Chapter 3 -- The Simple Keynesian ModelFundamental inflexibility

assumptions:

W -- inflexible

P -- inflexible

i -- inflexibleOverriding theme -- Production

Responds to Economic Activity (focus on goods and services expenditure)

Simplifying Assumptions

Business Saving = 0 (All private saving is personal saving)

Taxes don’t depend upon income.T = G (Balanced Budget)NX = 0

Assumptions imply that the “Magic Equation” is now S = I.

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 CConsumer Confidence (CC)

CC C

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 CReal Wealth (A)

A C

Measures -- YD C Relationship

Average Propensity to Consume (APC)

APC = C/YD

Marginal Propensity to Consume (MPC)

MPC = C/YD

Handling Multiple Causes of Consumption

Causes of Consumption -- Y, T, CC, i, e, A.

Autonomous Consumption (C0) -- changes in C due to causes other than Y.

Causes of Investment (I)

Business Confidence (BC)

BC IBusiness Taxes (BT)

BT I

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 INote: Investment does not depend

upon current income (Y)

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.

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

The Saving-Investment Relationship

Recall -- macro identity

S + (T - G) + -NX = IWith simplifying assumptions:

S = IWhy doesn’t S = I in numerical

example?

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.

Planned Expenditure (EP)

Planned Expenditure (EP) -- The total intended spending for various levels of income.

In equation form,

EP = C + I + G.

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

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

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

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

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

Properties of Equilibrium

No unintended inventory accumulation or depletion.

All intentions are realized.Intended Saving = Intended

Investment (only at equilibrium).EP = Y

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)

Keynesian Prediction -- State of the Economy

Y* < YN (sluggish economy)

Y* > 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.

The Keynesian Prescription

Achieve a new equilibrium by shifting the Ep curve.

If Y* < YN, seek to increase expenditure, described by shifting the EP curve upward.

If Y* > YN, seek to decrease expenditure, described by shifting the EP curve downward.

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.

Economic Policy

Purpose -- to move Y* closer to YN.

Method -- change autonomous expenditure (C0, I0, G0).

If economy is sluggish (Y* < YN), increase autonomous expenditure.

If economy has accelerating inflation (Y* > YN), decrease autonomous expenditure.

Strategies for Policy

Expansionary Policy -- Policy designed to address a sluggish economy (Y* < YN).

Contractionary Policy -- Policy designed to address an overstimulated, or accelerated inflation economy (Y* > YN).

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

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?

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

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.

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

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

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.

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

The Net Taxes Multiplier

Y* = -MPC T0

1 - MPCThe 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.

Application: The Obama Stimulus Plan

The Obama Stimulus Plan – A $787 B stimulus package passed in February 2009, to address sluggish US economy.

-- Tax Cuts = $288 B -- Extended unemployment benefits, education and health care = $224 B -- Federal contracts, grants, and loans = $275 B (Infrastructure improvements = $83 B)

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*.

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)

Removing the Simplifying AssumptionsInvestment depends upon current output

or income (Y).

I = I0 + dY,

d = marginal propensity

to investIncome Tax

T = T0 + tY,

t = marginal tax rate

Causes of Net Exports (NX = Exports - Imports)

Foreign output or income (Yf)

Yf Exports NXUS output or income (Y)

Y Imports NXBarriers to TradeReal exchange rate (e)

e NX

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

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

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

Same ResultsEquilibrium occurs where Ep = Y.True equilibrium, guided by unintended

inventory changes.Y* may be <. >, or = YN.Need for policy if Y* is different from

YN.Policy – change autonomous

expenditure (expansionary or contractionary).

More of the Same Results

Same options as before (C0, I0, G0).

Multiplier effect exists.Tax multiplier is smaller than the

autonomous spending multiplier.

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.

The Expanded Simple Keynesian Model

(1) EP = C + I + G + NX,

(2) C = C0 + b(Y - T),

(3) I = I0 + dY,

(4) G = G0,

(5) NX = NX0 – fY,

(6) T = T0 + tY,

(7) At equilibrium, EP = Y*.

More Realistic Multipliers

Substitute equations (2)-(7) into (1), solve for Y*.

Y* = 1 [C0 + I0 + G0 + NX0] (1 – b(1–t) – d + f)

- b [T0]. (1 – b(1–t) – d + f)

The Economy and the Federal BudgetRecall 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

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