Chapter 3 The Simple Keynesian Model

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Chapter 3 -- The Simple Keynesian Model

• Fundamental inflexibility assumptions
• W -- inflexible
• P -- inflexible
• i -- inflexible
• Overriding theme -- Production Responds to
  Economic Activity (focus on goods and services
  expenditure)

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Simplifying Assumptions

• Business Saving 0 (All private saving is
  personal saving)
• Taxes dont depend upon income.
• T G (Balanced Budget)
• NX 0
• Assumptions imply that Macro Identity is now S
  I.

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Causes of Consumption (C)

• Disposable Income (YD Y - T)
• YD? ? C?
• Real GDP, or Total Income (Y)
• Y? ? YD? ? C?
• Net Taxes (T)
• T? ? YD? ? C?
• Consumer Confidence (CC)
• CC? ? C?

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More Causes of Consumption (C)

• Real Interest Rate (r i - ?e)
• r? ? C?
• Nominal Interest Rate (i)
• i? ? r? ? C?
• Expected Inflation Rate (?e)
• ?e? ? r? ? C?
• Real Wealth (A)
• A? ? C?

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Measures -- YD ? C
Relationship

• Average Propensity to Consume (APC)
• APC C/YD
• Marginal Propensity to Consume (MPC)
• MPC ?C/?YD

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Handling Multiple Causes of Consumption

• Causes of Consumption -- Y, T,
  CC, i, ?e, A.
• We generally graph C versus Y.
• Autonomous Consumption (C0) -- changes in C due
  to causes other than Y.
• Changes in C0 -- described as shifts of the
  consumption graph (versus Y).

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Causes of Investment (I)

• Business Confidence (BC)
• BC? ? I?
• Business Taxes (BT)
• BT? ? I??

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More Causes of Investment

• Real Interest Rate (r i - ?e)
• r? ? I?
• Nominal Interest Rate (i)
• i? ? r? ? I?
• Expected Inflation Rate (?e)
• ?e? ? r? ? I?
• Note Investment does not depend upon current
  income (Y)

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Government Purchases of Good and Services (G)

• Government purchases of goods and services is a
  policy variable, controlled by the government ?
  no causing variables.
• The previous properties imply that I and G are
  completely autonomous.

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A Numerical Example

• Y T YD C S I G
• 5 5 0 10 -10 10 5
• 25 5 20 25 -5 10 5
• 45 5 40 40 0 10 5
• 65 5 60 55 5 10 5
• 85 5 80 70 10 10 5
• 105 5 100 85 15 10 5
• 125 5 120 100 20 10 5

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The Saving-Investment Relationship

• Recall -- macro identity
• S (T - G) -NX I
• With simplifying assumptions
• S I
• Why doesnt S I in numerical example?

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Intentions Versus Actual Occurrences

• Must distinguish between intended, desired,
  planned S and I versus actual or realized S and
  I.
• Intended S and I -- strategies, described by
  schedules and graphs.
• Actual S and I -- the numbers after the period is
  over.

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Planned Expenditure (EP)

• Planned Expenditure (EP) -- The total intended
  spending for various levels of income.
• In equation form,
• EP C I G.

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Planned Expenditure in the Numerical Example

• Y T YD C S I G EP
• 5 5 0 10 -10 10 5 25
• 25 5 20 25 -5 10 5 40
• 45 5 40 40 0 10 5 55
• 65 5 60 55 5 10 5 70
• 85 5 80 70 10 10 5 85
• 105 5 100 85 15 10 5 100
• 125 5 120 100 20 10 5 115

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An Equilibrium Level of Real GDP EP Y

• Y T YD C S I G EP
• 5 5 0 10 -10 10 5 25
• 25 5 20 25 -5 10 5 40
• 45 5 40 40 0 10 5 55
• 65 5 60 55 5 10 5 70
• 85 5 80 70 10 10 5 85
• 105 5 100 85 15 10 5 100
• 125 5 120 100 20 10 5 115

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Why is Y 85 an Equilibrium?

• Example 1 Suppose Y 105.
• Intended Actual
• C 85 C 85
• S 15 S 15
• I 10 I 10 5 15
• G 5 G 5
• EP 100
• Note -- Actual S Actual I

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Why is Y 85 an Equilibrium? (Continued)

• Example 2 Suppose Y 65.
• Intended Actual
• C 55 C 55
• S 5 S 5
• I 10 I 10 -5 5
• G 5 G 5
• EP 70
• Note -- Actual S Actual I

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Why is Y 85 an Equilibrium? (Finally)

• Example 3 Suppose Y 85.
• Intended Actual
• C 70 C 70
• S 10 S 10
• I 10 I 10
• G 5 G 5
• EP 85
• Note -- Actual S Actual I

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Properties of Equilibrium

• No unintended inventory accumulation or
  depletion.
• All intentions are realized.
• Intended Saving Intended Investment (only at
  equilibrium).
• EP Y

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Equilibrium and the Natural Level of Real GDP

• Fundamental Prediction of Keynesian models -- Y
  is not necessarily equal to YN.
• Classical Prediction Self-correcting economy ?
  Y YN. (Business cycle represents deviations
  from equilibrium)

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Keynesian Prediction -- State of the Economy

• Y lt YN (sluggish economy)
• Y gt YN (accelerating inflation)
• Y YN (desired state of economy)
• If Y ? YN, then one needs economic policy to
  achieve a new equilibrium closer to YN.

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The Keynesian Prescription

• Achieve a new equilibrium by shifting the Ep
  curve.
• If Y lt YN, seek to increase expenditure,
  described by shifting the EP curve upward.
• If Y gt YN, seek to decrease expenditure,
  described by shifting the EP curve downward.

