Transcript Intermediate Microeconomic Theory

Intermediate Microeconomic Theory
Buying and Selling
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An Endowment Economy
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We have now developed a theory of choice.
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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.
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So consider a “desert island” economy (a
“Robinson Crusoe” economy).
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An Endowment Economy
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Key feature of this simple economy, is that
there is no money, only goods.
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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.
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An Endowment Economy

For simplicity, assume there are only
two goods on island:
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coconut milk
mangos
Suppose Al (one of the inhabitants) has
endowment of wcA = 8 and wmA = 4 (8
gallons of coconut milk and 4 lbs. of
mangos).
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If there were no “markets” on the island,
how would we depict Al’s budget set?
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Budget Set in an Endowment Economy
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How would Al’s budget set change if 2 lb. of
mangos could be traded for 1 gallon coconut
milk?
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How about if 1/2 lb. of mangos could be traded
for 1 gal. coconut milk?
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How would Al’s budget set be affected by the
above price changes if his endowment was 10
gal. coconut milk, 0 mangos?
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Buying and Selling in an Endowment Economy
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Suppose the utility Al gets from coconut milk and mangos is
given by u(qc,qm).
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So, by consuming his endowment he gets utility of u(8, 4)
and his MRS at (8,4) is -1.
m
slope = -1
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8
c
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.
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What would Al do? Would this market make Al better off?
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Buying and Selling in an Endowment Economy
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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
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What would Al do? Would this market
make Al better off?
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Buying and Selling in an Endowment Economy
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So in an endowment economy with 2 goods,
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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.
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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.
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Buying and Selling in an Endowment Economy
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What relative price (i.e. terms of trade) would cause Al to
be neither a buyer or a seller of coconuts?
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Buying and Selling in an Endowment Economy
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Clearly what matters is relative price.
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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.
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1 lb of fish costs Y lbs of mangos
2 sharpened stones cost Z lbs. of mangos.
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Buying and Selling in an Endowment Economy
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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).
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So if mangos are numeraire good, and one gal coconut milk could be
traded for 2 lbs mangos and vice versa, then pc = 2.
What would be “price” of another lb of mangos?
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Are there historic examples of numeraire goods in primitive
economies?
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Note: Numeraire goods are completely distinct from composite
goods.
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Buying and Selling in an Endowment Economy Analytically
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Let’s consider Al again.
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Let his endowment be given by wcA and wmA.
Suppose mangos are the numeraire good and the relative price of
coconuts is pc.
Suppose Al’s preferences are captured by a Cobb-Douglas utility
function u(qc,qm) = qc0.5qm0.5
How do we analytically describe Al’s behavior?
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What is general form of his budget constraint?
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What is general expression for his optimal bundle?
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Buying and Selling in an Endowment Economy Analytically
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Define: qcA(pc, wcA,wmA) as Al’s gross demand for coconut milk
qmA(pc, wcA,wmA) as Al’s gross demand for mangos.
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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.
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
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Intuitively, if Al is buying coconut milk, he must be selling mangos, and
vice versa.
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Buying and Selling in an Endowment Economy Analytically
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Example:
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Let his endowment be given by wcA = 8 and wmA = 4.
Suppose the relative price of coconut milk in terms of lbs of mangos is pc = 2
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What will be Al’s gross and net demands for coconut milk?
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What will this mean about whether Al is a net demander or net supplier of
mangos?
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What if the relative price of coconuts (in terms of mangos) dropped to pc =
0.50?
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Buying and Selling in an Endowment Economy
Al’s Gross Demands when 1 coconuts
can be traded for ½ lb mango
(pc = 0.50)
Al’s Gross Demands when 1 coconut
can be traded for 2 mangos
(pc = 2)
qm
qm
9
10
4
4
qmA
qmA
8
qcA
5
8
12
qc
14 qc
qcA
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Revealed Preference
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Suppose:
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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)
At these prices, we know Bob is a net
demander of coconut milk.
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If price of gal. of coconut milk fell pc = 1,
would Bob still be net demander of
coconut milk?
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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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