Intermediate Microeconomic Theory

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 8 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). • What would Al do? Would this market make Al better off?

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 • 2 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) = qcaqmb • 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) = qcaqmb, 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:

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 of coconut milk, • If qcA(pc,wcA,wmA) – wcA < 0, Al sells coconut milk, or is net supplier 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 10 4 qmA qmA 8 16 qcA 5 8 12 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, but 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 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?