The Goods Market
• Some definitions (or identities):
– Value of final production  national income Y
– Total output sold  total output purchased
• If aggregate sales is the same as aggregate
purchases, we can break down Y into the
various kinds of demand for output.
• i.e. we can focus on the composition of
aggregate demand for output Y.
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Composition of aggregate demand Z
• Consumption
• Investment
C
I
– Fixed
• Residential (consumers)
• Non residential (firms)
– Inventories
• Government spending
• Net exports
– Exports
– Less Imports
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G
NX
X
IM
2
• Consumption
– Goods and services purchased by consumers
– Some might be some sort of investment like durables
• Investment (not financial)
– Firms invest in new plants and equipments
– Consumers invest in new houses
• Government spending (on goods and services
only)
– Excludes transfers (e.g. medicare, S.S.)
– and interest payments on gov’t debt
– (total would be called government expenditures)
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• Exports are foreign demand for domestic goods
and services (demand for Y) so they should be
included as demand for domestic output.
• Imports are domestic demand for foreign goods
(goods produced abroad) - they should not be
included in Y as they are not demand for
domestic output. However as they are already
included in consumption and other purchases they
must be subtracted.
• Net Exports = Exports - Imports
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• Inventories corresponds to goods that
were produced during a certain year
I.e. during a specific accounting period
but were not sold during the same
accounting period.
– To get an accurate account of production
during the year, we must
• Subtract inventories at the beginning of the
year (they were produced in the previous
year)
• Add inventories at the end of the year
(produced this year but not sold)
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Determination of aggregate demand Z
• By definition (identity):
Z  C + I + G + X - IM in an open economy
ZC+I+G
in a closed economy
• Let’s assume
– Fixed prices (short run Keynesian model)
– One good (everything is in real term)
– Closed economy
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Short run - medium run - long run
• Short run - period too short to allow prices
to adjust - fixed prices - unemployment
possible
• Medium run - economy is always at full
employment (labor market must adjust) prices adjust to bring economy back to full
employment - capital stock is fixed
• Long run - growth theory - capital stock
increases through investment in the
economy
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Determinants of consumption C
• Let’s define YD - disposable income - as
YD  Y - Tax + Transfer or Y - T (T is net tax)
• Consumption is determined by disposable
income: C increases as YD increases
• so consumption is a positive function of YD
C = C(YD) = C(Y-T)
this is a behavioral relation which can be
specified with the following linear form:
C = co + c 1 YD
c1 is the MPC
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Consumption function
C
C = C(YD)
co
YD=Y-T
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Endogenous versus exogenous variables
• Definition
– Endogenous variables are determined within the
model e.g. C , Y and YD
– Exogenous variables are determined outside of the
model, i.e. they are independent of any other variable
in the model
• Investment I is considered as an exogenous
variable in this chapter
• Government spending G and taxes T are also
exogenous variables - they are policy
instruments for the government.
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Model
• C = c0 + c1 (Y-T)
• I = I (exogenous - given)
• G = G (exogenous - policy
variable)
• Z  C + I + G by definition
• Y = Z (equilibrium condition)
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Algebraic Solution
• Since in equilibrium, supply of goods (Y) should
be equal to aggregate demand (Z), by replacing
we get:
• Y = c0 + c1 (Y-T) + I + G
= c0 + c1Y -c1T + I + G
_
1
1
e
e
Y =

