Welfare Economics Philip A. Viton May 17, 2012 Philip A. Viton CRP 781 () Welfare May 17, 2012 1 / 1
Economic Systems An economic system is a set of institutional arrangements for the exchange of goods and services between people and productive units (firms). Examples of economic systems: the command system; the dictatorial system; the capitalist system. An economic system results in an allocation: basically a list of who ends up with what. For an individual, we can speak of his or her individual allocation under a particular economic system. Of course, different economic systems will typically result in different allocations. Fundamental question: how can we compare the allocations delivered by different systems? Philip A. Viton CRP 781 () Welfare May 17, 2012 2 / 1
Pareto Optimality The standard approach to the fundamental question of comparing allocations is as follows: 1. We say that an allocation A is Pareto-Preferred to an allocation B if At least one person prefers his/her individual allocation in A Everyone else is indifferent between what he/she receives in A and B 2. We say that an allocation A is Pareto-Optimal if there is no feasible and Pareto-Preferred alternative allocation to it. Equivalently: If an allocation A is Pareto-Optimal, then there is no feasible allocation B such that (i) at least one person prefers B and (ii) everyone else is indifferent. If A is Pareto-Optimal, and B is Pareto-Preferred to A, then B is infeasible. Philip A. Viton CRP 781 () Welfare May 17, 2012 3 / 1
General Equilibrium An economic system is in (general) equilibrium if demands and supplies for all goods, services and inputs balance everywhere. That is, the total demand for each good/service/input equals total supply for that good/service/input. Philip A. Viton CRP 781 () Welfare May 17, 2012 4 / 1
The Competitive Economy We now describe a particular economic system, called the Competitive Economy (the competitive economic system). It is characterized by: All individuals are price-takers and maximize utility subject to their budget constraints. All firms are profit-maximizing price-takers in input and output markets. Philip A. Viton CRP 781 () Welfare May 17, 2012 5 / 1
Competitive Equilibrium We turn now to the construction of a equilibrium for the Competitive Economy. This is called a Competitive Equilibrium. Recall that this involves Supply = Demand for each good (including inputs) and service. So we need to construct aggregate (total) supply and demand functions for each good or service. We can arrive at aggregate demand and supply functions via horizontal addition of individual demand and supply functions. Philip A. Viton CRP 781 () Welfare May 17, 2012 6 / 1
Aggregate Demand in an Industry I p 1 D 11 D 21 p 1 D 1 x 11 x 21 x 11 +x 21 x 1 Philip A. Viton CRP 781 () Welfare May 17, 2012 7 / 1
Aggregate Demand in an Industry II We generate aggregate demand functions via horizontal addition of the individual demand functions. In the figure opposite, we consider the demand for a good x 1 by two utility-maximzing price-taking individuals, whose individual demand functions are D 11 and D 21. At price p 1 individual 1 demands x 11 and individual 2 demands x 21. So at price p 1 aggregate demand (by these two individuals) is x 11 + x 21. We can do this for any price and any number of individuals, and thus generate the aggregate demand function D 1 for good x 1. Philip A. Viton CRP 781 () Welfare May 17, 2012 8 / 1
Aggregate Supply in an Industry I p 1 S 11 S 21 S 1 p 1 x 11 x 21 x 11 +x 21 x 1 Philip A. Viton CRP 781 () Welfare May 17, 2012 9 / 1
Aggregate Supply in an Industry II We generate aggregate supply functions in the same way, via horizontal addition. In the figure opposite, we consider the supply for a good x 1 by two competitive (price-taking, profit-maximizing) firms, whose individual supply functions (the relevant portions of their MC curves) are S 11 and S 21. At price p 1 firm 1 supplies x 11 and firm 2 supplies x 21. So at price p 1 aggregate supply (by these two firms) is x 11 + x 21. We can do this for any price and any number of firms, and so generate the aggregate supply function S 1 for good x 1. Philip A. Viton CRP 781 () Welfare May 17, 2012 10 / 1
Industry Equilibrium and Individual Demand I p 1 D 11 D 21 S 1 p * 1 D 1 x * 11 x * 21 x * 1 x 1 Philip A. Viton CRP 781 () Welfare May 17, 2012 11 / 1
