101Lecture09FALL'12post

8/12/2019 101Lecture09FALL'12post

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PROCEDURAL ITEMS: : Exam is Tuesday October 23 7:30-

9:30pm. Bogan’s Friday precepts (CO5 and CO6) and Weicheng

Lian’s Thursday precept at 2:30pm (CO4) will take the midtermin McCosh 28. All other precepts will take the exam in McCosh 50

(Some students are making special arrangements with me)

Answers to problem sets are posted on the Blackboard under

assignments. They are posted on Weds after the problem sets have

been turned into the previous precept. When you get a problem set

returned (unless you got a 10) you should look at the answer sheet

to be certain you understand everything.

The Keynesian model and Aggregate Demand

Professor Bogan ECO 101

Lecture 9



2

The Algebra of Demand-Side

Equilibrium (3 sectors, no gov’t) In equilibrium GDP = Planned Expenditures

i.e. Y = C + I + X - IM

C = C0 + Y b Y = YD because there is no government

Therefore, Y = C0 + b Y + I + X - IM

Y - b Y = C0 + I + X - IM

(1 - b) Y = C0 + I + X - IM The simple

multiplier is1

1

b

Y

1

1 b

Co

I

X

IM



3

The Logic of the Multiplier

A) Suppose a native American tribe gets a new license to build a

casino.

I = $100 M

But, people are paid in wages, salaries, rent, interest, and

profits to build the casino. Therefore, the $100 M is income to

them.

One person’s spending is another’s income. B) Suppose the MPC = 3/4. Then these people will spend $75 M

= (3/4) I on shoes, meals in restaurants, jackets, etc. This is

income to the owners and employees of these businesses

They will spend (3/4) (3/4) I



4

The Logic of the Multiplier — 2

C) Thus, we have an infinite series:

Y = I + 0.75 I + (0.75)2 I +…+ (0.75)n I

The Mashantucket

Pequot tribe runs

Foxwoods, New

England’s largest

casino

Y 11.75

I 4(100)



5

Restrictive Assumptions Behind

the Simple Multiplier

A) Additional goods and services are available without

prices changing

B) Interest rates don’t change

C) It ignores income tax effects

D) It ignores international trade effects; actually IM = f (Y)

As we add more complexity to our model, these factors

reduce the actual multiplier



6

The Fourth Sector- Government

(affects disposable income)

II. Taxes (T) and Transfers (TR) affect disposable income and thus

desired consumption YD = Y - T + TR

For the moment, assume taxes are per-person, not on income

C = C0 + b YD

C = C0 + bY - bT + bTR

HHS handles a large

share of the nation’s

transfer payments

I. Government Spending (G) enters AD



7

Y =1

1 - b[C0 - bT + bTR + I + G + X - IM]

Y = C + I + G + X - IM

Y = C0 + bY - bT + bTR + I + G + X - IM

(1-b) Y = C0 - bT + bTR + I + G + X - IM

Demand-Side Equilibrium

(the 4 sector model)

Equilibrium on the Demand Side Requires:

C = C0 + bY - bT + bTR



8

The Effect of Income Taxes on

Demand-Side Equilibrium

T = T0 + tY

C = C0 + bY - btY = C0 + b (1-t)Y

Y = C0 + b(1-t)Y + I + G + X - IM

[1- b(1-t)]Y = C0 + I + G + X - IM The multiplier is

1

1-b(1-t)1

1-b(1-t) (C0 + I + G + X - IM)Y=

From now on redefine T to mean taxes net of transfers

Then YD = Y- T

let T0 = 0, so T = tY

C = C0 +b(Y-T) = C0 + bY - bT



9

Income Taxes Reduce the

Multiplier

Suppose b = 0.8 t = 0.3

The simple multiplier is:1

1 - 0.8= 5

But, the income tax

modified multiplier is:

1

1- 0.8 (1 - 0.3)= 2.27

1

1 b(1 t )



10

What If Taxes are a Function of Income

and Imports Are a Function of Income?

