1. Econ 102 SY 2008 2009 Lecture 9 General equilibrium and economic efficiency October 2, 2008

2. Econ 102 SY 2008 2009 Key concepts Uncertainty and risk

3. Econ 102 SY 2008 2009 General equilibrium theory: Components Description of the structure of the economy: preferences, endowments of consumers, and production possibility sets of producers Economic institutional arrangement: How the price mechanism works The behavior assumptions of agents: price taking behavior for consumers and firms, utility maximization and profit maximization. Predicting outcomes: positive analysis -- existence, uniqueness, and stability. Evaluating outcomes: normative analysis such as allocative efficiency of general equilibrium.

4. Econ 102 SY 2008 2009 Economic structure How many consumers? What are their utility functions? Demand functions? What are their sources of income? How do they spend their incomes? How many producers (firms)? What are their production functions? What do they produce? What are their supply functions? What are their inputs? What are their demand for input functions? Where do they buy their inputs? Is there a role of government? What would that be?

5. Econ 102 SY 2008 2009 A Simple Exchange Diagram: Consumption Only Entertainer Hunter

6. Econ 102 SY 2008 2009 Circular Flow Diagram: Modern Economy Prices of Outputs, By Item Consumers Businesses Product Demands Product Supplies Prices of Factors, By Resource Factor Supplies Factor Demands Income Factor Services Goods, Services Sales

7. Econ 102 SY 2008 2009 Economic Institutional arrangement Prices adjust to clear excess demands of commodities and factors How many “markets” are there in the model? How many commodities and factors? For each of these commodities and factors, what are their respective sources and destinations or sink? What is not considered in a price mechanism model? Non-market allocation such as those arising from contracts.

8. Econ 102 SY 2008 2009 Economic agents What is an economic agent in a general equilibrium model? Entity (e.g. person (natural or juridical like a firm or government) It has an income stream. It spends. Example of agents: consumers; Producers. What is the role of the government? Are there other agents? What are the behavioral assumptions of the agents?

9. Econ 102 SY 2008 2009 General equilibrium analysis What is general equilibrium: For all production activities: profits are non-negative. For all markets: excess demands are non-positive. For all agents: income = expenditure. How do we solve for general equilibrium? Analytical general equilibrium analysis Numerical general equilibrium analysis (CGE) Does it exist? Is it stable?

10. Econ 102 SY 2008 2009 Pure exchange economies

11. Econ 102 SY 2008 2009 Edgeworth Box Two individuals, H and F, each with an endowment of two goods, X and Y Length and Height of the box Competitive equilibrium relative to endowment Pareto efficient allocation Consumption efficiency line Y H Endowment Competitive equilibrium 0H0H 0F0F X H X F Y F U H1 U H,3 U H,2 U F,1 U F,2 U F,3 Consumption Efficiency curve Pareto efficient allocations

12. Econ 102 SY 2008 2009 Equations of the Pure Exchange General Equilibrium Model Model Summary: Two good (X and Y), two consumers (H and F), and pure exchange Structural Equations of the Model H Utility functions and endowment F Utility functions and endowment

13. Econ 102 SY 2008 2009 Walras’ Law Let  is excess demand. Walras Law: Values of excess demands sum up to zero. X is the numeraire, good whose price the rest of the prices are individually compared to. N-1 independent equilibrium conditions.

14. Econ 102 SY 2008 2009 General equilibrium conditions Pure exchange economy Market clearing for goods and services, i.e. zero excess demand functions Numeraire N-1 independent equations Equality of Income and expenditures for all consumers satisfied by Walras’ Law

15. Econ 102 SY 2008 2009 Solve in class

16. Econ 102 SY 2008 2009

17. Welfare properties of competitive equilibrium H and F want to maximize utility by trading Utility maximized: MRS of H for X and Y is equal to the relative price of X and Y What is marginal rate of substitution (MRS)? Pareto efficiency: Concept MRS’s the two consumer are equal In competitive equilibrium, relative prices of X and Y are the same for both H and F Hence, MRS’s are equal and goods allocation of both individuals are Pareto efficient

18. Econ 102 SY 2008 2009 Pareto efficiency in exchange Pareto efficiency There is no way of allocating the endowments of x and y in the economy to increase the satisfaction of one individual without reducing that of the other. Competitive equilibrium of an exchange economy is Pareto efficient.

19. Econ 102 SY 2008 2009 How do we show this Individuals equate MRS with the relative price of X and Y. In competitive equilibrium, the relative price of X and Y is the same for both individuals. Therefore, the MRS’s of both individuals have to be equal. If both MRS’s are equal, then competitive equilibrium is Pareto efficient. YHYH Endowment Competitive equilibrium 0H0H 0F0F X H X F Y F U B,1 U B,3 U B,2 U K,1 U K,2 U K,3 Competitive Equilibrium Price ratio Pre-trade Equilibrium Price ratio for H Pre-trade equilibrium price ratio for F

20. Econ 102 SY 2008 2009 MPS/GE Background Tom Rutherford Sample program file How to run MPS/GE Model title How many production sectors How many markets? How many consumers? Demands and Endowments of consumers? Cobb Douglas demand functions numeraire

21. Econ 102 SY 2008 2009 Solution File

22. Econ 102 SY 2008 2009 Economies with production

23. Econ 102 SY 2008 2009 General equilibrium with production Consider now that X and Y are produced by an undetermined number of price-taking firms They use capital and labor. Factor supplies are fixed and endowed to the consumers

24. Econ 102 SY 2008 2009 A Price-taking firm’s behavior Maximize profits First order condition for profit maximization At any level of output, cost is minimized. Output is set where Marginal cost is equal to price, MC=p.

25. Econ 102 SY 2008 2009 Graphical representation 0X0X LXLX KXKX Q 1,X Q 2,X Q 3,X Cost is Minimized Cost is higher Expansion path Iso-quant Iso-cost line C 1,X C 2,X C 3,X C 1.5,X

26. Econ 102 SY 2008 2009 Factor allocation Two industries, X and Y, using state of art production technologies Fixed supplies of L and K Length and width of the Edgeworth box Pareto efficiency in production line Full employment K X 0X0X 0Y0Y L X LYLY K Y X1X1 X3X3 X2X2 Y1Y1 Y2Y2 Y3Y3 Y4Y4 Pareto production efficiency line

27. Econ 102 SY 2008 2009 Structure of the General Equilibrium Model with Production Model Summary: Two good (X and Y), and two factors, L and K Structural Equations of the Model Representative Consumer H Utility functions and factor endowment Producers of X and Y Production functions

28. Econ 102 SY 2008 2009 Structural Equations Production functions of X and Y Utility functions of representative consumers Factor endowments of representative consumers

29. Econ 102 SY 2008 2009 Walras Law

30. Econ 102 SY 2008 2009 GE conditions Clearing of product markets, X and Y Clearing of factor markets, L and K Zero profit conditions for production activities in X and Y

31. Econ 102 SY 2008 2009 End of Lecture 12 General equilibrium and economic efficiency