1 General Equilibrium APEC 3001 Summer 2006 Readings: Chapter 16

2 Objectives General Equilibrium –Exchange Economy –With Production First & Second Welfare Theorems

3 General Equilibrium Definition: –The study of how conditions in each market in a set of related markets affect equilibrium outcomes in other markets in that set. Example of Exchange Economy –Two people: Mason & Spencer –Initial Endowments: Mason: 75 pieces of candy & 50 pieces of gum. Spencer: 25 pieces of candy & 100 pieces of gum. Total: 100 pieces of candy & 150 pieces of gum. Edgeworth Exchange Box: –A diagram used to analyze the general equilibrium of an exchange economy.

4 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Graphical Example of Edgeworth Exchange Box

5 Question: Can Mason & Spencer do better? To answer this question, we need to know something about Mason & Spencer’s preferences. Assume: –Complete –Nonsatiable –Transitive –Convex Implication: –Mason & Spencer have utility functions that produce indifference curves that represent higher levels of satisfactions as we move away from the origin, are ubiquitous, are downward sloping, cannot cross, & are bowed toward the origin.

6 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Edgeworth Exchange Box With Indifference Curves I0MI0M I1MI1M I2MI2M I 2 M > I 1 M > I 0 M I 2 S > I 1 S > I 0 S I0SI0S I1SI1S I2SI2S

7 How can Mason & Spencer do better? Pareto Superior Allocation: –An allocation that at least one individual prefers and others like at least equally as well. Pareto Optimal Allocation: –An allocation where it is impossible to make one person better off without making at least one other person worse off. Consider the indifferences curves for Mason & Spencer that intersect the initial endowment.

8 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Gains From Trade IEMIEM IESIES PARETO SUPERIOR ALLOCATIONS

9 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Pareto Optimal Allocations IEMIEM IESIES PARETO SUPERIOR ALLOCATIONS I PI S I PI M a b

10 What are the Pareto Optimal allocations? Contract Curve: –The set of all Pareto optimal allocations.

11 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum The Contract Curve IEMIEM IESIES PARETO SUPERIOR ALLOCATIONS I PI S I PI M a b Contract Curve

12 How can Mason & Spencer get to a Pareto Optimal allocation? Suppose the price of candy is P C 0 & the price of gum is P G 0. Implications: –Mason’s Income: M 0 M = P C P G 0 50 –Spencer’s Income: M 0 S = P C P G 0 100

13 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Income Constraint With Prices P C 0 and P G 0 for Candy and Gum Slope = -P G 0 /P C 0 M 0 S /P G 0 M 0 M /P G 0

14 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Mason’s and Spencer’s Optimal Consumption Given Prices P C 0 and P G I0SI0S I0MI0M Slope = -P G 0 /P C 0 M 0 S /P G 0 M 0 M /P G 0 C0MC0M G0MG0M G0SG0S C0SC0S

15 Is this a market equilibrium? No! –C 0 M + C 0 S < 100  Excess supply of candy! –G 0 S + G 0 S > 150  Excess demand for gum! So now what can we do? –Offer a higher price for gum or lower price for candy! –For example, P C 1 P G 0.

16 Mason Spencer Mason’s Candy Spencer’s Candy Mason’s Gum Spencer’s Gum Mason’s and Spencer’s Optimal Consumption Given Equilibrium Prices P C 1 and P G I0SI0S I0MI0M Slope = -P G 0 /P C 0 M 0 S /P G 0 M 0 M /P G 0 C0MC0M G0MG0M G0SG0S C0SC0S Slope = -P G 1 /P C 1 M 0 M /P G 1 M 0 S /P G 1 I1MI1M I1SI1S G1SG1S G1MG1M C1SC1S C1MC1M

17 Is this a market equilibrium? Yes! –C 0 M + C 0 S = 100  There is no excess demand or supply of candy! –G 0 M + G 0 S = 150  There is no excess demand or supply of gum! What is true at this point? –MRS M = MRS S –We are on the contract curve, so we are at a Pareto Optimal allocation! First Welfare Theorem: –Equilibrium in competitive markets is Pareto Optimal. Second Welfare Theorem: –Any Pareto optimal allocation can be sustained as a competitive equilibrium.

