1. Chapter 16 General Equilibrium, Efficiency, and Equity McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

2. Main Topics The nature of general equilibrium Positive analysis of general equilibrium Normative criteria for evaluating economic performance General equilibrium and efficient exchange Equity and redistribution 16-2

3. The Nature of General Equilibrium Already studied competitive equilibrium in a single isolated market: partial equilibrium analysis Useful when supply and demand for a good are largely independent of activities in other markets However, markets are often interdependent (e.g., if complements or substitutes) General equilibrium analysis is the study of competitive equilibrium in many markets at the same time Allows us to understand the consequences of interdependence among markets Factors that affect supply and demand in one market can have ripple effects in other markets Accounts for feedback between markets Markets can be linked because the price or production of one good affects the demand or cost of another….think substitutes or complements. 16-3

4. Figure 16.1: General Equilibrium 16-4 Above is the general equilibrium in the markets for Pie and Ice cream. Both equilibriums take the other product (and product price) into account in identifying its own product clearing price and quantity.

5. Positive Analysis of General Equilibrium General equilibrium analysis can provide more accurate answers than partial equilibrium analysis does to positive questions Examine the effects of a sales tax on ice cream Assume pie and ice cream are complements Assume no supply linkages General equilibrium effects of the tax include: Demand curve for pie shifts downward, so price of pie falls This produces a feedback effect on the ice cream market Effects of the tax ripple back and forth between the markets Need a new tool to determine the prices that will prevail in both markets in a general equilibrium 16-5

6. Market-Clearing Curves First step in identifying a general equilibrium is to find the market-clearing curve for each good Shows the combinations of prices for that good and related goods that bring supply and demand for the good into balance Prices of the goods are on the axes For two goods that are complements, the market-clearing curves will be downward sloping Example: an increase in the price of pie reduces the demand for ice cream, which lowers the partial equilibrium price of ice cream For substitutes, the curves will be upward sloping 16-6

7. Figure 16.2: A Market-Clearing Curve 16-7 Slide A shows the ice cream curve with 3 different demand curves that correspond to different prices for pie. Slide B is the general equil. market-clearing curve for both products.

8. Figure 16.2: A Market-Clearing Curve 16-8 Slide A shows the pie curve with 3 different demand curves that correspond to different prices for ice cream. Slide B is the general equil. market-clearing curve for both products.

9. General Equilibrium in Two Markets If a price combination lies on both market- clearing curves, then both markets are in equilibrium This is a general equilibrium Find a general equilibrium by plotting both market-clearing curves on the same graph Horizontal axis shows the price of one good; vertical axis shows the price of the other good Intersection of the two market-clearing curves reveals the general equilibrium prices The two goods markets clear at these prices 16-9

10. Figure 16.4: General Equilibrium Price Combination General equilibrium prices are $12 per pie and $6 per gallon of ice cream Pie and ice cream markets both clear at these prices 16-10

11. Effects of a Sales Tax: Partial Equilibrium Continue the ice cream example Examine effects of $3 per gallon sales tax on ice cream Begin from initial equilibrium price of $6 per gallon, 25 million gallons Tax shifts supply curve upward by $3 New partial equilibrium is at intersection of the new supply curve and initial demand curve Price of pie held constant at $12 per pie (Consumer) Price of ice cream rises by $1.67 per gallon, less than the amount of the tax 16-11

12. Effect of a Sales Tax: Gen. Equilibrium Need new market-clearing curve for ice cream, to find general equilibrium effects of tax Tax shifts market-clearing curve for ice cream upward New curve lies exactly $1.67 above the old one Magnitude of the shift equals partial equilibrium effect of the tax Look for intersection of new market-clearing curve for ice cream and old market-clearing curve for pie Shows new general equilibrium Pie price is $11 per pie, ice cream price is $8 per gallon These prices clear both markets 16-12

13. Effect of a Sales Tax: Gen. Equilibrium 16-13

14. Sales Tax Effect : General Equilibrium As a result of the tax, demand curves for both goods shift Sales tax on ice cream reduces the price of a pie by $1 Because pie and ice cream are complements Partial equilibrium analysis understates the effect of the tax on the price of ice cream Based on partial anal., ice cream prices rise only by $1.67, but based on general equil, prices rise by $2. Lower pie price leads to greater demand for ice cream Reinforces pressure for ice cream price to rise General equilibrium analysis accounts for this feedback; partial equilibrium analysis does not 16-14

