 1 D = 12 – 3p 1 + p 2 Q 1 s = 2 + p 1 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 1) Find Reaction Functions Market 1 equilibrium: Q 1 D = Q 1 s 12 – 3p 1 + p 2 = 2 + p 1 p 1 = 10/4 + p 2 /4 Market 2 equilibrium: Q 2 D = Q 2 s 4 – 2p 2 + p 1 = 1 + p 2 p 2 = 1 + p 1 /3

6 GE: Two Markets Q 1 D = 12 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 10/4 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 2) Find Prices p 1 = 10/4 + p 2 /4 p 1 = 10/4 + [1 + p 1 /3 ]/4 p 1 = 11/4 + p 1 /12 (11/12)p 1 = 11/4 p 1 = 3 p 2 = 1 + p 1 /3 p 2 = 1 + 3/3 p 2 = 2

7 GE: Two Markets Q 1 D = 12 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 10/4 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 p 1 = 3p 2 = 2 3) Find Quantities Q 1 * = 2 + p 1 Q 1 * = 2 + 3 Q 1 * = 5 Q 2 * = 1 + p 2 Q 2 * = 1 + 2 Q 2 * = 3

8 GE: Two Markets Q 1 D = 12 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 10/4 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 p 1 = 3p 2 = 2 Q 1 * = 5Q 2 * = 3 In general equilibrium, market 1 sells 5 goods for \$3 each, and market 2 sells 3 goods for \$2 each.

9 Q2Q2 P 2 = Q 2 s - 1 P 2 = 4 + P 1 /2 - Q 2 D /2 2 e2e2 3 P2P2 Market 2 Equilibrium in Two Markets

10 Q1Q1 P 1 = Q 1 s - 2 P 1 = 4 + P 2 /3 – Q 1 D /3 3 e1e1 5 P1P1 Market 1 Equilibrium in Two Markets

11 Shifts in Two Markets Suppose an exogenous shock increases demand in market 1 to: Q 1 D = 22 – 3p 1 + p 2 What is the new general equilibrium? If either market faces a shift in demand or supply, the ENTIRE PROCESS must be redone:

12 GE: Two Markets Shifts Q 1 D = 22 – 3p 1 + p 2 Q 1 s = 2 + p 1 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 1) Find Reaction Functions Market 1 equilibrium: Q 1 D = Q 1 s 22 – 3p 1 + p 2 = 2 + p 1 p 1 = 5 + p 2 /4 Market 2 equilibrium: Q 2 D = Q 2 s 4 – 2p 2 + p 1 = 1 + p 2 p 2 = 1 + p 1 /3

13 GE: Two Markets Shifts Q 1 D = 22 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 5 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 2) Find Prices p 1 = 5 + p 2 /4 p 1 = 5 + [1 + p 1 /3 ] /4 p 1 = 5.25 + p 1 /12 (11/12)p 1 = 5.25 p 1 = 5.73 p 2 = 1 + p 1 /3 p 2 = 1 + 5.73 /3 p 2 = 2.91

14 GE: Two Markets Shifts Q 1 D = 22 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 5 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 p 1 = 5.73 p 2 = 2.91 3) Find Quantities Q 1 * = 2 + p 1 Q 1 * = 2 + 5.73 Q 1 * = 7.73 Q 2 * = 1 + p 2 Q 2 * = 1 + 2.91 Q 2 * = 3.91

15 GE: Two Markets Shifts Q 1 D = 22 – 3p 1 + p 2 Q 1 s = 2 + p 1 p 1 = 5 + p 2 /4 Q 2 D = 4 – 2p 2 + p 1 Q 2 s = 1 + p 2 p 2 = 1 + p 1 /3 p 1 = 5.73 p 2 = 2.91 Q 1 * = 7.73 Q 2 * = 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.

