Transcript Intermediate Microeconomic Theory

Intermediate Microeconomic Theory
Exchange
1
What can a market do?

We’ve seen that markets are interesting in that if one exists, and
someone chooses to join, it must make him or her better off.

But how are prices determined? What are they reflecting?

Why are markets a potentially useful way for allocating scarce
resources?

What are potential concerns about using markets as a way of allocating
scarce resources?
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Creating an Economy

We showed in our simple economy how an
individual can potentially be made better off by
interacting in market,


Market opens up the possibility of consuming
preferred bundles to his or her endowment bundle,
where newly available bundles depend on market
prices.
Next, let us consider how market prices are
determined. To do so, let us consider our desert
island again.
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An Endowment Economy


Consider Al and Bill.

Al: endowed with wc,A = 8 and wm,A = 4.

Bill: endowed with wc,B = 4 and wm,B = 6.
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)
Bill’s endowment
qm
Al’s endowment
qm
10
10
6
4
ICA
8
Al
4
12 qc
Bill
coconut milk for Al

ICB
12 qc
coconut milk for Bill
Are there feasible allocations that make both individuals better off
than simply consuming what they are endowed with?
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Edgeworth Box (Preferences)
Bill’s endowment
qm
Al’s endowment
qm
10
10
6
4
ICA
8
Al
4
12 qc
Bill
coconut milk for Al

ICB
12 qc
coconut milk for Bill
First, how do we picture all of the feasible allocations?
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Edgeworth Box (Preferences)
endowment allocation
coconut milk for Bill
coconut milk for Bill
qm
Al’s endowment
qc 12
qm
4
12
4
Bill
10
Bill
10
6
4
lbs. of
mangos
for Bill
lbs. of
mangos
for Bill
lbs. of
mangos
for Al
6
4
10
8
Al
coconut milk for Al

12 qc
qm
8
Al
Bill’s endowment
10
12 qc
coconut milk for Al
How do we picture all of the feasible allocations?

Where do dimensions for Edgeworth Box come from?
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Edgeworth Box (Preferences)
Bill’s endowment
qm
Al’s endowment
qm
10
10
6
4
ICA
8
Al
4
12 qc
Bill
coconut milk for Al

ICB
12 qc
coconut milk for Bill
So, are there feasible allocations that make both individuals better
off than simply consuming what they are endowed with?
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Edgeworth Box (Preferences)
Al’s endowment
coconut milk for Bill
coconut milk for Bill
qm
qc 12
4
qm
12
10
Bill
Bill
4
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 qc
10
qm
Bill’s endowment
Al
8
10
12 qc
coconut milk for Al
So, are there feasible allocations that make both individuals better
off than simply consuming what they are endowed with?
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Efficiency in an Endowment Economy

Pareto Superior (or Pareto Improving) – An
allocation A is said to be Pareto Superior (Pareto
Improving) to an allocation B if A makes at least one
person better off without making anyone else worse off
than B.

Pareto Efficiency – An allocation is Pareto Efficient if
there exists no allocation that makes at least one person
better off without making anyone else worse off (i.e. if
an allocation is Pareto Efficient then there are no Pareto
Superior allocations to that allocation).