C = C0 + b YD = C0 + b (Y-T) = C0 + b (Y-tY)T = t Y

IM = mY Y = C0 + b(1-t)Y + I + G + X - mY

Y = C + I + G + X - IM

Y-b(1-t)Y+ mY = C0 + I + G + X

{1-b(1-t) + m}Y = C0 + I + G + X

Y 1

1 b(1 t ) m(Co I G X )



11

The Keynesian multiplier with income

taxes, and imports a function of income

the import-adjusted

multiplier:

1

1-b (1-t) + m

Both taxes and imports reduce the

multiplier effect on domestic spending

Free Trade Rorsach Test



12

Another look at Equilibrium in the

Keynesian Model without price variation

Y

Planned

Expenditures

C,I,G,X-IMC+I+G+X-IM

YE



13

Three ways of looking at Equilibrium in the

Keynesian Cross Model

Equilibrium is reached when:

1. Real planned expenditures (C + I + G + X - IM) equal real GDP

2. Planned saving equals planned investment

3. There are no unplanned inventory changes

(Assumes constant prices and interest rates)



14

We return to the 2-Sector Economy (Y= C+I) to

emphasize three ways of describing the same equilibrium

No change in prices or interest rates

Households and Businesses

(YD = Y as no government)

Y = C + I

C = 100 + (3/4) YD

1) Real GDP = Real Expenditures

Equilibrium income = 600

2) Planned saving = planned investment

S = - C0 + (1-b)Y S = -100 + (1/4)(600) = 50

I = 50

600 = 550 + 50

I = 503) No unplanned change in inventories at equilibrium. At Y=600

households buy 550 and Businesses 50, so no unplanned change ininventories

S h i il



15

Suppose the economy is temporarily at

Y= 800. Then C=700, S=100 But I=50

This is not an equilibrium

Y=800

Planned

Expenditures

C, I

C+I

YE=600

C = 100 + 3/4(YD)



16

Forces toward equilibrium

If planned expenditures< current production Y

Then planned saving >planned investment

There is unplanned inventory accumulation

=>cut output, fire people

If planned expenditures> current production Y

Then planned saving < planned investmentInventories are falling

=>increase output: hire people



17

Equilibrium with 4 Sectors

Keynesian Cross model

Y = C + I + G + X - IM

SG + SP + SF = I

SG = (T - G) using T as Taxes net of transfers

SF = (IM - X)

SP = - C0 + (1-b) YD SP = - C0 + (1-b) (Y - T)

3) No unplanned change in inventories

1) National income = planned expenditures

2) Planned saving by government, the private sector and the

foreign sector = planned investment



18

Reminder of difference NIPA

and income determination model NIPA: Y = C + I + G + X - IM ex post accounting

Dollar amounts at the end of the year

Income determination: output must equal planned

expenditures. Y = C + I + G + X-IM now means:

Equilibrium Y = planned C + planned I + G +planned (X - IM)

Planned C = Co + bYD

Planned investment --function of expected

profitability, but we usually give an amount

Planned imports may be a function of Y

Equilibrium occurs where plans are fulfilled



19

Demand-Management Counter-

Cyclical Fiscal Policy Increase G, increase Transfer Payments, or lower Taxes to

fight a recession

Lower G, decrease Transfers, or raise taxes to close an

inflationary gap

Note: activist fiscal policy need not necessarily mean bigger

Government

One could fight a recession by decreasing taxes, and fight

inflation by decreasing G and transfer payments.



20

If the Price Level Varies, How Is the

Keynesian Model Affected?

C + I + G1 + X - IM

with P1

Planned

Expenditure

Y

Y

P

AD1 P1

C’ + I + G1 + X’ - IM’

with P2

P2

Forcing pricechanges into

the Keynesian

model lets us

derive an AD

curve



When prices vary the Keynesian

cross model does not give a

unique solution to determining

national income, Y.For each price level it gives a

point on the Aggregate Demand function.



The algebra of putting P in the

Keynesian model

22

C = Co + b (Y-T) +w(W/P)

where Co is the autonomous level of consumption

b is the MPC

Y is national incomeT is taxes net of transfers

w is the marginal propensity to consume out of real wealth

(We have discussed the effect of P on imports and exports, but

we are not going to put Imports or Exports as a function of P

into our introductory model)

Then using the consumption function above calculate

Y= C+I+G+X-IM you will have Y as a function of P i.e. AD



23

The movement in equilibrium income from change in

G or I in the Keynesian cross is now the increase in

AD

600 800

600 800

P

Planned

expenditures

Y

Y

AD moves right by the

Keynesian multiplier

times ( G)

AD1

AD2

∆Y=the

Keynesian

multiplier times

∆G

P1

101Lecture09FALL'12post

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