 General Equilibrium and Welfare

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

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

 Primitive, two-person economy o Geoffrey, Elizabeth o Harvest & gather fruit Apples, raspberries o Voluntary trade – beneficial o Options Consume all Trade some 4

 Edgeworth box o Graphical device to analyze the process of trade o Its size equals the total amount of goods o A point in the box represents a possible/ feasible allocation of goods 5

 No-trade allocation o Feasible allocation o No trade o Individuals consume their own harvest 6

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

8 Raspberries to Geoffrey 0 28 Apples to Geoffrey 8 10 f Apples to Elizabeth 2 Raspberries to Elizabeth 06 Geoffrey Elizabeth I 1g I 1e

 Equilibrium allocation o Once reached o No incentive to further trade  Block o Prevent a trade o Coalition – each gets more  Individually rational trade o Higher utility - than no trade 9

10 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. Raspberries to Geoffrey Apples to Geoffrey f Apples to Elizabeth 2 4 Raspberries to Elizabeth 064 h g j i I 1g I 1e I 2e I 3e I 3g I 2g

 Pareto-optimal (efficient) allocation o Allocation of goods across people o No other allocation can make one person better off without making the other worse off.  Not an efficient allocation o Indifference curves cross  Efficient allocation o Indifference curves – tangent o MRS the same for both  Contract curve o Curve in Edgeworth box o All efficient trades 11

0S0S 0J0J US1US1 US2US2 US3US3 UJ1UJ1 UJ2UJ2 UJ3UJ3 Contract Curve

0S0S 0J0J US1US1 US2US2 US3US3 UJ1UJ1 UJ2UJ2 UJ3UJ3 For any initial allocation we can see where trade may lead.

 Core of economy o Set of equilibrium trades o Portion of contract curve Between no-trade indifference curves o Individually rational o Cannot be blocked 14

0S0S 0J0J US1US1 US2US2 US3US3 UJ1UJ1 UJ2UJ2 UJ3UJ3 F is the “fair” allocation and E is the initial allocation. E F It is not possible with voluntary exchange. Coercion would make Smith better off but Jones worse off.

 Assume a simple economy comprised of o Identical consumers o 2 Firms o Two goods X and Y o Consumers own all factors of production/ all firms

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

Quantity of X Quantity of Y The indifference curves represent consumer preferences: “demand curve” U1U1 U2U2 U3U3

Quantity of X Quantity of Y E Point E is economically efficient: it both is productively efficient (on the PPF) and it maximizes utility. U1U1 U2U2 U3U3 Compare point E to point F F

 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

 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.

 How to find a perfect competitive equilibrium? o It is a price vector that clears the market o 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

 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

Quantity of X Quantity of Y Firms will maximize profits by producing here.

Quantity of X 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 Quantity of Y U2U2 U3U3 Consumers maximize utility given the prices observed and their income Consumers will want to consume at this point

Quantity of X Quantity of Y U2U2 U3U3 Excess demand for X

Quantity of X Quantity of Y U2U2 U3U3 Excess supply of Y

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

Quantity of X Quantity of Y U2U2 U3U3 Firms will maximize profits by producing here. Consumers will want to consume at this point But we still have excess demand for X and excess supply of Y

Quantity of X Quantity of Y U2U2 U3U3 Firms will maximize profits by producing here. Consumers will want to consume at this point

 At equilibrium: o Firms are maximizing profits. o Given the income consumers earn from that level of production consumers are maximizing utility. o At equilibrium the amount of X and Y producers wish to supply is equal to the amount of X and Y that consumers demand.

 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.

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