Chapter 7: Competitive General Equilibrium Decentralization markets are promoting the economic prosperity more effectively than state planning or intervention. Is this view true? Up to some level is true, so, today we may see many phenomena like liberalization, deregulation, privatization …etc. In the U k, the failure of keynesianism in the 1970 to delver non- inflationary growth Competitive general equilibrium is a Pareto-efficient outcome. The aim of this chapter is to: - Study deeply the model of competitive general equilibrium and its links with Pareto efficiency. - Study how equilibrium prices are determined in the model. - look at a different version of the model using neoclassical analysis of consumer and firm behaviors. - finally, the chapter will look at the normative or welfare properties of competitive equilibrium outcomes, and the policy conclusions.

2. Competitive general equilibrium (Walrasian M.): The model is based on the individual choices of economic agents in response to given market prices and the exogenous variables of preferences, resource endowments and technology. The kaleidoscope of economic activity assumed to be fixed for a moment. The model assumed also equilibrium in every market, in order to find out whether individual choices are consistent. Walrasian rule, supposes that a positive excess demand requires an increase in price and the opposite is correct. This would prompt the auctioneer to call out to change the price. For illustration we will use partial equilibrium analysis of one market in which the prices of other goods are held constant. We will use excess demand curve which shows the difference between the quantity demanded and the quantity supplied of a good at each level of price.

0 Q a S Q b D Q E QaD QbS Quantity Excess Demand Excess supply Price Pb PEPaPEPa SDSD Zb 0 Z a Excess Demand Price pbpb pEpE papa Figure 7.1 Demand, supply and excess demand in a single market. Q a D – Q aS = Z a Q b D – Q b s = Z b Figure 7.1 shows just one market with the price and excess demand curve The exogenous variables are the price of all other goods, prference, resources endowments and technology and supposed all are constant. If any of these exogenous variable changed there would be a shift of the excess demand curve. In a general equilibrium model, supposed to look at all markets simultaneously and so the excess demand for any good is dependent on all prices. (can not show in graph)

3 The Determination of prices. The Walrasian auctioneer, Competitive markets How equilibrium prices are actually arrived at in real situations where markets are out of equilibrium! Walras suggested that a competitive market process of price adjustment could be imagined as an auction. The process of auction still continuous until excess demands are eliminated. Then the trade actually take place at the announced prices. (stock exchanges and trading markets) Mathematical models of the process of Walrasian price adjustment discovered that if an excess demand curve is negatively sloped throughout its range, then the Walrasian rule for price adjustment will work fine towards a single equilibrium price. If the opposite case the rule will not work. Z a 0 Z b Excess Demand Pb Pb Price Z P E Pa Z b 0 Z c Z a Excess Demand PbPb Price Z P E Pc Pa

4. Some more models of general equilibrium. Consumer’s preferences may be represented by using an indifference map as in figure 7.6. The consumer reach to his utility maximization when or where the budget line is tangent to an indifference curve and this occurs at point A. At point A, the marginal rate of substitution of good G for good F, MRS G,F, is equal to the relative price of G in terms of F, so, MRS G,F =P G /P F General Equilibrium of exchange and consumption:. A At A, MRS G,F = P G /P F G B Good G Good F Figure 7.6 Utility maximization

- By using the same principle of utility maximization, the simple general equilibrium model of exchange and consumption will be developed in a competitive economy has two individuals and two goods. - The model can be illustrated using the Edgeworth box diagram in figure Each individual receives a bundle of goods as an initial endowment. (50 kilos of figs (good F) and 60 kilos of grapes (good G) -In this exchange economy, individuals can increase their utility only by exchange some of their goods with each other. - P B A Grape s Figs Xerxes Figure 7.7 An Edgeorth box diagram showing an initial allocation of two goods between two consumers, and a price line. Figs 10 F 15 G Grape s Yvonne The bundles that can be reached by exchange at a particular relative price can be represented by drawing a price line in figure 7.7 The price of grapes in terms of figs is 2/3 for example.

