1. Intermediate Microeconomic Theory
Buying and Selling

2. An Endowment Economy We have now developed a theory of choice.
Given this theory, we can already consider the role of prices and markets in an economy.
As is the norm in economic theory, we start with the simplest possible world and build up.
So consider a “desert island” economy (a Robinson Crusoe economy).

3. An Endowment Economy
Key feature of this simple economy, is that there is no money, only goods.
Specifically, an individual is “endowed” with a given amount of various goods.
If there is a market, an individual can potentially choose to trade some of his endowed amount of one good for more of another.

4. An Endowment Economy
For simplicity, assume there are only two goods on island:
coconut milk
mangos
Budget Set:
Suppose Al (one of the inhabitants) has endowment of wc = 8 and wm = 4 (8 gallons of coconut milk and 4 lbs. of mangos).
If there were no “markets” on the island, how would we graphically depict Al’s budget set?

5. Budget Set in an Endowment Economy
How would Al’s budget set change if 1gallon coconut milk could be traded for 1/2 lb. of mangos and vice versa (i.e., 1 gal coconut milk “costs” ½ lb mangos)?
How about if 1gallon coconut milk could be traded for 2 lbs. of mangos (i.e., 1 gal coconut milk “costs” 2 lbs mangos)?
How would Al’s budget set be affected by the above price changes if his endowment was 10 gal. coconut milk, 0 mangos?

6. Buying and Selling in an Endowment Economy
Preferences:
Suppose the utility Al gets from coconut milk and mangos is given by some utility function u(qc,qm) that exhibits DMRS.
Further suppose that by consuming his endowment he gets utility of u(8, 4) and his MRS at (8,4) is -1. qm 4
slope = -1 qc

7. Buying and Selling in an Endowment Economy
Market Participation:
Suppose a market opened up where 1 gal. milk costs 1/2 lb. of mangos (or equivalently, 1 lb of mangos costs 2 gal of milk).
What would Al do? Would this market make Al better off?
Suppose instead a market opened up where 1 gal. milk costs 2 lbs. of mangos (or equivalently, 1 lb of mangos costs 1/2 gal of milk).

8. Buying and Selling in an Endowment Economy
So in an endowment economy with 2 goods,
If an individual chooses to consume a bundle with more of good 1 than he is endowed with (and therefore less of good 2 than he is endowed with), he must be a buyer of good 1 and a seller of good 2.
If an individual chooses to consume a bundle with less of good 1 than he is endowed with (and therefore more of good 2 than he is endowed with), he must be a seller of good 1 and a buyer of good 2.

9. Buying and Selling in an Endowment Economy
What relative price (i.e. terms of trade) would cause Al to be neither a buyer or a seller of coconuts?

10. Buying and Selling in an Endowment Economy
Clearly what matters is relative price.
We have been calculating the price of a gallon of coconut milk in terms of lbs of mangos
e.g. 1 more gal coconut milk costs X lbs of mangos.
Note: this system could be adopted for any number of goods.
1 lb of fish costs Y lbs of mangos
1 sharpened stones cost Z lbs. of mangos.

11. Buying and Selling in an Endowment Economy
Therefore, for a market with K goods, we only need K-1 prices, and make one good a numeraire (a good we compute every other good’s price relative to).
So we have been using lbs of mangos as numeraire, meaning pc = 2 implies one more gal coconut milk costs 2 lbs mangos.
What would be “cost” of another lb of mangos if mangos are numeraire?
Alternatively, we could use coconut milk as numeraire good, then pm = 1/2 implies that one would need to trade 1/2 gal coconut milk for one more lb. of mangos.
Note that regardless of which good we select as numeraire, relative terms of trade are the same (i.e. 2 lbs mangos traded for 1 gal coconut milk is equivalent to 1 lb mangos traded for ½ lb coconut milk)

12. Buying and Selling in an Endowment Economy
Are there historic examples of numeraire goods in primitive economies?
In what way did numeraire type goods come up in NYT article on barter goods in Russia?
Note: Numeraire goods are completely distinct from composite goods.

13. Buying and Selling in an Endowment Economy Analytically
Let’s consider Al again.
Let his endowment be given by {wc ,wm}
Suppose mangos are the numeraire good and the relative price of coconuts is pc.
Suppose Al’s preferences are captured by a generic Cobb-Douglas utility function u(qc,qm) = qccqmd
How do we analytically describe Al’s behavior?
What is general form of his budget constraint?
So what is general expression for his optimal bundle?

14. Buying and Selling in an Endowment Economy Analytically
So for generic Cobb-Douglas preferences u(qc,qm) = qccqmd, with endowment {w1,w2} and relative prices such that one more unit of good 1 costs p1 units of good 2 (the numeraire), the optimal bundle will again be given by the corresponding demand functions, which will now be:
Value of endowment in terms of numeraire

15. Buying and Selling in an Endowment Economy Analytically
Define: qcA(pc, wcA,wmA) as Al’s gross demand for coconut milk qmA(pc, wcA,wmA) as Al’s gross demand for mangos.
If qcA(pc, wcA,wmA) – wcA > 0, Al buys coconut milk, or is net demander/buyer of coconut milk,
If qcA(pc, wcA,wmA) – wcA < 0, Al sells coconut milk, or is net supplier/seller of coconut milk.
Analogue holds for mangos.
Also note that:
If qcA(pc, wcA,wmA) – wcA > 0, then qmA(pc, wcA,wmA) – wmA < 0, and
If qmA(pc, wcA,wmA) – wmA > 0, then qcA(pc, wcA,wmA) – wcA < 0
Intuitively, if Al is buying coconut milk, he must be selling mangos, and vice versa.

16. Buying and Selling in an Endowment Economy Analytically
Example:
Let his preferences be captured by U= qc0.5qm0.5 and
endowment be given by wc = 8 and wm = 4.
Let mangos be numeraire and the relative price of coconut milk in terms of lbs of mangos is pc = 2
What will be Al’s gross and net demands for coconut milk?
What will this mean about whether Al is a net demander or net supplier of mangos?
What if the relative price of coconuts (in terms of mangos) dropped to pc = 0.50?

17. Buying and Selling in an Endowment Economy
Al’s Gross Demands when 1 gal coconut milk costs ½ lb mango (pc = 0.50)
Al’s Gross Demands when 1 gal. coconut milk costs 2 mangos (pc = 2) qm 8 4 qm 20 10 4
qmA
qmA
qcA qc
qcA

18. Buying and Selling in an Endowment Economy Analytically
Example (alternate numeraire):
What would happen if we used coconut milk as numeraire, with pm = 0.5, and let Al’s endowment again be given by wc = 8 and wm = 4?
What will be Al’s gross and net demands for coconut milk?
What will this mean about whether Al is a net demander or net supplier of mangos?

19. Revealed Preference Suppose:
Bob is endowed with 4 gal. coconut milk and 4 lbs. mangos.
Current price of 1 gal. coconut milk in terms of lbs of mangos is 2 (i.e. pc = 2)
Suppose we don’t know anything else about Bob’s preferences other than at these prices Bob is a net demander/buyer of coconut milk.
If price of gal. of coconut milk fell pc = 1, can we know whether Bob will still be net demander of coconut milk?
What if price of gal. of coconut milk rose to pc = 3, would Bob still be a net demander of coconut milk?