General Equilibrium Theory and Collective Decision MakingOutline1. General vs partial equilibrium theory2. Transformation functions and general equilibriumi. productionii exchange3. Collective Decision making1. General vs partial equilibrium theoryGeneral equilibrium theory or GE differs from partial equilibrium theory in thatthe latter examines a single market ignoring what goes on in other markets and may,even, assume that other markets are in equilibrium where p=mc (this gets into issues ofsecond best which we do not consider here). GE takes the perspective that what happensin one market can have repercussions throughout a large number of directly andindirectly related markets. GE is the economists perspective of 'Systems analysis' in thatthe analysis looks beyond an individual market or setting. The boundaries of GE aresomewhat difficult to establish. Early on a GE problem would limit itself to severalmarkets since computing the equilibrium was difficult but with the computer poweravailable today, large scale computable GE models are common. All of this is not tocastigate partial equilibrium analysis. It remains a power analytical approach providedparticular conditions are met. First, if the problem is dealing with a good or service forwhich there are few substitutes or complements or these are considered in the analysis orthe good or service has a low income elasticity of demand, partial equilibrium analysiswill do a very good job.2. Transformation functions and exchangei. productionGE takes account of the impact of changes in one market and examines how it may affectthe equilibrium condition sin other markets; input and output markets are consideredtogether. It may happen that an increase in demand for trucking services not only affectsthe trucking market but also the rail and air cargo market as well as the factor markets forcapital, fuel and labor; this is the 'stuff' of GE models.Although all of these things happen simultaneously I treat them in a sequence or holdother things constant. Consider first the factor market in a two good world in which thereis a fixed amount of capital, K and labor, L. These two inputs produce two products Xand Y with production functions; X=fx(k,l) and Y=fy(k,l). I could treat n outputs and minputs but the conclusions would not change.The markets can be illustrated graphically with the use of an "Edgeworth-Bowly Box"diagram. The dimensions of the box are defined by the amount of K and L. If there werean increase in total K, for example, the length of the box would increase. Note that capitalis used in the production of X and Y with no unemployment. One can handle unemployedresources in this framework but this is not of concern to us at this point.Consider point A, at this point the ration of marginal products of k and l are differentbetween two industries, X and Y. There are opportunities for gain by industry X usingexcess labor to but capital and industry Y using excess capital to but labor. This tradingwill continue until a point such as E where the two MRTS are equal. Note that we couldjust have easily moved to a point such as B along x's isoquant rather than along y's.Realistically we would likely end up somewhere in between on the 'contract curve'. Thisis the locus of points along which the MRTS in X is equal to the MRTS in Y. Note that apoint such as E defines a given output of X and a given output of Y. The same is true allalong the contract curve. Therefore, the contract curve determines the productionpossibilities frontier or production possibilities curve (PPC). It is clear that the contractcurve will be determined by the production functions or shape of the isoquants.Therefore, any change in these isoquants will show up as a change in the PPCPoint E will be a point on the PPC and will define a given output of X and Y. Individualsi and j earn income from their labor in producing X and Y and in their ownership (if any)of capital in producing X and Y.ii. ExchangeThe figure below illustrates the 'exchange box'. The process is the same as that whichoccurred in the factor market equilibrium. Point B on the PPC defines how much of goodX and Y are produced. Suppose the initial endowment point in exchange space is point f.Here we can see the MRS for individual i is not equal to the MRS for individual j, atpoint f the indifference curves cross. As before there are gains from trade. Individual igives up x in order to buy y and individual j gives up y in order to buy x. They move toan equilibrium point such as e where the MRS for i = MRS for j = price x/price y. That isthe trading by i and j for x and y with their incomes derived from labor and the ownershipof capital, will result in a Pareto optimal point such as e. All points on the contract curveare Pareto optimal.YXB•0i0j0••I1iI1jI2jX1iX0iX1jX0jY1iY0iY1jY0jefHow does one select from among the set of Pareto Optimal points? There have been anumber of 'welfare' criteria introduced into economics. One criteria is called the Kaldorcriteria. It states that one point on the contract curve is better than another if the gainerscan compensate the losers so neither will be worse off; in other words, if the gainers gainsufficient amounts that they can compensate the losers to make them as well off as theywere previously and still have sufficient left over to gain, the new equilibrium is better.3. Collective Decision makingThus far the assumption has been that decisions are made on the basis of a single criteriondeterministic - cost minimization or output maximization- individual utility- net social benefitstochastic - maximum payoff- expected utilityA single criteria approach assumes that all affected parties agree to it and that personswho do accept the criteria can impose it on those who do not.When does everyone agree? This was established in the above section on GE. Contractcurves provide the set of Pareto efficient outcomes. Maximization of Net Social Benefitgets us to a Pareto Efficient allocation - given the distribution of income. However, aPareto efficient outcome is not necessarily Pareto superior. NSB does not determinewhere on the contract curve is better. As we saw another criteria such as the Kaldorcriteria needs to be introduced.The reasons not all improvements can be made Pareto superior are:- transactions cost- attaining true valuations- endorsement of the status quo distributionWith any case in which there are winners and losers, there is difficulty on the