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1 Intermediate Microeconomic Theory Exchange
1
Intermediate Microeconomic Theory
Exchange
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)
Are there feasible allocations that make both individuals better off than simply consuming what they are endowed with?
8 12 qc
qm
10
4
qm
10
6
4 12 qc
Al Bill
ICA ICB
coconut milk for Al coconut milk for Bill
Al’s endowment
Bill’s endowment
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Edgeworth Box (Preferences)
First, how do we picture all of the feasible allocations?
8 12 qc
qm
10
4
qm
10
6
4 12 qc
Al Bill
ICA ICB
coconut milk for Al coconut milk for Bill
Al’s endowment
Bill’s endowment
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Edgeworth Box (Preferences)
How do we picture all of the feasible allocations? Where do dimensions for Edgeworth Box come from?
8 12 qc
qm
10
4 6
10
qm
qc 12 4
Al
Bill
qm
10
4
8 12 qc
4
6
Al
Bill
lbs. of mangos for Al
coconut milk for Al
coconut milk for Bill
lbs. of mangos for Bill
coconut milk for Al
lbs. of mangos for Bill
coconut milk for Bill
Al’s endowment
Bill’s endowment
endowment allocation
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Edgeworth Box (Preferences)
So, are there feasible allocations that make both individuals better off than simply consuming what they are endowed with?
8 12 qc
qm
10
4
qm
10
6
4 12 qc
Al Bill
ICA ICB
coconut milk for Al coconut milk for Bill
Al’s endowment
Bill’s endowment
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Edgeworth Box (Preferences)
So, are there feasible allocations that make both individuals better off than simply consuming what they are endowed with?
8 12 qc
qm
10
4 6
10
qm
qc 12 4
Al
Bill
ICA
ICB
qm
10
4
8 12 qc
ICA
4
ICB
6
Al
Bill
lbs. of mangos for Al
coconut milk for Al
coconut milk for Bill
lbs. of mangos for Bill
coconut milk for Al
lbs. of mangos for Bill
coconut milk for BillAl’s endowment
Bill’s endowment
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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)
2 7 8 12 qc
qm
10
5
4
qm
10
6
5
4 5 10 12 qc
Al Bill
Consider a market where 1 lb. mango must be traded for 1 gal. coconut milk (i.e. gal. coconut milk is numeraire and pm = 1)
Al’s endowment
Bill’s endowment
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Edgeworth Box (Budget Sets)
2 7 8 12 qc
qm
10
5
4
5
6
10
qm
qc 12 10 5 4
Al Bill
qm
10
5
4
2 7 8 12 qc
10 5 4
5
6
Al
Bill
Consider a market where 1 lb. mango must be traded for 1 gal. coconut milk (i.e. gal. coconut milk is numeraire and pm = 1)
Al’s endowment
Bill’s endowment
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Edgeworth Box (Budget Sets)
2 6 8 12 qc
qm
10
8
5
4
2
2
5
6
8
10
qm
qc 12 10 6 4
Al Bill
qm
10
8
5
4
2 2 7 8 12 qc
10 5 4
5
6
Al
Bill
How do things change when 1 lb. mangos costs 2 gal. of coconut milk (pm = 2)?
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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,A
0.5 wc,A = 8 wm,A = 4 Bill: uB(qc,qm) = qc,B
0.5qm,B0.5 wc,B = 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
qm
10
4
Al 8 12 qc
4 Bill
6qm,A(1,8,4)=6
qc,A(1, 8, 4) = 6
qm,B(1,4,6)=5
qv,B(1, 4, 6) = 5
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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:
qc,A(pc*
,pm*, 8, 4) + qc,B(pc
* ,pm
*, 4, 6) = 8 + 4
qm,A(pc*
,pm*, 8, 4) + qm,B(pc
* ,pm
*, 4, 6)= 4 + 6
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?
Al’s endowment of coconut milk
Bill’s endowment of coconut milk
Al’s endowment of mangos
Bill’s endowment of mangos
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Gross Demands in Equilibrium
qm
10
4
Al 8 12 qc
4 Bill
6qm,A(1.2,8,4)=5.33
qc,A(1.2, 8, 4) = 6.4
qm,B(1.2,4,6)=4.66
qc,B(1.2, 4, 6) = 5.6
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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 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 Thm 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
10
7
Al 10 12 c
2 Bill
3
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 an 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
10
7
5
Al 5 10 12 c
7 2 Bill
3
5contract curveHow can this allocation be supported in a market equilibrium?
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Equity and Efficiency in an Edgeworth Box
m
10
7
Al 10 12 c
2 Bill
3
How can this allocation be supported in a market equilibrium?
Reallocate endowments to this allocation, then find equilibrium price.
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7
5 5
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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.
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 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).
What does curvature of each individual’s production frontier imply? What does comparing intercepts across individuals reveal?
mangos12
Al 12 coconut milk
mangos
8
Bill 9 coconut milk
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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.
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!
mangos12
5
Al 3 12 coconut milk
mangos
8
2
Bill 4 9 coconut milk
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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.
However, while Al has an absolute advantage in both goods, Bill has a comparative advantage in producing coconut milk.
mangos12
7
5
Al 3 7 9 12 coconut milk
Bill4
2
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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.
With specialization, a total of 12 lbs. of mangos and 9 gal. of coconut milk will be produced and consumed.
mangos12
5
Al 3 7 9 12 coconut milk
mangos
12
Bill
9 coconut milk
4
2
4
2
Bill
Al
without trade or specialization with trade and specialization
9
5
3
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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.”
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!
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”
Appropriate Social Goals? “Behind the Veil of Ignorance”
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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?)