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Shifting the EP Curve

• Key -- Change Autonomous Consumption, Autonomous
  Investment, or Government Purchases (or, later,
  Autonomous Net Exports).
• Change C0 -- change T, CC, i, ?e, A
• Change I0 -- change BC, BT, i, ?e
• Change G0.

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Economic Policy

• Purpose -- to move Y closer to YN.
• Method -- change autonomous expenditure (C0, I0,
  G0).
• If economy is sluggish (Y lt YN), increase
  autonomous expenditure.
• If economy has accelerating inflation (Y gt YN),
  decrease autonomous expenditure.

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Strategies for Policy

• Expansionary Policy -- Policy designed to address
  a sluggish economy (Y lt YN).
• Contractionary Policy -- Policy designed to
  address an overstimulated, or accelerated
  inflation economy (Y gt YN).

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Quantitative Effects -- Changes in C0, I0, or G0

• Y T YD C S I G EP
• 5 5 0 10 -10 10 5 25
• 25 5 20 25 -5 10 5 40
• 45 5 40 40 0 10 5 55
• 65 5 60 55 5 10 5 70
• 85 5 80 70 10 10 5 85
• 105 5 100 85 15 10 5 100
• 125 5 120 100 20 10 5 115

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• Note MPC ?C 25 - 10 0.75
• ?YD 20 - 0
• Example -- If autonomous government purchases are
  changed by 5, how much will Y change as a result?

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Solution -- Numerical Example

• Y EP EP (?G0 5)
• 5 25 30
• 25 40 45
• 45 55 60
• 65 70 75
• 85 85 90
• 105 100 105
• 125 115 120

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The Multiplier Effect

• The Multiplier Effect -- Given an initial change
  in autonomous consumption, autonomous investment,
  or government purchases of goods and services,
  the resulting change in equilibrium output will
  be a multiple of the initial change.

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The Multiplier Effect in Equation Form

• ?Y m (?C0, ?I0, ?G0, or ?NX0),
• where m the multiplier.
• m 1/(1 - MPC)
• Our Example (?G0 5 ? ?Y 20)
• (20) (4)(5)
• MPC 0.75 ? m 1/(1 - 0.75) 4

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Tracing the Effect on ?Y ?G0 5, with MPC
0.75

• Added Added
• Round Spending Income
• 1 5
  5
• 2 5(0.75) 5(0.75)
  
• 3 5(0.75)2
  5(0.75)2
• ... ...
  ...
• ?Y 20 20

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Properties Multiplier Effect

• The multiplier varies positively with the MPC,
  i.e. MPC? ? m?.
• Applies for either increases or decreases in C0,
  I0, G0, or NX0.
• Applies to changes both policy-induced and
  otherwise.
• Changes in autonomous net taxes (T0) have a
  multiplier effect, but not the same multiplier.

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Changing G0 Versus Changing T0, MPC 0.75

• Added Spending
  
• Round ?G0 5 ?T0 -5
• 1 5
  5(0.75)
• 2 5(0.75)
  5(0.75)2
• 3 5(0.75)2
  5(0.75)3
• ... ...
  ...
• ______________________________
• ?Y 20 15

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The Net Taxes Multiplier

• ?Y -MPC ?T0
• 1 - MPC
• The Net Taxes Multiplier is smaller than the
  regular multiplier (less of an impact on Y for
  the same initial change).
• Tax or transfer policy is not as powerful as G
  policy, but less likely to overshoot YN.

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The Simple Keynesian Model -- The Algebra

• The model in equation form.
• (1) EP C I G,
• (2) C C0 b(Y - T),
• (3) I I0,
• (4) G G0,
• (5) T T0,
• (6) At equilibrium, EP Y.

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Solving for Y

• Substitute equations (2), (3), (4), (5), and
  (6) into (1)
• ? Y C0 b(Y - T0) I0 G0.
• Solve for Y
• ? Y 1 C0 I0 G0 -b T0.
• (1 - b)
  (1 - b)

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Removing the Simplifying Assumptions

• Investment depends upon current output or income
  (Y).
• I I0 dY,
• d marginal propensity
• to invest
• Income Tax
• T T0 tY,
• t marginal tax rate

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Causes of Net Exports (NX Exports -
Imports)

• Foreign output or income (Yf)
• Yf? ? Exports? ? NX?
• US output or income (Y)
• Y? ? Imports? ? NX?
• Barriers to Trade
• Real exchange rate (e)
• e? ? NX?

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A Model for Net Exports in Equation Form

• NX NX0 - fY
• NX0 Autonomous Net Exports
• (made up of causes other
• than Y)
• f marginal propensity to import

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The Model Without the Simplifying Assumptions
What Results Are The Same?

• Answer -- All the qualitative results are the
  same!!

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The Model Without the Simplifying Assumptions
What Results Are Different?

• More possibilities for policy.
• -- autonomous net taxes (T0)
• -- marginal tax rate (t)
• -- trade policy (NX0)
• Different multipliers for autonomous spending and
  net taxes.

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The Economy and the Federal Budget

• Recall that the Federal Budget is given by
• Budget T - G.
• Substitute income tax function for T (with Y
  Y)
• Budget (T0 tY) - G.
• Note that Y? ? Budget?

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The Economy and the Balance of Trade

• Recall that the Balance of Trade (BOT) is
  approximated by Net Exports (NX).
• Also recall that the Net Exports equation is (Y
  Y)
• NX NX0 - fY.
• Note that Y? ? BOT?