Transcript Intermediate Microeconomic Theory

Intermediate Microeconomic Theory
Exchange
1
Creating an Economy

So far, we showed how an individual can
potentially be made better off by a market,

Market opens up the possibility of consuming
preferred bundles to his or her endowment.

What we have to consider however, is how
market prices are determined.

To do so, let us consider our desert island again.

Al: endowed with wAc = 8 and wAm = 4.

Bill: endowed with wBc = 4 and wBm = 6.
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An Endowment Economy

This means on the whole island, there are



8 + 4 = 12 gallons of coconut milk
4 + 6 = 10 lbs. of mangos.
Consider first each person’s well-being in the
absence of any market.


Each person must simply consume his endowment.
What is “wrong” with this allocation of island
resources?
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Edgeworth Box (Preferences)
m
m
10
10
6
4
ICA
8
Al

ICB
4
12 c
12 c
Bill
Are there feasible bundles that make both individuals better off?
4
Edgeworth Box (Preferences)
coconut milk for Bill
coconut milk for Bill
m
m
c
12
4
4
Bill
10
Bill
10
4
6
ICA
lbs. of
mangos
for Bill
lbs. of
mangos
for Bill
lbs. of
mangos
for Al
6
4
ICA
ICB
ICB
8
Al
coconut milk for Al

12 c
10
m
Al
8
12 c
coconut milk for Al
Are there feasible bundles that make both individuals better off?
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Efficiency in an Endowment Economy

Pareto Efficiency – There exists no allocation
that makes at least one person better off without
making anyone else worse off.

Pareto Superior – An allocation that makes at
least one person better off without making anyone
else worse off.

In Edgeworth Box, which allocations are Pareto
Superior to allocation where each person consumes
his endowment?
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An Endowment Economy (Buying and Selling)

What happens if there is a market where
coconuts can be traded for mangos?


Can this be Pareto Improving (i.e. make at least
one of them better off while making no one
worse off)?
Suppose 1 gal. coconut milk can be traded for
1 lb. of mangos.

How will this affect each person’s budget set?
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Edgeworth Box (Budget Sets)
Consider a market where 1 lb. mango must be traded for 1 gal. coconut milk (coconut
milk is numeraire and pm = 1)
m
m
m
10
10
5
4
Bill
10
10
6
5
5
4
2
Al
7 8
12 c
4
5
10
12 c
5
5
4
6
Al
2
7
8
12 c
Bill
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Edgeworth Box (Budget Sets)
How do things change when 1 lb. of mango costs 2 gal. of coconut milk (pm = 2)?
m
m
m
6
4
Bill
10
10
10
8
8
8
2
5
5
4
6
2
8
6
5
5
4
2
2
6
Al
8
12 c
4
6
12 c
Al
6
8
12 c
Bill
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Edgeworth Box (Budget Sets)
So like with Buying and Selling, change in price simply rotates budget constraint around
endowment point.
m
m
m
10
4
Bill
10
10
10
8
8
2
8
6
4
6
2
8
4
2
2
8
Al
12 c
4
10 12 c
Al
8
12 c
Bill
Rise in price of mangos (in terms of coconut milk) flattens B.C.
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Equilibrium Prices

The key question then is what prices
can be maintained in an equilibrium?
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Equilibrium Prices


Consider Al and Bill.
 Al:
uA(qc,qm) = qc0.5qm0.5
 Bill: uB(qc,qm) = qc0.5qm0.5
wAc = 8 wAm = 4
wBc = 4 wBm = 6
In equilibrium, can price pm = 1 (where pc implicitly equals 1)?
 What is Al’s budget constraint? Bill’s?

How much coconut milk will Al demand? How about Bill?

How much mango will Al demand? How about Bill?
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Gross Demands in an Edgeworth Box
qBc(1, 4, 6) = 5
m
4
Bill
10
qBm(1,4,6)=5
qAm(1,8,4)=6
6
4
Al
8
12
c
qAc(1, 8, 4) = 6
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Gross Demands and Equilibrium


So at prices pm = 1 and where pc =1 (i.e. when 1 lb. of mangos can
be traded for 1 gal. of coconut milk ), there is:

A excess demand for mangos (6 + 5 = 11 lbs. are demanded, but only 10
lbs. exist)

A excess supply of coconut milk (6 + 5 = 11 gallons are demanded, but
12 gallons exist).
Equilibrium prices must be market clearing, or equate demand with
supply.
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Equilibrium Prices

So Equilibrium prices {pc* ,pm*} are such that:
Al’s endowment of coconut milk
qcA(pc* ,pm*, 8, 4) + qcB(pc* ,pm*, 4, 6) = 8 + 4
Bill’s endowment of coconut milk
Al’s endowment of mangos
qmA(pc* ,pm*, 8, 4) + qmB(pc* ,pm*, 4, 6)= 4 + 6
Bill’s endowment of mangos

What are the demand functions for each good for Al and Bill given arbitrary
prices?

How do we use these demand functions to find the (relative) prices that can be
maintained in equilibrium?
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Gross Demands in Equilibrium
qBc(1, 4, 6) = 5.6
m
4
Bill
10
qBm(1,4,6)=4.66
qAm(1,8,4)=5.33
6
4
Al
8
12
c
qAc(1, 8, 4) = 6.4
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Equilibrium Prices

So in equilibrium, a pound of mangos cannot be
obtained for 1 gal. of coconut milk.

