Download Welfare Economics Economic Systems Pareto Optimality General

Economic Systems
An economic system is a set of institutional arrangements for the
exchange of goods and services between people and productive units
(…rms).
Welfare Economics
Examples of economic systems: the command system; the dictatorial
system; the capitalist system.
Philip A. Viton
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.
May 17, 2012
Of course, di¤erent economic systems will typically result in di¤erent
allocations.
Fundamental question: how can we compare the allocations delivered
by di¤erent systems?
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
1 / 19
Pareto Optimality
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
2 / 19
General Equilibrium
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 indi¤erent 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:
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.
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 indi¤erent.
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 / 19
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
4 / 19
The Competitive Economy
Competitive Equilibrium
We turn now to the construction of a equilibrium for the Competitive
Economy.
We now describe a particular economic system, called the Competitive
Economy (the competitive economic system). It is characterized by:
This is called a Competitive Equilibrium.
All individuals are price-takers and maximize utility subject to their
budget constraints.
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.
All …rms are pro…t-maximizing price-takers in input and output
markets.
Philip A. Viton
CRP 781 ()— Welfare
We can arrive at aggregate demand and supply functions via
horizontal addition of individual demand and supply functions.
May 17, 2012
5 / 19
Aggregate Demand in an Industry I
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
6 / 19
Aggregate Demand in an Industry II
p1
D11
We generate aggregate demand functions via horizontal addition of
the individual demand functions.
D21
In the …gure opposite, we consider the demand for a good x1 by two
utility-maximzing price-taking individuals, whose individual demand
functions are D11 and D21 .
p1
At price p1 individual 1 demands x11 and individual 2 demands x21 .
So at price p1 aggregate demand (by these two individuals) is
x11 + x21 .
D1
We can do this for any price and any number of individuals, and thus
generate the aggregate demand function D1 for good x1 .
x11
Philip A. Viton
x21
x11+x21
CRP 781 ()— Welfare
x1
May 17, 2012
7 / 19
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
8 / 19
Aggregate Supply in an Industry I
Aggregate Supply in an Industry II
p1
S11
We generate aggregate supply functions in the same way, via
horizontal addition.
S1
S21
In the …gure opposite, we consider the supply for a good x1 by two
competitive (price-taking, pro…t-maximizing) …rms, whose individual
supply functions (the relevant portions of their MC curves) are S11
and S21 .
p1
At price p1 …rm 1 supplies x11 and …rm 2 supplies x21 .
So at price p1 aggregate supply (by these two …rms) is x11 + x21 .
We can do this for any price and any number of …rms, and so
generate the aggregate supply function S1 for good x1 .
x11
Philip A. Viton
x21
x1
x11+x21
CRP 781 ()— Welfare
May 17, 2012
9 / 19
Industry Equilibrium and Individual Demand I
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
10 / 19
Industry Equilibrium and Individual Demand II
p1
D11
D21
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.
S1
The (competitive) equilibrium price in this industry is where
aggregate demand equals aggregate supply.
p*1
In the …gure opposite, p1 is the equilibrium price in this industry.
D1
x*11 x*21
Philip A. Viton
Corresponding to the equilibrium price, the individual equilibrium
demands are x11 (for individual 1) and x21 (for individual 2).
x1
x*1
CRP 781 ()— Welfare
May 17, 2012
11 / 19
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
12 / 19
Industry Equilibrium and Firm Supply I
Industry Equilibrium and Firm Supply II
p1
S11
S21
S1
Corresponding to the equilibrium price p1 , …rm 1 supplies x11 and
…rm 2 supplies x21
p*1
We can carry out these constructions for each (privately produced)
good or service in the economy.
D1
x*11
Philip A. Viton
x*21
x1
x* 1
CRP 781 ()— Welfare
May 17, 2012
13 / 19
Philip A. Viton
CRP 781 ()— Welfare
May 17, 2012
Equilibrium in the Competitive Economy
Optimality in a 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.
Second question: does a competitive equilibrium have any attractive
properties?
First question: does an equilibrium necessarily exist for our competitive
economy?
Condition C : all indi¤erence curves and isoquants are
convex-inwards (ie have the bowed-in shapes that we’ve always drawn
them, except for indi¤erence 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 / 19
14 / 19
Condition M : (existence of markets). Each good or service that
enters into someone’s indi¤erence 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 / 19
Commentary on These Results
The Third Theorem
It is important to note that there will generally be many possible
Pareto-Optimal allocations.
Let A be your preferred Pareto-Optimal allocation.
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 / 19
Considerations for Planning
Note that our de…nition 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 …nd 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 / 19
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 / 19