The Economics Book

212

It was known that a single market
could achieve this balance, or
equilibrium, but it was not clear
that a whole set of markets could
do the same thing.
The problem of “general
equilibrium” was rigorously solved
in 1954 by French mathematician
Gérard Debreu and US economist
Kenneth Arrow (p.209). Applying
advanced mathematics, they
showed that under certain
circumstances a set of markets
could achieve an overall
equilibrium. In a sense Arrow
and Debreu had reworked Adam
Smith’s argument that free
markets would lead to social order.
But Smith made a stronger claim
than the purely factual one that
markets tend toward a point of

stability. He also said that this

equilibrium was desirable

because it entailed a free society.

Pareto-efficient outcomes

Modern economists measure

desirability using a concept known

as “Pareto efficiency” (pp.130–31).

In a Pareto-efficient situation it

is impossible to make one person

better off without making another

person worse off. An improvement

takes place in an economy if goods

change hands in such a way that at

least one person’s welfare increases

and no one else’s falls. Arrow and

Debreu connected market

equilibrium with Pareto efficiency.

In doing so they rigorously probed

Smith’s ultimate contention that

market outcomes are good. They

MARKETS AND SOCIAL OUTCOMES

An Edgeworth box is a way of showing the distribution of goods in an
economy. In this example the economy contains two people—Ben and Sarah
—and two goods—20 apples and 10 pears. Each point in the box represents a
possible distribution of apples and pears between Ben and Sarah. The yellow
line is the contract curve, which represents the possible allocation of goods
that could be reached by Ben and Sarah after trading with each other.
Trading to points on this curve leads to Pareto efficiency.

did this by proving two theorems,

known as the “fundamental

theorems of welfare economics.”

The first welfare theorem holds

that any pure free market economy

in equilibrium is necessarily

“Pareto efficient”—that it leads to a

distribution of resources in which

it is impossible to make someone

better off without making someone

else worse off. Individuals begin

with an “endowment” of goods.

They trade with each other and

reach an equilibrium, which the

theorem holds will be efficient.

Pareto efficiency is a weak

ethical criterion. A situation in

which one rich person has all of a

desired good and eveyone else has

none of it would be Pareto efficient

because it would be impossible to

remove some of the good from the

rich person without making him

worse off. So this first welfare

theorem says that markets are

efficient but says nothing about

the critical issue of distribution.

The second welfare theorem

deals with this problem. In an

economy there are typically many

Pareto-efficient allocations of

resources. Some will be fairly equal

distributions, some highly unequal.

How this coordination

[of supply and demand]

takes place has been a

central preoccupation

of economic theory since

Adam Smith.

Kenneth Arrow

BEN’S APPLES

Contract

curve

SARAH’S APPLES

SARAH’S PEARS

BEN’S PEARS Ben (10 apples, 5 pears)

Sarah (10 apples, 5 pears)

Ben (6 apples, 2 pears)

Sarah (14 apples, 8 pears)

Ben (15 apples, 9 pears)

Sarah (5 apples, 1 pear)

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4 6

6 4

8

10

8

10

2

0 5 10 15 20

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