Intermediate microeconomic theory
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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.

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Intermediate Microeconomic Theory

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Intermediate microeconomic theory

Intermediate Microeconomic Theory

Buying and Selling


An endowment economy

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).


An endowment economy1

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.


An endowment economy2

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?


Budget set in an endowment economy

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?


Buying and selling in an endowment economy

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


Buying and selling in an endowment economy1

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?


Buying and selling in an endowment economy2

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.


Buying and selling in an endowment economy3

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?


Buying and selling in an endowment economy4

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.


Buying and selling in an endowment economy5

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)


Buying and selling in an endowment economy6

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.


Buying and selling in an endowment economy analytically

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?


Buying and selling in an endowment economy analytically1

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:


Buying and selling in an endowment economy analytically2

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.


Buying and selling in an endowment economy analytically3

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?


Buying and selling in an endowment economy7

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


Buying and selling in an endowment economy analytically4

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?


Revealed preference

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?


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