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CHAPTER5: THE BASIC MARKET CLEARING MODEL

Three aggregate consistency conditions must hold:
o
Since consumption is the only use of output in the model, total production
equals total consumption, that is
t
t
C
Y
=
.
o
Each dollar lent by someone is borrowed by someone else. Hence, the
aggregate stock of bonds must equal zero in every period, that is
0
=
t
B
.
o
Since the stock of money does not change over time, the total that people
hold in each period,
t
M
, equals the given quantity,
0
M
.

What guarantees the fulfillment of the aggregate consistency conditions in every
period?

Interest rate and price level adjusts to ensure that
o
the total of commodities supplied equals the total demanded.
o
the total of desired holdings of bonds is zero, and
o
the total of money demanded equals the aggregate quantity of money.

This is referred to as the general market clearing.

Note that each household regards the interest rate and price level as given.
However, the aggregate of households’ choices determine R and P to satisfy the
market clearing conditions.
WALRAS’ LAW OF MARKETS

Consider the budget constraint of a household. Let
s
y
1
be the quantity of goods
that the household decides to produce and supply to the commodity market during
period 1. Likewise, let
d
c
1
represent the quantity of goods that a household offers
to buy or equivalently, demands from the market. Finally let
d
b
1
and
d
m
1
be the
household’s planned stocks of financial assets for period 1. The budget constraint
of the household for period 1 is the following:
P
m
P
b
c
P
m
P
R
b
y
d
d
d
s
/
/
/
/
)
1
(
1
1
1
0
0
1
+
+
=
+
+
+

Summing up this equation over all households gives:
P
M
P
B
C
P
M
P
R
B
y
d
d
d
s
/
/
/
/
)
1
(
1
1
1
0
0
1
+
+
=
+
+
+

The capital letters refer to the economywide aggregate figures. Given that
0
0
=
B
, rearranging the terms we have:
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)
/
/
(
)
/
(
)
(
0
1
1
1
1
=

+
+

P
M
P
M
P
B
Y
C
d
d
s
d

The above equation tells us that market clearing conditions are
o
The total demand for commodities equals the total supply
o
Any dollar that someone lends corresponds to a dollar that someone else
wants to borrow.
o
People willing to hold the outstanding stock of money.

Note that if two of these three conditions hold then the third condition holds
automatically. This is referred to as Walras’ law of markets.
CLEARING THE COMMODITY MARKET
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This note was uploaded on 09/28/2010 for the course ECON 3080 taught by Professor Li,guanyi during the Fall '08 term at Colorado.
 Fall '08
 LI,GUANYI

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