Slides for Part III-B

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Slides for Part III-B
These slides will take you through the basics of
income-expenditure analysis. The following is
based on Dornbusch Fisher, Chapter 3 (on
reserve)
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Introduction to the Keynesian system

• The Keynesian system is based on the principle of
  aggregate demand, which can be stated as follows
  in the short period (that is, the time period in
  which productive capacity is fixed within narrow
  limits), real output and employment are
  determined by aggregate demand.
• Aggregate demand (AD) is defined as total or
  aggregate spending for newly produced goods and
  services.

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Components of Aggregate Demand (AD)
For an open economy with government
AD C I G NX
C, I, and G mean the same thing as always NX is
net exports
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Equilibrium with constant AD
AD Y
IU is unplanned inventory investment
IU gt 0
Aggregate demand
E
AD
6
IU lt 0
450
0
6
Output
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Properties of equilibrium

• Planned spending is equal to real output, meaning
  the plans of spending and producing units match
  up.
• Unplanned inventory investment is equal to zero.
• Firms on average have no reason to expand or
  contract the scale of production. Nor do they
  have a reason to offer more or less employment.

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8 trillion is a disequilibrium value of real
output
AD Y
IU Y - AD
Aggregate demand
IU 2 trillion
E
AD
6
IU lt 0
450
0
6
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Output (trillions)
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My spending is your income.

• Let
• Y is real output or real GDP.
• YD is real disposable income.

? For a closed economy without a public sector,
the following must be true AD Y YD
1
? In a closed economy with no public sector AD
C I 2 ? Thus, developing a theory of
aggregate demand logically begins with a theory
of consumption and a theory of investment.
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The consumption function
The consumption function is given by
0 lt c lt 0

• C is the intercept of the consumption function,
  or the component of planned household spending
  determined independent of income.
• c is the marginal propensity to consume-the
  change in consumption resulting from a one unit
  change in disposable income.

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The saving function
The slope of the saving function is given by MPS
S
S -30 .3Y
30
0
Y
200
100
-30
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The consumption function and aggregate demand
AD Y
E
AD0
Aggregate demand
450
0
Y0
Income, Output
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The multiplier effect
?Kahns Problem a What would be the limit of new
employment created if the government undertook to
stimulate employment growth by spending for
public works projects?
Chain of causation

• Expenditure for public works
• Increase in employment in construction trades
  and building supplies industries
• Increase in income of people employed in these
  industries
• Increase in spending for consumption goods
  increase in employment in consumption goods
  industries.

a R.F. Kahn. The Relation of Home Investment to
Unemployment, Economic Journal, June 1931.
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Example
Let Y C I C 100 .75YD I 300 Thus we
have
Now, allow for a 100 increase in autonomous
investment, that is
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AD Y
AD2
AD1
Aggregate demand
?Y0
500
?I
400
450
0
1600
2000
Y
Output, Income
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Deriving the multiplier
Let Y ? C I (1) Therefore ?Y ?C ?I
(2)where
(3)
(4)
Let
Thus
(5)
Rearrange (5)
(6)
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Rearrange (6)
The multiplier
Example
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The multiplier
Round Increase in demand this round Increase in production this round Total increase in income
1
2
3
4
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . .
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Be advised that the multiplier effectworks in
bothdirections
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The government sector

• Let
• YD denote disposable income
• TR is transfer payments
• TA is taxes

Thus, we can say YD Y TR TA Also
(4a, p. 69)
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Specification of fiscal policy
Fiscal policy is public policy with respect of
government spending, transfer spending, and the
structure of taxes or revenue collection
We assume that
where t is the marginal propensity to tax out of
national income (Y), that is t ?TA/?Y, where 0
lt t lt 1
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The closed model with government
(1)
(2)
(3)
(4)
(5)
(6)
Substitute (5) and (6) into (2) to obtain (7)
(7)
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Substitute (7), (3) and (4) into (1) to obtain (8)
(8)
Rearrange (8) to obtain (9)
(9)
Let
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Now rewrite (9) as follows
(10)
Rearrange (10) to obtain (11)
(11)
tax multiplier
To find equilibrium Y (Y0)
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Problem
Use the following set-up to answer the questions
on the next slide
Y C I G C 75 .75YDI 110G 180TR
240TA .2Y
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1. What is the value of the tax multiplier?
2. Solve for equilibrium output (Y0) and illustrate
   with an income expenditure diagram.
3. Calculate disposable income (YD) when Y Y0.
4. Calculate saving (S) when Y Y0
5. Calculate the change in output (?Y0) resulting
   from a 20 decrease in investment.
6. Assuming the equilibrium value of income is equal
   to that which you computed in (2) above, what is
   the value of unplanned inventory investment if
   actual output is equal to 1400?