**Chapter 10** General Equilibrium and Welfare

**Introduction** • Partial vs. General equilibrium analysis • Partial Equilibrium: narrow focus • General equilibrium: framework of analysis that considers the working of several markets together

**Objective** • General Equilibrium model of exchange • Given an economy where individuals are allocated a certain amount of goods, we will • Investigate barter exchange • Define equilibrium trade • Investigate the emergence of competitive markets

**Harvesting & Gathering: Need for Trade** • Primitive, two-person economy • Geoffrey, Elizabeth • Harvest & gather fruit • Apples, raspberries • Voluntary trade – beneficial • Options • Consume all • Trade some

**Edgeworth Box & Feasible Trades** • Edgeworth box • Graphical device to analyzethe process of trade • Its size equals the total amount of goods • A point in the box represents a possible/ feasibleallocation of goods

**Edgeworth Box & Feasible Trades** • No-trade allocation • Feasible allocation • No trade • Individuals consume their own harvest

**The Edgeworthbox: Dimensions** 10 Apples 0 8 Raspberries Dimensions of the Edgeworth box represent total amount of each good. There are 10 apples and 8 raspberries

**The Edgeworth box: Geoffrey and Elizabeth** Raspberries to Elizabeth Elizabeth 6 0 10 f 8 2 Apples to Elizabeth Apples to Geoffrey I1e 0 2 8 I1g Raspberries to Geoffrey Geoffrey

**Finding Equilibrium Trades** • Equilibrium allocation • Once reached • No incentive to further trade • Block • Prevent a trade • Coalition – each gets more • Individually rational trade • Higher utility - than no trade

**Utility-improving trades** Raspberries to Elizabeth 6 4 0 f g 10 i h j 8 2 Apples to Elizabeth Apples to Geoffrey 4 6 I3e I3g I1e I2e I2g 0 2 4 8 I1g Raspberries to Geoffrey The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f .

**Efficient / Pareto-Optimal Allocation** • Pareto-optimal (efficient) allocation • Allocation of goods across people • No other allocation can make one person better off without making the other worse off. • Not an efficient allocation • Indifference curves cross • Efficient allocation • Indifference curves – tangent • MRS the same for both • Contract curve • Curve in Edgeworth box • All efficient trades

**The Contract Curve** 0J UJ1 Contract Curve UJ2 US3 UJ3 US2 US1 0S

**The core** 0J UJ1 UJ2 US3 UJ3 US2 US1 0S For any initial allocation we can see where trade may lead.

**The Core** • Core of economy • Set of equilibrium trades • Portion of contract curve • Between no-trade indifference curves • Individually rational • Cannot be blocked

**Efficiency and Equity** 0J F is the “fair” allocation and E is the initial allocation. UJ1 UJ2 F US3 UJ3 US2 E US1 0S It is not possible with voluntary exchange. Coercion would make Smith better off but Jones worse off.

**A Simple General Equilibrium Model** • Assume a simple economy comprised of • Identical consumers • 2 Firms • Two goods X and Y • Consumers own all factors of production/ all firms

**A Simple General Equilibrium Model** PPF: shows the combinations of X and Y that can be produced if resources are used efficiently Quantity of Y It also shows the relative opportunity cost of good X in terms of Y Quantity of X

**A Simple General Equilibrium Model** Quantity of Y The indifference curves represent consumer preferences: “demand curve” U3 U2 U1 Quantity of X

**A Simple General Equilibrium Model** Point E is economically efficient: it both is productively efficient (on the PPF) and it maximizes utility. Quantity of Y F Compare point E to point F E U3 U2 U1 Quantity of X

**A Simple General Equilibrium Model** • The slope of the PPF shows the opportunity cost of X in terms of Y. As more X is produced, the opportunity cost rises. The slope is the rate of product transformation. • The slope of the indifference curve shows the rate at which consumers are willing to trade one good for another in consumption. The slope is the marginal rate of substitution. • At the efficient point the RPT = MRS

**The Efficiency of Perfect Competition** • We now have an idea of where we want to be: point E. • How do we get there? • First Welfare Theorem says that a perfectly competitive price system will bring about an economically efficient allocation of resources.

**The Efficiency of Perfect Competition** • How to find a perfect competitive equilibrium? • It is a price vector that clears the market • Given the prices of the two goods • Producers supply an amount of x and y • Consumers demand an amount of x and an amount of y • Demand for x by all consumers= total production of x • Demand for y by all consumers= total production of y

**A Perfectly Competitive System** • Consumers own all resources • Consumers offer resources to firms • Firms produce goods and sell them • Revenue from sales used to pay all resource owners • Consumers earn an income where Income = value of goods

**Firm’s Side** Quantity of Y • Lets assume prices for both goods, and and see if these prices constitute a perfect competitive equilibrium • The prices can be represented graphically by many straight lines with a slope -/ • Firms choose a combination of X and Y that maximizes Profit • All points on the PPF cost the same, since all resources are used. Firms will maximize profits by producing here. Quantity of X

**The budget line for consumers** • Total product of firms represent income to consumers • Consumers income is M= + • The budget equation + = + = + • The budget line has a slope of - /and goes through point ,

**The Economy’s Budget line** Quantity of Y • The budget line for consumers: • Represents all points possible to consume at the price ratio • Goes through the point of production of firms Quantity of X

**Consumers’ Side** Quantity of Y Consumers will want to consume at this point U3 • Consumers maximize utility given the prices observed and their income U2 Quantity of X

**The Efficiency of Perfect Competition** Quantity of Y U3 U2 Excess demand for X Quantity of X

**The Efficiency of Perfect Competition** Quantity of Y Excess supply of Y U3 U2 Quantity of X

**The Efficiency of Perfect Competition** • What’s the problem? • At the initial set of prices the decisions of firms and consumers don’t match up. • There is an excess demand for X and an excess supply of Y. • What will happen to the prices of X and Y? • The price of X will increase and the price of Y will decrease. • The budget line will pivot and become steeper.

**The Efficiency of Perfect Competition** Quantity of Y Consumers will want to consume at this point Firms will maximize profits by producing here. U3 U2 But we still have excess demand for X and excess supply of Y Quantity of X

**The Efficiency of Perfect Competition** Quantity of Y Consumers will want to consume at this point U3 Firms will maximize profits by producing here. U2 Quantity of X

**The Efficiency of Perfect Competition** • At equilibrium: • Firms are maximizing profits. • Given the income consumers earn from that level of production consumers are maximizing utility. • At equilibrium the amount of X and Y producers wish to supply is equal to the amount of X and Y that consumers demand.

**Prices, Efficiency and Laissez Faire** • The natural effort of every individual to better his own condition, when suffered to exert itself with freedom and security, is so powerful a principle that it is alone, and without any assistance, not only capable of carrying on the society to wealth and prosperity, but of surmounting a hundred impertinent obstructions with which the folly of human laws too often encumbers its operations.

**Why Markets Fail to Achieve Efficiency** • What do we mean by “market failure”? • Imperfect Competition • A market in which some buyers and/or sellers have some influence on the prices of goods and services • Externalities • The effect of one party’s economic activities on another party that is not taken into account by the price system (pollution) • Public Goods • Goods that are both non-exclusive and non-rival • Imperfect Information