16 Q1Q1 2 7.73 P 1 = Q 1 s - 2 P 1 = 4 + P 2 /3 – Q 1 D /3 3 5 P1P1 Market 1 Shifts in Two Markets P 2 ‘= 7.33 + P 1 /2 - Q 2 D /25.73

17 Q2Q2 P 2 = Q 2 s - 1 P 2 = 4 + P 1 /2 - Q 2 D /2 2 2.91 3 P2P2 Market 2 Shifts in Two Markets 3.91

18 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…..

19 Chapter 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

20 Chapter 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: Supply Good A = Demand Good A Supply Good B = Demand Good B Supply Input A = Demand Input A Supply Input B = Demand Input B

22 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 Food Q F D = 20 –3p F + p H Q F s = p F Q H D = 40 – p H + 2p F Q H s = 10 + p H 1) Find Reaction Functions Fast Food equilibrium: Q F D = Q F s 20 –3p F + p H = p F p F = 5 + p H /4 Health Food equilibrium: Q H D = Q H s 40 – p H + 2p F = 10 + p H p H = 15 + p F

24 Fast Food and Healthy Food Q F D = 20 –3p F + p H Q F s = p F p F = 5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F 2) Find Prices p F = 5 + p H /4 p F = 5 + (15 + p F )/4 p F = 8.75+ p F /4 p F = \$11.67 p H = 15 + p F p H = 15 + \$11.67 p H = \$26.67

25 Fast Food and Healthy Food Q F D = 20 –3p F + p H Q F s = p F p F = 5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F p F = \$11.67 p H = \$26.67 3) Find Quantities Q F * = p F Q F * = 11.67 Q H * = 10 + p H Q H * = 10 + \$26.67 Q H * = 36.67

26 Fast Food and Healthy Food Q F D = 20 –3p F + p H Q F s = p F p F = 5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F p F = \$11.67 p H = \$26.67 Q F * = 11.67 Q H * = 36.67 In general equilibrium: 11.67 people buy fast food for \$11.67, and 36.67 people buy healthy food for \$26.67.

27 QFQF P F = Q F Assume a \$2 tax imposed on sellers of fast food. PFPF Comparative Statics - Tax P F = Q F +2 2

28 Comparative Statics - Tax Q F D = 20 –3p F + p H Q F s = p F -2 Q H D = 40 – p H + 2p F Q H s = 10 + p H 1) Find Reaction Functions Fast Food equilibrium: Q F D = Q F s 20 –3p F + p H = p F -2 p F = 5.5 + p H /4 Health Food equilibrium: Q H D = Q H s 40 – p H + 2p F = 10 + p H p H = 15 + p F

29 Comparative Statics - Tax Q F D = 20 –3p F + p H Q F s = p F -2 p F = 5.5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F 2) Find Prices p F = 5.5 + p H /4 p F = 5.5 + (15 + p F )/4 p F = 9.25+ p F /4 p F = \$12.33 p H = 15 + p F p H = 15 + \$12.33 p H = \$27.33

30 Comparative Statics - Tax Q F D = 20 –3p F + p H Q F s = p F -2 p F = 5.5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F p F = \$12.33 p H = \$27.33 3) Find Quantities Q F * = p F -2 Q F * = 12.33-2 Q F * = 10.33 Q H * = 10 + p H Q H * = 10 + \$27.33 Q H * = 37.33

31 Comparative Statics - Tax Q F D = 20 –3p F + p H Q F s = p F -2 p F = 5.5 + p H /4 Q H D = 40 – p H + 2p F Q H s = 10 + p H p H = 15 + p F p F = \$12.33 p H = \$27.33 Q F * = 10.33 Q H * = 37.33 After the tax: ∆Q F * = 10.33-11.67= -1.34 ∆p F = \$12.33 -\$11.67= \$0.66 ∆Q H * = 37.33 - 36.67 = 0.66 ∆p H = \$27.33 -\$26.67 = \$0.66

32 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

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 C. Statics – More Markets Effect of an energy tax on energy, food, and labor markets.

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