1 / 19

# Intermediate Microeconomic Theory - PowerPoint PPT Presentation

Intermediate Microeconomic Theory. Buying and Selling. 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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Intermediate Microeconomic Theory' - gloria-todd

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Intermediate Microeconomic Theory

• 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).

• 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.

• 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?

• 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?

• 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

• 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?

• 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.

• What relative price (i.e. terms of trade) would cause Al to be neither a buyer or a seller of coconuts?

• 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.

• 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)

• 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.

• 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?

• 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:

• 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.

• 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?

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

• 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?

• 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?