Rather, 6/5 gal. of coconut milk must be traded
for a pound of mangos.

Why is this the case?
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Equilibrium Prices

This reveals an important property of equilibrium
prices.

They serve as a way of rationing finite resources.

Does this rationing mechanism (i.e. a market) lead
to a Pareto improving allocation in equilibrium?

What will be true at a Pareto Efficient allocation?

Does market lead to Pareto Efficient allocation?
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Markets and Efficiency

First Welfare Theorem – Under Perfectly
competitive markets, all market equilibria are
Pareto Efficient regardless of initial distributions
of resources (i.e. endowments)

While distribution of initial resources does not
affect efficiency of market allocation, it will
affect equity.
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Equity and Efficiency in an Edgeworth Box
m
2
Bill
10
3
7
Al
10
12 c
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Equity and Efficiency in the Market

So while efficiency is one criteria for a “good”
allocation, another criteria might be that it meets
certain equity principles.

Are these goals always in conflict?

Not necessarily

Consider all the possible Pareto Efficient
Allocations (contract curve).

Which of these allocations can be maintained in
a market equilibrium given appropriate
redistributions of endowments?
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Equity and Efficiency in an Edgeworth Box
m
7
2
Bill
10
contract curve
7
3
5
5
How can this
allocation be
supported in a
market
equilibrium?
Al
5
10
12 c
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Equity and Efficiency in an Edgeworth Box
m
7
2
Bill
10
7
3
5
5
Al
5
10
12 c
How can this
allocation be
supported in a
market
equilibrium?
Reallocate
endowments
to this
allocation,
then find
equilibrium
price.
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Equity and Efficiency with Re-distribution

Second Welfare Theorem – (If all individuals have convex
preferences) There will always be a set of prices such that each
Pareto Efficient allocation can be maintained in a market
equilibrium given an appropriate re-distribution of endowments.
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Discussion of Welfare Theorems

First Welfare Theorem


Reveals that markets can provide a mechanism that ensure Pareto Efficient
outcomes, even if any given individual’s information is very limited.
Second Welfare Theorem

Reveals that issues of efficiency and distribution can potentially be separated.

Society can decide on what is a just distribution of welfare, and markets can
potentially be used to achieve it.

In other words, markets can potentially be part of the solution to achieving a
“more just” distribution of welfare.

Market prices should be used to reflect relative scarcity,

Endowment/Lump-sum transfers should be used to adjust for
distributional goals.

John Rawls “Behind the Veil”
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Efficiency in a Market with Production

Now, suppose that instead of simply being endowed with coconut
milk or mangos, Al and Bill had to produce them.

In particular, suppose each of their production possibilities sets are
given below (i.e. all the bundles they could produce).
mangos
mangos
12
8
Al


12 coconut milk
Bill
8 coconut milk
What does curvature of each individual’s production frontier imply?
What does comparing intercepts across individuals reveal?
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Efficiency in a Market with Production

In absence of trade, production possibility sets are effectively each
person’s budget set.

Therefore, in absence of trade, each person picks the bundle in
production possibilities set/budget set that gets him to highest I.C.
mangos
mangos
12
8
5
2
Al


3
12 coconut milk
Bill
4
9 coconut milk
So in the absence of trade, a total of 5 + 2 = 7 lbs. of mangos and 3 + 4
= 7 gal. of coconut milk will be produced and consumed.
Neither person specializes!
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Efficiency in a Market with Production

Note that without a market, neither person would choose to specialize in
only producing one thing since they like to consume both.

The Edgeworth Box view of this non-trade world is depicted below.
mangos
12
Bill
4
2
5
Al

3
7
9
12 coconut milk
However, while Al has an absolute advantage in both goods, Bill has a
comparative advantage in producing coconut milk.
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Efficiency in a Market with Production

Therefore, suppose Bill specializes in producing coconut milk, Al
specializes in producing mangos, and then both trade.
without trade and specialization
mango
s
mangos
12
4
Bill
Bill
2
2
5

9
12
4
Al
with trade and specialization
3
7
9
5
12 coconut milk
Al
3
9 coconut milk
With specialization, a total of 12 lbs. of mangos and 9 gal. of coconut
milk will be produced and consumed.
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Efficiency in a Market with Production

Adam Smith’s “Invisible Hand”


Relatedly, William Easterly relates the old joke:


“It is not from the benevolence of the butcher, the brewer, or the baker,
that we expect our dinner, but from their regard to their own interest. We
address ourselves, not to their humanity but to their self-love, and never
talk to them of our necessities but of their advantages.”
“Heaven is where the chefs are French, the police are British, the lovers
are Italian, the car mechanics are German, and it is all organized by the
Swiss. Hell is where the chefs are British, the police are German, the
lovers are Swiss, the car mechanics are French and it is all organized by
the Italians.”
Specialization doesn’t necessarily involve innate abilities. Rather
each person (or country) does a task repeatedly and practice makes
perfect. We can then trade this greater number of products that arise
through specialization and all become better off.
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Why Can the Welfare Theorems Fail?

Welfare Theorems are why “free market” policies are often imposed
on developing or transitioning economies as a pre-condition to aid.

Problem: Well functioning markets are not assured. Numerous
conditions are necessary for markets to function well.


What does Easterly highlight in “You Can’t Plan a Market”?
Other Limitations?
 What if agents act strategically rather than as price takers?
 What if one person’s consumption affects another person’s utility
or one firms production affects another firm’s costs?
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