15. Figure 16.6: Effects of a Tax, part 2 16-15

16. Normative Criteria for Economic Performance Economists have clear criteria for measuring efficiency Equity and fairness are more difficult to determine and evaluate An allocation of resources is Pareto efficient if it’s impossible to make any consumer better off without hurting someone else Proposed by Italian economist Vilfredo Pareto Assume each person knows what’s best for her The utility possibility frontier shows the utility levels associated with all efficient allocations of resources 16-16

17. Figure 16.7: Pareto Efficient Outcomes Points on the boundary are Pareto efficient Point A is inefficient 16-17

18. Equity Equity is harder to define and measure than efficiency Process-oriented notions of equity focus on the procedures used to arrive at an allocation of resources Focus on what could be chosen instead of what is chosen. Is the free market a fair process? Outcome-oriented notions focus on whether the process used to allocate resources yields fair results Some focus on the distribution of well-being, e.g., utilitarianism (equal weight on w-b of every person) Rawlsianism – focus should be on the w-b of the worst-off member of society Others focus on the distribution of consumption, e.g., egalitarianism (equal division of resources to every member of society) 16-18

19. Social Welfare Functions Economists use social welfare functions to summarize judgments about resource allocations For each possible allocation, the function assigns a number that indicates the overall level of social welfare Higher numbers reflect greater social well-being First, assign utility levels to every consumer using utility functions Second, apply a function that converts those utilities into social welfare Higher levels of individual utility imply higher levels of social welfare Can capture concerns for both efficiency and outcome- oriented notions of equity 16-19

20. Figure 16.8: Applying Social Welfare Functions Indifference curves farther from the origin correspond to higher levels of social welfare Point A is the best possible outcome Since Point A is on the utility possibility frontier, it is Pareto efficient The social welfare function reflects a preference for efficiency 16-20

21. General Equilibrium in Exchange Economies In an exchange economy, people own and trade goods but no production takes place. This is a starting model to explain the concept. An endowment is the bundle of goods an individual starts out with before trading Simple example: Humphrey and Lauren are the only consumers Two goods: food and water Humphrey’s initial endowment is 8 pounds of food and 3 gallons of water Lauren’s initial endowment is 2 pounds of food and 7 gallons of water If food sells for $1 per pound and water sells for $1 per gallon this is not a general equilibrium Supply and demand for the two people match if food costs $2 per pound and water sells for $1 per gallon This is a general equilibrium 16-21

22. Figure 16.9: General Equilibrium in an Exchange Economy 16-22

23. The Edgeworth Box The Edgeworth box is a diagram that shows two consumers’ opportunities and choices in a single figure Often used for a simple exchange economy Introduced by British economist Francis Edgeworth in 1881 Each point describes an allocation of resources between the two consumers Dimensions of the box are determined by the total amounts of each good available in the economy When the economy is in general equilibrium the points representing the two consumers’ choices after trading coincide 16-23

24. Equilibrium in an Edgeworth Box Point A represents initial endowment Point C is the general equilibrium resource allocation Food costs $2 per pound Water costs $1 per gallon Notice how they coincide. Also, the curves are opposite due to the inverse nature of the graph. 16-24

25. The First Welfare Theorem First welfare theorem: in a general equilibrium with perfect information the allocation of resources is Pareto efficient Clarifies what Adam Smith mean by the “invisible hand” Use Edgeworth box to understand first welfare theorem At general equilibrium allocation, two consumers face the same equilibrium prices Line representing these prices serves as the budget line for both consumers Impossible to choose an allocation at equilibrium prices, other than equilibrium allocation, that helps one consumer without hurting the other The general equilibrium is Pareto efficient 16-25

26. Figure 16.11: First Welfare Theorem in an Exchange Economy 16-26 They like points on the budget line equally. But the points of D and E are not as well liked as choosing either of them would hurt the other party.

