1. 1 Intermediate Microeconomic Theory Buying and Selling

2. 2 An Endowment Economy We have now developed a theory of choice. Given this theory, we can already consider the role of markets and prices. 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. 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, he can potentially choose to trade some of his endowed amount of one good for more of other.

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

5. 5 Budget Set in an Endowment Economy How would Al’s budget set change if 2 lb. of mangos could be traded for 1 gallon coconut milk? How about if 1/2 lb. of mangos could be traded for 1 gal. coconut milk? How would Al’s budget set be affected by the above price changes if his endowment was 10 gal. coconut milk, 0 mangos?

6. 6 Buying and Selling in an Endowment Economy Suppose the utility Al gets from coconut milk and mangos is given by u(q c,q m ). So, by consuming his endowment he gets utility of u(8, 4) and his MRS at (8,4) is -1. Suppose a market opened up where Al could trade 1/2 lb. of mangos for 1 gal. coconut milk (or equiv. 1 lb. mangos for 2 gal coconut milk) and vice versa. What would Al do? Would this market make Al better off? 8 c m4m4 slope = -1

7. 7 Buying and Selling in an Endowment Economy Suppose instead market was such that Al could trade 2 lbs. of mangos for 1 gal. milk (or equivalently 2 lb mango for ½ gal coconut milk) and vice versa What would Al do? Would this market make Al better off?

8. 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. 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. 10 Buying and Selling in an Endowment Economy Clearly what matters is relative price. We have been calculating the price 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. 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 if mangos are numeraire good, and one gal coconut milk could be traded for 2 lbs mangos and vice versa, then p c = 2. What would be “price” of another lb of mangos? Are there historic examples of numeraire goods in primitive economies? Note: Numeraire goods are completely distinct from composite goods.

12. 12 Buying and Selling in an Endowment Economy Analytically Let’s consider Al again. Let his endowment be given by w c A and w m A. Suppose mangos are the numeraire good and the relative price of coconuts is p c. Suppose Al’s preferences are captured by a Cobb-Douglas utility function u(q c,q m ) = q c 0.5 q m 0.5 How do we analytically describe Al’s behavior? What is general form of his budget constraint? What is general expression for his optimal bundle?

13. 13 Buying and Selling in an Endowment Economy Analytically Define: q c A (p c, w c A,w m A ) as Al’s gross demand for coconut milk q m A (p c, w c A,w m A ) as Al’s gross demand for mangos. If q c A (p c, w c A,w m A ) – w c A > 0, Al buys coconut milk, or is net demander of coconut milk, If q c A (p c, w c A,w m A ) – w c A < 0, Al sells coconut milk, or is net supplier of coconut milk. Analogue holds for mangos. If q c A (p c, w c A,w m A ) – w c A > 0, then q m A (p c, w c A,w m A ) – w m A < 0, and if q m A (p c, w c A,w m A ) – w m A > 0, then q c A (p c, w c A,w m A ) – w c A < 0 Intuitively, if Al is buying coconut milk, he must be selling mangos, and vice versa.

14. 14 Buying and Selling in an Endowment Economy Analytically Example: Let his endowment be given by w c A = 8 and w m A = 4. Suppose the relative price of coconut milk in terms of lbs of mangos is p c = 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 p c = 0.50?

15. 15 Buying and Selling in an Endowment Economy q c A 5 8 12 q c 8 14 q c qm94qm94 Al’s Gross Demands when 1 coconut can be traded for 2 mangos (p c = 2) Al’s Gross Demands when 1 coconuts can be traded for ½ lb mango (p c = 0.50) qmAqmA qcAqcA qmAqmA q m 10 4

16. 16 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. p c = 2) At these prices, we know Bob is a net demander of coconut milk. If price of gal. of coconut milk fell p c = 1, would Bob still be net demander of coconut milk? What if price of gal. of coconut milk rose to p c = 3, would Bob still be a net demander of coconut milk?