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 wAc = 8 and wAm = 4.
Bill: endowed with wBc = 4 and wBm = 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? m 10 4 m 10 6
ICA
ICB c c Al
Bill

5. Edgeworth Box (Preferences)
Are there feasible bundles that make both individuals better off?
coconut milk for Bill
coconut milk for Bill
Bill m 10 4 m 10 4 4 c
Bill 6 10 m
lbs. of mangos for Bill
lbs. of mangos for Al
lbs. of mangos for Bill 6
ICA
ICA
ICB
ICB c Al c Al
coconut milk for Al
coconut milk for Al

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?
Prices: 1 coconut can be traded for 2 mangos
If Al sold all 10 of his coconuts, he would have = 24 mangos
But there are on 14 coconuts total, so the most he could do is sell 5 coconuts and end up with = 14 mangos and 5 coconuts
If Al sold all 4 of his mangos, he would have = 12 coconuts and have zero mangos
Prices: 2 coconuts for 1 mango
If Al sold all 10 of his coconuts, he would have = 9 mangos
If Al sold all 4 of his mangos, he would have = 18 coconuts
However, since there are only 14 coconuts total, the most he could do is to sell 2 of his mangos, giving him = 14 coconuts and 2 mangos.

8. 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 10 5 4 m 10 6 5 m 10 5 4
Bill 5 6 c c Al c
Bill Al

9. Edgeworth Box (Budget Sets)
How do things change when 1 lb. of mango costs 2 gal. of coconut milk (pm = 2)? m 10 8 5 4 2 m 10 8 5 4 2 m 10 8 6 5 2
Bill 2 5 6 8
So if 2 coconuts can be traded for one mango, the
Al could trade 2 of his mangos for 4 more coconuts (for a total of all 14)
Al could trade all 10 of his coconuts for 5 more mangos (for a total of 9)
Bill could trade 5 of his mangos for 10 more coconuts (giving him all 14 coconuts)
Bill could trade all 4 of his coconuts for 2 more mangos (giving him a total of 12 mangos) c c Al c
Bill Al

10. Edgeworth Box (Budget Sets)
So like with Buying and Selling, change in price simply rotates budget constraint around endowment point. m 10 8 4 2 m 10 8 4 2 m 10 8 6 2
Bill 2 6 8
So if 2 coconuts can be traded for one mango, the
Al could trade 2 of his mangos for 4 more coconuts (for a total of all 14)
Al could trade all 10 of his coconuts for 5 more mangos (for a total of 9)
Bill could trade 5 of his mangos for 10 more coconuts (giving him all 14 coconuts)
Bill could trade all 4 of his coconuts for 2 more mangos (giving him a total of 12 mangos) c c Al c
Bill Al
Rise in price of mangos (in terms of coconut milk) flattens B.C.

11. 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) = qc0.5qm wAc = wAm = 4
Bill: uB(qc,qm) = qc0.5qm wBc = 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?

13. Gross Demands in an Edgeworth Box10 4 Al
qBc(1, 4, 6) = 5 6
Bill
qBm(1,4,6)=5
So at these prices there is an excess demand for coconuts and an excess supply of mangos!
What has to happen to prices to equate demand and supply?
Price of coconuts must rise relative to the price of mangos.
What will this do to budget constraint? Steepen it!
qAm(1,8,4)=6 c
qAc(1, 8, 4) = 6

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.

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

16. Gross Demands in Equilibrium10 4 Al
qBc(1, 4, 6) = 5.6 6
Bill
qBm(1,4,6)=4.66
So at these prices there is an excess demand for coconuts and an excess supply of mangos!
What has to happen to prices to equate demand and supply?
Price of coconuts must rise relative to the price of mangos.
What will this do to budget constraint? Steepen it!
qAm(1,8,4)=5.33 c
qAc(1, 8, 4) = 6.4

17. 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?

18. 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?

19. 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.
Show Graphically!

20. Equity and Efficiency in an Edgeworth Boxm 10 7 Al
Bill 3
So even though market makes both Al and Bill better off, if initial allocation is very unequal, market allocation may also be unequal. c

21. 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?

22. Equity and Efficiency in an Edgeworth Boxm 10 7 5 Al
Bill 3 5
contract curve
How can this allocation be supported in a market equilibrium? c

23. Equity and Efficiency in an Edgeworth Boxm 10 7 Al 7
Bill 3 5 5
How can this allocation be supported in a market equilibrium?
Reallocate endowments to this allocation, then find equilibrium price. c 5

24. 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.

25. 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”
Reveals that markets can provides a mechanism that ensure Pareto Efficient outcomes,
With only two people, this wouldn’t be too difficult of a problem.
But with thousands, or millions, obviously determining a Pareto efficient allocation is complicated.
With markets, no individual needs very much information to get resources allocated to a Pareto superior allocation. A person only needs to know his preferences and prices. Under a well functioning market, competitive prices will be sufficient to achieve an efficient allocation.

26. 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?
mangos 8
mangos 12
Bill Al
12 coconut milk
8 coconut milk

27. 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 = 7 lbs. of mangos and = 7 gal. of coconut milk will be produced and consumed.
Neither person specializes!
mangos 8 2
mangos 12 5
Bill Al
coconut milk
coconut milk

28. 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.
mangos 12 5
Bill 4 2 Al
coconut milk

29. 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.
without trade and specialization
with trade and specialization
mangos 12
mangos 12 5 9 4
Bill
Bill 4 2 2 5 Al 3 Al
coconut milk
9 coconut milk

30. 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.”
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.

31. 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?