18 General Equilibrium with Production Production Possibility Frontier: –The set of all possible output combinations that can be produced with a given endowment of factor inputs.

19 Firm C (Candy) Firm G (Gum) Firm C’s Capital Firm G’s Capital Firm C’s Labor Firm G’s Labor KEKE LELE KEKE LELE Edgeworth Box for Candy and Gum Production G0G0 C2C2 C0C0 C1C1 C 2 > C 1 > C 0 G1G1 G2G2 G 2 > G 1 > G 0

20 Firm C (Candy) Firm G (Gum) Firm C’s Capital Firm G’s Capital Firm C’s Labor Firm G’s Labor KEKE LELE KEKE LELE Efficient Production of Candy and Gum Production C1C1 G1G1 G2G2 C2C2 More gum with same amount of candy! More candy with same amount of gum! PARETO SUPERIOR ALLOCATIONS

21 Firm C (Candy) Firm G (Gum) Firm C’s Capital Firm G’s Capital Firm C’s Labor Firm G’s Labor KEKE LELE KEKE LELE Contract Curve for Candy and Gum Production C1C1 G0G0 G1G1 C2C2 G2G2 C0C0 MRTS C = MRTS G C 2 > C 1 > C 0 G 2 > G 1 > G 0

22 Competitive Cost Minimizing Production MRTS C = MP L C /MP K C = w/r MRTS G = MP L G /MP K G = w/r So, MRTS G = w/r = MRTS G Competitive production will result in Pareto Efficient production!

23 Graphical Example of Production Possibility Frontier Candy Gum G0G0 G1G1 G2G2 C0C0 C1C1 C2C2 Slope =  C/  G

24 Production Possibility Frontier Marginal Rate of Transformation: –The rate at which one output can be exchanged for another at a point along the production possibility frontier: |  C/  G|.

25 Note that TC G = wL G + rK G and TC C = wL C + rK C   TC G = w  L G + r  K G and  TC C = w  L C + r  K C Also, L G = L E – L C and K G = K E – K C   L G = –  L C and  K G = –  K C Therefore,  TC G = -w  L C - r  K C = -  TC C   TC G / (  G  C) = -  TC C / (  C  G)  MC G /  C = -MC C /  G  |  C/  G| = MC G /MC C The Marginal Rate of Transformation is the ratio of Marginal Cost!

26 Profit Maximization in Competitive Industry MC C = P C MC G = P G Implications: –MRT = MC G /MC C = P G /P C

27 Utility Maximization with Competitive Markets MRS M = P G /P C MRS S = P G /P C Implications: –MRT = MRS M = MRS S

28 Competitive Equilibrium with Production Candy Gum |Slope| = P G /P C Mason Spencer IMIM ISIS GMGM CMCM CSCS GSGS

29 Summary For a general equilibrium with production to be Pareto Efficient, three types of conditions must hold: –Firms must equate their marginal rates of technical substitution. –Consumers must equate the marginal rates of substitution. –Consumers’ marginal rates of substitution must equal the marginal rate of transformation. Competitive Markets Yield This Outcome!

30 Competitive markets result in the Pareto efficient production and distribution of goods and services! Any Pareto efficient production and distribution of goods can be supported by a competitive market. Adding Production Does Not Change The Implications of The First and Second Welfare Theorems!

31 So, is there anything that can mess up these welfare theorems? Yes! Government Intervention –Taxes –Subsidies Market Failure –Externality: Either a benefit or a cost of an action that accrues to someone other than the people directly involved in the action. –Public Goods: (1) nondiminishability and (2) nonexcludability of consumption. Noncompetitive Behavior –Monopoly –Oligopoly

32 What You Should Know General Equilibrium Conditions –Exchange Economy –With Production Pareto Optimal Allocations First & Second Welfare Theorems & Caveats