In Edgeworth Box,


Which allocations are Pareto Superior to allocation where
each person consumes his endowment?
What will be true at a Pareto Efficient allocation?
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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 could be bought or sold for 1 gal. coconut milk
(i.e. gal. coconut milk is numeraire and pm = 1)
qm
Bill’s endowment
qm
10
10
6
5
5
4
2
Al
7 8
12 qc
4
5
10
12 qc
Bill
Al’s endowment
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Edgeworth Box (Budget Sets)
Consider a market where 1 lb. mango could be bought or sold for 1 gal. coconut milk
(i.e. gal. coconut milk is numeraire and pm = 1)
qm
Al’s endowment
qc 12 10
qm12 10
5 4
10
4
Bill
10
5
5
5
4
2
Al
5
7 8
12 qc
6
6
10
10
qm
Bill
5
4
Al
2
7
8
12 qc
Bill’s endowment
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Edgeworth Box (Budget Sets)
How do things change when 1 lb. mangos could be bought or sold for 2 gal. of
coconut milk (pm = 2)?
qm
qc 12 10
6
qm 12 10
10
4
10
6
4
8
Bill
8
2
5
5
4
6
5
6
2
8
4
8
10
2
10
12 qc
2
Al
6
8
12 qc
Bill
qm
2
5
Al
2
6
8
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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) = qc,A0.5qm,A0.5
 Bill: uB(qc,qm) = qc,B0.5qm,B0.5
wc,A = 8
wc,B = 4
wm,A = 4
wm,B = 6
In equilibrium, can price pm = 1 (where coconut milk is
numeraire so pc implicitly equals 1)?
 What is Al’s budget constraint? Bill’s?


How much coconut milk will Al demand? How about
mangos?
What about Bill’s demands?
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Gross Demands in an Edgeworth Box
qv,B(1, 4, 6) = 5
qm
12
4
Bill
10
qm,B(1,4,6)=5
qm,A(1,8,4)=6
6
4
Al
8
10
12
qc
qc,A(1, 8, 4) = 6
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Gross Demands and Equilibrium


So at relative price of pm = 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.

So what must happen to relative prices?
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Equilibrium Prices

So Equilibrium prices {pc* ,pm*} are such that:
Al’s endowment of coconut milk
qc,A(pc* ,pm*, 8, 4) + qc,B(pc* ,pm*, 4, 6) = 8 + 4
Bill’s endowment of coconut milk
Al’s endowment of mangos
qm,A(pc* ,pm*, 8, 4) + qm,B(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?

What will be each person’s demands at these equilibrium prices?
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Gross Demands in Equilibrium
qc,B(1.2, 4, 6) = 5.6
qm
12
4
Bill
10
qm,B(1.2,4,6)=4.66
qm,A(1.2,8,4)=5.33
6
4
Al
8
10
12 qc
qc,A(1.2, 8, 4) = 6.4
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Equilibrium Prices

This reveals an important property of equilibrium
prices.


They serve as a way of rationing finite resources.
Moreover, does this rationing mechanism (i.e. a
market) lead to a Pareto Improving allocation to
the endowment 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)

Also notable is that First Welfare Theorem holds
even if market participants know nothing about
each others’ preferences!

Great! We have nothing to worry about, the
MARKET can solve all our problems!
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Equity and Efficiency in an Edgeworth Box
m
12
2
Bill
10
3
7
10
Al
10
12 c
While initial distribution of resources does not affect efficiency of
market allocation, it will affect equity of outcomes.
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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.

How do we choose between a more equitable but
inefficient allocation vs. an efficient but unequal
allocation?
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Equity and Efficiency in the Market

Are equity and efficiency 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
12
7
2
Bill
10
“contract curve”
7
3
5
5
10
Al
5
10
How can this
allocation be
supported in a
market
equilibrium?
12 c
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Equity and Efficiency in an Edgeworth Box
m
12
7
2
Bill
10
3
7
5
Al
5
5
10
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.
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Efficiency in a Market with Production

So far our model is awfully simple, goods just fall from trees. How
do things change when goods have to be produced?

The rest of the class will consider this question. For now, let us add
very simple production to our very simple desert island model.
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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
9 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
7
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 or 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”

“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.”
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Discussion of Welfare Theorems

Welfare Theorems suggest that efficiency and other social
objectives do not have to be in conflict.

Great! Now we know we have nothing to worry about, the
MARKET can solve all our problems!

Appropriate Social Goals?


“Behind the Veil of Ignorance”
Re-distribution of endowments?
 “Efficiency/Equity Tradeoff”

So how do we try to re-distribute to minimize this trade-off?
 Note: One way to think about endowment is property rights
(think of Al and Bill), or maybe more simply “rights”
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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. What does
Easterly highlight in “You Can’t Plan a Market”?

Other Limitations? (why did our economy tank in 2008?)
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