I

G

c
T)
Y
(c(c

I

G
c
T)
0
1
0
1
1c
1- c 1
1
1/(1-c1) is the multiplier m
and (c0 + I + G - c1T) is autonomous spending Z0
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Graphical solution
Y=Z
Z
Z = Z0+c1Y
Z0
Ye
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Y
13
The multiplier
• Assume a specific consumption function
C = 500 + .8(Y-T) i.e. MPC = .8
The multiplier m = 1/(1-c1) = 5
Since Ye = m (c0 + I + G - c1T)
If G increases by ∆G, Y will increase by
∆Y = m ∆G
In the example above an increase in G equal
to 100 will result in an increase in Y of 500
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Effect of an increase in G
Z
Y=Z
Z = Z0+c1Y
4
2
∆G
Z’ = Z0+ ∆G +c1Y
3
1
Z0
Ye
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Y’e
∆Y
Y
15
Explanation
• Starting at 1, the economy is in equilibrium.
• An increase in G equal to ∆G immediately translates into an
equal increase in aggregate demand : 1 to 2
• In 2 the economy is not in equilibrium as Z > Y so firms
must increase production by ∆G to meet the additional
demand: from 2 to 3
• In 3 the economy is still not in equilibrium (below ZZ’)
• As production increases by ∆G , income increases equally
so consumption demand will increase by c1 ∆G: this is an
additional increase in aggregate demand : 3 to 4
• Then production must increase again by c1 ∆G this time to
meet this new increase in aggregate demand and so on…
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Rational
• Production (income) depends on demand
as Y = Z
in equilibrium
• Demand depends on income
as Z = C + I + G
and C = C(Y)
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• When there is an exogenous increase in demand,
production will increase equally, and this increase in
production (i.e. in income) results in an additional
increase in demand.
• However the additional increase in demand is smaller
than the original increase because the marginal
propensity to consume is less than 1 (some of the
increase in income is saved): this process will not result
in an infinite increase in output as the additional
increases in demand get smaller and smaller and tend
towards zero.
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Alternative calculation of the multiplier
Per
iod
1
2
3
4
∆G ∆G
Total increase
(many periods)
∆G
c1 ∆G c12 ∆G
∆Y
∆G
∆C
c1 ∆G c12 ∆G c13 ∆G
(1+c1+c12+ …) ∆G
1
=
G
1- c1
(c1+c12+c13+ …) ∆G
3 ∆G (1+c +c 2+c 3+ …) ∆G
∆Z ∆G c1 ∆G c12 ∆G c1
1 1
1
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Alternative approach: Investment = saving
• Approach used by Keynes in the “General Theory
of Employment, Interest and Money” 1936
• By definition, private saving is what is not
consumed out of disposable income:
Sp  YD - C
hence Sp  Y - T - C
or Y  C + Sp + T
• The equilibrium condition of the model above was:
Y=C+I+G
By replacing, it becomes I = Sp + T - G
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Interpretation
• In a one person economy, investment equals
savings because the decision to save and to
invest is made by the same person.
e.g. Robinson Crusoe’s island
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Role of government:
• In the above equation, the government
1. takes a share of income in the form of tax
2. spends it in the economy in the form of G
so T - G corresponds to the amount of tax receipts
that the government did not spend, i.e. that the
government saved.
• In sum, T - G (the budget surplus) can be
interpreted as the government saving Sg.
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Solution of the model using the
alternative equilibrium condition
• Let’s derive the saving function from the
consumption function (c1 is the MPC)
• C = c0 + c1YD and Sp  YD - C
• SP = YD - c0 - c1YD = - c0 + (1 - c1)YD
• Sp = - c0 + (1 - c1)(Y - T) with MPS = (1 - c1)
– Note that MPC + MPS = 1 as mentioned earlier
• We can now use the saving function and the new
equilibrium condition to find equilibrium Y (Ye)
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• I = Sp + (T - G) (equilibrium condition)
= - c0 + (1 - c1)(Y - T) + T - G
= - c0 + (1 - c1)Y - (1 - c1)T + T - G
= - c0 + (1 - c1)Y - T + c1T + T - G
(1 - c1)Y = c0 + I + G - c1T
Finally
_
1
e
Y 
(c 0  I G - c1T)
1- c1
as before.
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Problem # 2 P. 62
C = 160 + 0.6 YD
I = 150
G = 150
T = 100
a. In equilibrium Y = 160 + 0.6 (Y-T) + 150 + 150
i.e. Y - 0.6Y = 160 - (0.6*T) + 150 + 150
Y = [1/(1-0.6)] (160 - 60 + 150 + 150)
Y = 2.5 * 400 = 1000
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b. YD = Y - T = 1000 - 100 = 900
c. C = 160 + 0.6*900 = 700
Problem # 3
a. Z = C + I + G = 700 + 150 + 150 = 1000
so Y = Z = 1000 (equilibrium condition)
b. If G = 110 ∆G = - 40
as the multiplier m = 2.5 and ∆Y = m ∆G
∆Y = - 100 and the new equilibrium Y is 900
consumption drops by c1* ∆Y or - 60 to 640
And Z = C’ + I + G’ = 640 + 150 + 110 = 900
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c. Private savings Sp = Y - T - C
= 900 - 100 - 640 = 160
Government savings Sg = T - G
= 100 - 110 = -10
Equilibrium condition: I = Sp + Sg
150 = 160 - 10 = 150
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