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
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