Industry Equilibrium and Individual Demand II In a monetary economy, the feature that brings demand and supply into conformity is prices. An economy is in equilibrium relative to a set of prices in this case the equilibrium prices. The (competitive) equilibrium price in this industry is where aggregate demand equals aggregate supply. In the figure opposite, p1 is the equilibrium price in this industry. Corresponding to the equilibrium price, the individual equilibrium demands are x11 (for individual 1) and x 21 (for individual 2). Philip A. Viton CRP 781 () Welfare May 17, 2012 12 / 1
Industry Equilibrium and Firm Supply I p 1 S 11 S 21 S 1 p * 1 D 1 x * 11 x * 21 x * 1 x 1 Philip A. Viton CRP 781 () Welfare May 17, 2012 13 / 1
Industry Equilibrium and Firm Supply II Corresponding to the equilibrium price p 1, firm 1 supplies x 11 and firm 2 supplies x 21 We can carry out these constructions for each (privately produced) good or service in the economy. Philip A. Viton CRP 781 () Welfare May 17, 2012 14 / 1
Equilibrium in the Competitive Economy In the competitive economy, a competitive equilibrium consists of a set of market and input (factor) prices such that at those prices, demand equals supply for each good or input. First question: does an equilibrium necessarily exist for our competitive economy? Condition C : all indifference curves and isoquants are convex-inwards (ie have the bowed-in shapes that we ve always drawn them, except for indifference curve for addictive goods). Theorem (Debreu: First Theorem of Welfare Economics): If condition C holds, then a competitive equilibrium exists. Philip A. Viton CRP 781 () Welfare May 17, 2012 15 / 1
Optimality in a Competitive Economy Second question: does a competitive equilibrium have any attractive properties? Condition M : (existence of markets). Each good or service that enters into someone s indifference curve or into a production function has a market price. Theorem (Arrow and Debreu: Second Theorem of Welfare Economics): If Condition M holds, then a Competitive Equilibrium is Pareto Optimal. Philip A. Viton CRP 781 () Welfare May 17, 2012 16 / 1
Commentary on These Results It is important to note that there will generally be many possible Pareto-Optimal allocations. Just because an allocation is Pareto-Optimal does not mean that it is ethically desirable (think of the dictatorial allocation). Note that when we try to rank Pareto-Optimal allocations using ethical criteria, we are going beyond the notion of Pareto-Optimality. We cannot guarantee that competition (ie the outcome of the competitive economic system) will result in your ethically preferred Pareto-Optimal allocation, though (if condition M holds) it will result in some Pareto-Optimal allocation. Philip A. Viton CRP 781 () Welfare May 17, 2012 17 / 1
The Third Theorem Let A be your preferred Pareto-Optimal allocation. Theorem (Third Theorem of Welfare Economics). If it is possible to redistribute initial resources (incomes), then we can do so in such a way that A is realized as the result of a competitive economy. In other words, redistribute incomes and let the competitive economy evolve with no further intervention. If we have done the redistribution correctly, the end result will be the pre-selected allocation A. Philip A. Viton CRP 781 () Welfare May 17, 2012 18 / 1
Considerations for Planning Note that our definition of the competitive economy contained no mention of planning, at least as we city planners think of it. We are not saying that the competitive economy could exist with no government at all it probably needs a minimal government, if only to enforce contracts freely entered into (cf Nozick s Night-Watchman State). But it certainly does not include the interventions typically envisioned by planners. So don t these results imply that planning cannot make things better? We know that under competition we arrive at a Pareto Optimal allocation (if M holds); and if we can redistribute income, we can end up with any Pareto-Optimal allocation we like. Can planning improve on that? That is, can we find a role for planning that results in an improvement over what we could achieve with a no-planning competitive economy? Philip A. Viton CRP 781 () Welfare May 17, 2012 19 / 1