27. Efficiency in Exchange 16-27

28. Efficiency in Exchange Whenever an allocation is inefficient, there are gains from trade Whenever an allocation is efficient there are no mutually beneficial trades The Exchange efficiency condition holds if every pair of individuals shares the same MRS for every pair of goods Holds as long as consumers’ indifference curves are smooth and have declining MRS A test for existence of potential gains from trade between consumers When consumers’ MRS differ, they can both gain by trading Contract curve shows every efficient allocation of consumption goods in an Edgeworth box Starts at the southwest corner and ends at the northeast corner Every allocation on the contract curve corresponds to a point on the utility possibility frontier, and vice versa 16-28

29. Figure 16.13: Contract Curve 16-29

30. General Equilibrium and Efficient Production If add production, competitive equilibria remain Pareto efficient Exchange efficiency is not enough; production must also be efficient Two requirements for production efficiency: Input efficiency Output efficiency Input efficiency: there is no way to increase any firm’s output of one good without decreasing the output of another good Holding constant the total amount of each input used in the economy Pareto efficiency requires input efficiency 16-30

31. Input Efficiency Example Two inputs: Labor, total of 50 workers Capital, total of 25 machines Two firms: MunchieCo, produces food CribCo, produces housing Use an Edgeworth box to illustrate allocations of inputs between firms Allocations where two isoquants cross are inefficient At points where the two firms’ isoquants touch but do not cross, the two inputs are allocated efficiently There is no way to increase the output of one good without decreasing the output of the other 16-31

32. Figure 16.15: Input Efficiency 16-32

33. A Condition for Input Efficiency Production contract curve shows every efficient allocation of inputs between two firms in an Edgeworth box At efficient allocations, on firm’s MRTS LK is the same as the other’s The firms’ isoquants lie tangent to the same straight line Slope of this line shows the rate at which both firms can substitute labor for capital without changing their output Input efficiency criterion holds if every pair of firms shares the MRTS between every pair of inputs As long as the firms’ isoquants are smooth and have declining MRTS Allocations that satisfy this condition are efficient A test for existence of potential gains from trade between firms 16-33

34. Production Possibilities Production possibility frontier shows the combinations of outputs that firms can produce when inputs are allocated efficiently among them Given their technologies and the total inputs available Relationship between the PPF and the production contract curve is the same as the relationship between the utility possibility frontier and the contract curve Each input allocation on the production contract curve is associated with a point on the PPF and vice versa PPF always slopes downward Upward slope would imply that, starting on the frontier, it’s possible to increase the production of both goods without changing the total amount of any input But this would mean that the allocation of inputs on the frontier is inefficient and, by definition, the PPF includes only efficient combinations 16-34

35. Figure 16.16: Production Possibility Frontier 16-35

36. Marginal Rate of Transformation Downward slope of the PPF reflects tradeoffs involved in production If we choose to produce more of one good, we must produce less of another Marginal rate of transformation from good X to good Y is the additional amount of Y that can be produced by sacrificing one unit of X At any point on the PPF, the marginal rate of transformation is equal to the slope of a straight line drawn tangent to the frontier at the point, times negative one Marginal rate of transformation is also related to the firms’ marginal products Frontier gets steeper moving from left to right Marginal rate of transformation from X to Y rises Reflects decreasing returns to scale in the production technologies 16-36

37. Output Efficiency Output efficiency means there is no way to make all consumers better off by shifting production from one good to another Among allocations satisfying exchange efficiency and input efficiency Achieve input efficiency by picking a point on the production contract curve Equivalent to picking a point on the PPF To achieve output efficiency, need to pick the right point Allocation satisfies the output efficiency condition if, for every pair of goods, every consumer’s MRS equals the marginal rate of transformation 16-37

38. Figure 16.17: Output Efficiency 16-38

39. Justification for Free Markets Advocates of free markets argue that government should not play a significant role in overseeing, directing, or conducting economic activity Doctrine of laissez-faire holds that the government should adopt a “hands off” approach to private commerce First welfare theorem provides some support for this position Says a perfectly competitive economy would produce an efficient outcome Opponents have two main reservations Few economists describe the real economy as perfectly competitive A market failure is a source of inefficiency in an imperfectly competitive economy Many people express concerns that free markets can produce inequitable outcomes 16-39

40. Equity and Redistribution First welfare theorem says that a competitive equilibrium is Pareto efficient May not convince you that competitive markets are desirable Efficient allocations can be extremely inequitable Even if the competitive equilibrium is on the contract curve, may be other points on that curve that are more equitable Second welfare theorem says that every Pareto efficient allocation is a competitive allocation for some initial allocation of resources If the initial allocation of resources heavily favors certain individuals, the equilibrium will favor them as well In principle, societies can use competitive markets to achieve both efficiency and equity If society can redistribute the initial allocation of resources appropriately, then competitive markets will deliver the most equitable Pareto efficient allocation 16-40

41. Figure 16.20: Second Welfare Theorem 16-41