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)

•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.

Introduction to the Keynesian system

AD = C + I + G + NX

Components of Aggregate Demand (AD)

For an open economy with government

C, I, and G mean the same thing as always;

NX is net exports

Equilibrium with constant AD

Output

Agg

rega

te d

eman

d

0

450

AD = Y

AD

6

6

IU > 0

IU < 0

E

IU is unplanned inventory investment

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.

$8 trillion is a disequilibrium value of real output

Output (trillions)

Agg

rega

te d

eman

d

0

450

AD = Y

AD

6

6

IU = $2 trillion

IU < 0

E

IU = Y - AD

8

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]

“My spending is your income.”

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.

The consumption function

The consumption function is given by:

cYCC 0C 0 < c < 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.

Y0

-30 100 200

30

S

S = -30 + .3Y

The saving function

)( cYCYCYS

The slope of the saving function is

given by MPS

The consumption function and aggregate demand

Income, Output

Agg

rega

te d

eman

d

0

450

AD = Y

AD0

E

Y0

C

AI

cYCC

c

IC

c

AY

11

0

a R.F. Kahn. “The Relation of Home Investment to Unemployment,” Economic Journal, June 1931.

Kahn’s 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?

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.

The multiplier effect

Let Y = C + I

C = 100 +.75YD

I = 300

Thus we have:

160025.

400

75.1

300100

10

c

ICY

Now, allow for a $100 increase in autonomous investment, that is:

100I

AD1

AD2

AD =Y

400

500

Agg

rega

te d

eman

d

Y0 1600 2000

Y0I

Output, Income

450

YcCC

Deriving the multiplier

Let

Y C + I (1)

Therefore:

Y = C + I (2)where

(3)

II (4)

Let

YcIY

0C

(5)

Thus:

Rearrange (5)

IYc )1( (6)

Rearrange (6)

cIY

1

1

Example:

400)4)(100(75.1

1100

1

1

cIY

Round Increase in demand this round

Increase in production this

roundTotal increase in

income

1

2

3

4

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . .

A

AcAc 2

Ac 3

A

Ac

Ac 2

Ac 3

A

Ac )1(

Acc )1( 2

Accc )1( 32

Ac

1

1

The multiplier

The Multiplier Round by Round

round

Increase indemand this

round

Increase inproduction this

roundTotal increase in

income

1 $100 $100 $100

2 75.00 75.00 175.00

3 56.25 56.25 231.25

4 42.19 42.19 273.44

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . $400.00

Be advised that the multiplier effectworks in both

directions

The government sector

Let

•YD denote disposable income;

•TR is transfer payments;

•TA is taxes

Thus, we can say:

YD = Y + TR – TA

Also:

)( TATRYcCcYDCC (4a, p. 69)

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:

GG

RTTR

tYTA where t is the marginal propensity to tax out of national income (Y), that is

t = TA/Y, where 0 < t < 1

The closed model with government

GICY

cYDCC II

GG RTTR

tYT

Substitute (5) and (6) into (2) to obtain (7)

)( tYRTYcCC

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Substitute (7), (3) and (4) into (1) to obtain (8)

GItYRTYcCY )(

Rearrange (8) to obtain (9)

GIYtcRTcCY )1(

Let:

GIRTcCA

(8)

(9)

YtcAY )1(

AYtc )]1(1[(

To find equilibrium Y (Y0):

)1(1

1

)1(10

tcA

tc

AY

Now rewrite (9) as follows:

Rearrange (10) to obtain (11):

(10)

(11)

Use the following set-up to answer the questions on the next slide

Y = C + I + G

C = 75 + .75YDI = 110G = 180TR = 240TA = .2Y

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?