Lecture 8
1 Lecture 8
.1 The Normative Theory of Equilibrium 1.1 Pareto Efficiency of Allocation Economists concerns about efficiency of allocation,which means Pareto Efficiency It provides a minimum criterion for efficiency of using resources ·Two basic questions: 2
2 •1 The Normative Theory of Equilibrium • 1.1 Pareto Efficiency of Allocation • Economists concerns about efficiency of allocation, which means Pareto Efficiency • It provides a minimum criterion for efficiency of using resources • Two basic questions:
.(1)If a market equilibrium exists,is it Pareto Efficient? (2)Can any Pareto Efficient allocation be obtained through the market mechanism by redistribution endowments? The concept of Pareto Efficiency is not just to study the efficiency of a market economy,but it also can be used to study the efficiency of any economic system
3 • (1) If a market equilibrium exists, is it Pareto Efficient? • (2) Can any Pareto Efficient allocation be obtained through the market mechanism by redistribution endowments? • The concept of Pareto Efficiency is not just to study the efficiency of a market economy, but it also can be used to study the efficiency of any economic system
Definition 1 (Pareto Improvement):An allocation can have a Pareto improvement if it is feasible and there is another feasible allocation such that one person would be better off and all other persons are not worse off Definition 2 (Pareto Efficiency):An allocation is Pareto efficient or Pareto optimal (P.O)if there is no Pareto improvement,that is,if it is feasible and there is no other feasible allocation such that one person would be better off and all other persons are not worse off
4 • Definition 1 (Pareto Improvement): An allocation can have a Pareto improvement if it is feasible and there is another feasible allocation such that one person would be better off and all other persons are not worse off • Definition 2 (Pareto Efficiency): An allocation is Pareto efficient or Pareto optimal (P.O) if there is no Pareto improvement, that is, if it is feasible and there is no other feasible allocation such that one person would be better off and all other persons are not worse off
More precisely,for exchange economies,a feasible allocation x is P.O if there is no other allocation such that 1.x<=2w i-1 1 2.x,x,for all and xk for some k=1,...n For production economy,(x,y)is P.O if and only if: 1.x≤y+w 2.There is no feasible allocation(x,y)s.t xi,for alli xkx for some k A weaker concept about economic efficiency is the so-called weak Pareto efficiency
5 More precisely, for exchange economies, a feasible allocation x is P.O if there is no other allocation such that 1. 2. for all and for some k=1,…,n For production economy, (x, y) is P.O if and only if: 1. x ≤ y + w 2. There is no feasible allocation s.t for all i for some k A weaker concept about economic efficiency is the so-called weak Pareto efficiency. = = = n i xi wi 1 n i 1 ' . i x i x k k ' i x i x ' ' ( , ) x y x k k ' ' i x i k x ' x
Definition 3(Weak Pareto Efficiency) An allocation is weakly Pareto efficient if it is feasible and there is no other feasible allocation such that all persons are better off. Proposition 1 Under the continuity and strict monotonicity of preferences,weak Pareto efficiency implies Pareto efficiency. The set of Pareto efficient allocations can be shown with the Edgeworth Box.Every point in the Edgeworth Box is attainable. Point A is the starting point and not weak Pareto Optimal.Point B is Pareto optimal
6 • Definition 3 (Weak Pareto Efficiency) An allocation is weakly Pareto efficient if it is feasible and there is no other feasible allocation such that all persons are better off. • Proposition 1 Under the continuity and strict monotonicity of preferences, weak Pareto efficiency implies Pareto efficiency. • The set of Pareto efficient allocations can be shown with the Edgeworth Box. Every point in the Edgeworth Box is attainable. • Point A is the starting point and not weak Pareto Optimal. Point B is Pareto optimal
The locus of all Pareto efficient allocations is called the contract curve. Equity and Pareto efficiency are two different concepts.The point O and Og are Pareto optimal points,but these are extremely unequal. To make an allocation be relatively equitable and also efficient,government needs to implement some institutional arrangements such as tax,subsidy to balance between equity and efficiency,but this is a value judgment and policy issue
7 • The locus of all Pareto efficient allocations is called the contract curve. • Equity and Pareto efficiency are two different concepts. The point and are Pareto optimal points, but these are extremely unequal. • To make an allocation be relatively equitable and also efficient, government needs to implement some institutional arrangements such as tax, subsidy to balance between equity and efficiency, but this is a value judgment and policy issue. OA OB
When Pareto efficient points are given by tangent points of two persons'indifference curves,it should satisfy the following conditions: MRS A(,x2)=MRS(x,x2) 8
8 • When Pareto efficient points are given by tangent points of two persons’ indifference curves, it should satisfy the following conditions: ( , ) ( , ) 1 2 1 2 MRS x x MRS x x A B =
1.2 The First Fundamental Theorem of Welfare Economics There is a well-known theorem and one of the most important theorems in economics,which characterizes a desirable nature of the competitive market institution. It claims that every competitive equilibrium allocation is Pareto efficient. A remarkable part of this theorem is that the theorem requires few assumptions,much fewer than those for the existence of competitive equilibrium Some implicit assumptions in this section are that preferences are orderings,goods are divisible, and there are no public goods,or externalities
9 1.2 The First Fundamental Theorem of Welfare Economics • There is a well-known theorem and one of the most important theorems in economics, which characterizes a desirable nature of the competitive market institution. • It claims that every competitive equilibrium allocation is Pareto efficient. • A remarkable part of this theorem is that the theorem requires few assumptions, much fewer than those for the existence of competitive equilibrium • Some implicit assumptions in this section are that preferences are orderings, goods are divisible, and there are no public goods, or externalities
Theorem 1 (The First Fundamental Theorem of Welfare Economics)If(x,y,p) is a competitive equilibrium,then x is weakly Pareto Efficient,and further under local non-satiation,it is Pareto efficient If the local non-satiation condition is not satisfied,a competitive equilibrium allocation x may not be Pareto optimal, for the case of thick indifference curves. Note that neither convexity of preference nor convexity of production set is assumed in the theorem. 10
10 • Theorem 1 (The First Fundamental Theorem of Welfare Economics) If (x, y, p) is a competitive equilibrium, then x is weakly Pareto Efficient, and further under local non-satiation, it is Pareto efficient • If the local non-satiation condition is not satisfied, a competitive equilibrium allocation x may not be Pareto optimal, for the case of thick indifference curves. • Note that neither convexity of preference nor convexity of production set is assumed in the theorem