-The question here is, if the individuals were to trade with each other at this price, excess demand for both goods would be zero! - In order to examine that we shall use the Edgeworth box diagram in figure 7.8 since the indifference maps of both individuals. - the two indifference maps show that there are a number of points of common tangency between the two sets of indifference curves. - The points of common tangency represent positions of simultaneou utility maximization by Xerxes and Yvonne, subject to different common prices which are shown by the different price lines, P1, P2, P3 and P4. - The contract curve, is the line joined up all the points of common tangency of all the indifference curves. - These points (at contract curve), the simultaneous utility maximization is possible for two consumers, subject to different price. Uy0Uy0 B A Grap es Figs Xerxes Figure 7.8 Simultaneous utility maximization Figs U y3 Grap es Yvonn e U y2 U y1 U x3 P1 P2 P3 P4 Ux0Ux0 C C 0x0x 0y0y - The core of a two-person exchange economy is that portion of the contract curve that is preferred by both consumers to the initial endowment. - Starting with an initial allocation at A, the equilibrium outcome must lie within the core, but where within the core?

Starting with an initial allocation at A, the equilibrium outcome must lie within the core, but where within the core? U y0 A Grapes Figs Xerxes Figure 7.9 A competitive equilibrium Figs Grapes Yvonne U yE P U x0 C C 0x0x 0y0y U xE E

Equilibrium in production: -The aim of this section is finding out the amounts of the two goods produced and the price at which they are sold. -The model considers all possible combinations of quantities of the two goods that could be produced given existing technology & different techniques of production. -The model is using the production possibility frontier (PPF). ΔF/Δ ΔF/Δ -The slope of the PPF, ΔF/ΔG, is negative and its value shows the rate at which figs have to be sacrificed in order to produce one more unit of grapes. (opportunity cost) and is called marginal rate of transformation (MRT G, f = - ΔF/ΔG) -MRT between two goods measures the rate at which production of one has to be reduced in order to increase production of the other by one unit. And this equal to the marginal cost of good since it is the cost of the last unit produced.. B Production possibility frontier Good G B Grapes G Figs F Figure 7.13 Production possibility frontiers for figs and raps Slope = ΔF/ΔG Good F FBFB GBGB 0. B ’ -The marginal cost of producing one extra unit of good G, is the amount of good F it costs to produce that unit of good G. -In fact, this is just the marginal rate of transformation of good G for good F. and that means: MC G = MRT G,F

-When the economy has more goods, then, the model would have use terms of ratios of marginal costs of one good in terms of another would be equal to the ratio of their marginal costs. So in general MRT G, F = MC G / MC F. -In a competitive economy, profit maximization required firms to produce at the level which, marginal costs are equal to output prices. -So that, in equilibrium, MC G / MC F = PG/PF -This means, the marginal rate of transformation between the two goods is equal to their relative price, MRT G, F = P G /P F -This result explains that profit maximizing under competitive conditions results in the relative output price being equal to the value of the slope of the production possibility frontier at point E in the graph E Good G B Grapes G Figs F Figure 7.15 Competitive output At E, MRT G, F = P G /P F Good F FEFE GEGE 0 P Now we would like to expand the model of the exchange economy to include production in order to check whether there exists a relative price that will support a general equilibrium of exchange and production simultaneously!!!

General Equilibrium with production: The task here is finding the equilibrium relative price and the output mix of figs and grapes, with the amounts consumed by Xerxes and Evonne. We learned before, the consumer optimization under price taking results in, the marginal rate of substitution of grapes for figs is equal to the ratio of prices for both consumers: MRS G, F = P G /P F And since the profit maximization under price taking results in, the marginal rate of transformation of grapes for figs being equal to the ratio of prices: MRT G, F = P G /P F. This means, in equilibrium in a competitive economy, the marginal rate of substitution must be equal to the marginal rate of transformation, this is: MRS G, F = P G /P F = MRT G, F This fact can be explained by combining the box diagram of exchange and consumption with the production possibility frontier diagram. See Fig. no E Good G B Grapes G Figs F Figure 7.16 Competitive equilibrium in exchange, consumption and production. At E, MRT G, F = P G /PF = MRT G, F Good F FEFE GEGE 0 P P U xE UyEUyE E’E’

Final notes: The production possibility frontiers shows the competitive profit-maximizing output mix at, E, where F E of figs and G E of grapes are produced, subject to the price line P. These amounts of figs and grapes provide the dimensions for an Edgeworth box with the competitive utility-maximizing consumption bundles of figs and grapes at E’, subject to the price line P. The MRS for each consumer equals the MRT because both equal the relative price. This implies that the MRS and MRT lines are parallel because they have the same slope, MRS G, F = P G /P F = MRT G,,F The diagram also shows the complete equilibrium model, since, the consumers and producers are maximizing their utility and profit functions. In the meanwhile, the excess demand is zero.