intermediate microeconomic theory

1

Intermediate Microeconomic Theory

Exchange

2

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 wc

A = 8 and wmA = 4.

Bill: endowed with wcB = 4 and wm

A = 6.

3

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?

4

Edgeworth Box (Preferences)

Are there feasible bundles that make both individuals better off?

8 12 qc

qm

10

4

qm

10

6

4 12 qc

Al Bill

ICA ICB

coconut milk for Alcoconut milk for Bill

5

Edgeworth Box (Preferences)

Are there feasible bundles that make both individuals better off?

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 Bill

6

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?

7

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)

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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)

10


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?

12

Equilibrium Prices

Consider Al and Bill. Al: uA(qc,qm) = qc

0.5qm0.5 wc

A = 8 wmA = 4

Bill: uB(qc,qm) = qc0.5qm

0.5 wcB = 4 wm

B = 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 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

qcA(1, 8, 4) = 6

qmB(1,4,6)=5

qvB(1, 4, 6) = 5

14

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. So what must happen to relative prices?

15

Equilibrium Prices

So Equilibrium prices {pc*

,pm*} are such that:

qcA(pc

* ,pm

*, 8, 4) + qcB(pc

* ,pm

*, 4, 6) = 8 + 4

qmA(pc

* ,pm

*, 8, 4) + qmB(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)=5.3

qcA(1.2, 8, 4) = 6.4

qmA(1.2,4,6)=4.66

qcB(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.

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?

18

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

10

7

Al 10 12 c

2 Bill

3

20

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?

21


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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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.

5

7

5 5

23

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.

24

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”

25

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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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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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

5

Al 3 7 9 12 coconut milk

Bill4

2

28


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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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.”

Relatedly, William Easterly relates the old joke: “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?

intermediate microeconomic theory

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