1

National Income Determination

Two approaches:  To Determine National Income Equilibrium:

1.Total Approach.

2.Injection-Leakage Approach.

  Total Approach:

• Equilibrium may occur when planned aggregate expenditure is equivalent to planned output.

(AE=Y) or (AD = AS) (aggregate demand = aggregate supply).

Leakage-Injection Approach: • Equilibrium also can be determined when: INJECTION = LEAKAGE

Injections are additional spending from: investments (I),

government purchases (G) and exports (X).

Leakages are withdrawals from: savings (S),

tax payment (T) and imports (M). • So, at equilibrium, (I+G+X = S+T+M) (INJECTION = LEAKAGE)

DETERMINATION OF EQUILIBRIUM NATIONAL INCOME

• Aggregate demand is the total amount of expenditure on domestic goods and services.

AD= C + I + G + (X – M)

Y = C + I + G + (X – M)

The higher the level of aggregate demand or aggregate expenditure, the higher the level of output and employment.

Components of Aggregate Expenditure:

1. CONSUMPTION, C = f (Yd)2. INVESTMENT, I = f (i, Y)3. GOVERNMENT EXPENDITURE, G4. NET EXPORT (X – M)

1. Consumption and Saving

Disposable Income is used for Consumption spending and Saving. Yd = C + S

and, C = f (Yd), S = f (Yd) Both C and S is a function of income,Y and having a positive

relationships. ( Y rises, C and S also will rise).

Given that;Consumption function: C = a + bYd

and Saving function: S = – a + (1 – b) Yd

There is (two)2 components of Consumption spending by households: C1, Autonomous Consumption = a

C2, Induced Consumption = bYd

Where, b is the Marginal Propensity to Consume

(MPC).

Autonomous Consumption,C1 = a

is the vertical intercept of the consumption function,

It is the amount of consumption that would

occur even if the household earned nothing, Y=0. when Y= 0 (no income earned), C = a. (basic consumption for living).

C C = a + b Yd

a 0 Y

Autonomous Consumption (a) and Induced Consumption (bY)

C1 = a is a fixed amount irrespective of the income earned,

is the part of consumption which does not vary with the level of income (Y increases but “a” is constant).

C2 = bY is an amount that depends on the disposable income,

is the amount of consumption spending by households that is induced by disposable income (Y increases, C2 increases).

CONSUMPTION, C•Consumption function, C

C = a + bYd a Yd

The slope of consumption function is given by: b = C/ Y = Marginal Propensity to Consume (MPC)

Consumption and Saving scheduleY C S 0 60 -60

100 120 -20 200 180 20 300 240 60 400 300 100 500 360 140

With no income earned, Y = 0 , autonomous C = a = 60 and dissaving = - a = - 60.While Y = C + S , if Y = 0 , then C = - S.

How is the increase in income will increase consumption?

Consumption is induced by the value of b (that is =

MPC),

since,

C = a + bY

FOR EXAMPLE: Given that C = a + bY, therefore, if b = 0.6 , how large is the increase in consumption if there is an increase in income?Since C = a + 0.6Y, thus C will increase by 0.6Y , (given a = autonomous consumption) , so, C will increase by 60% out of total income, Y. Meaning that, for any increase in income, 40% can be saved and 60% will be spend on consumption.

Consumption and Saving scheduleY C S 0 60 -60

100 120 -20 200 180 20 300 240 60 400 300 100 500 360 140

In a 2-sector economy, C = a + bY .Since C = a + 0.6Y, and a = 60 thus C = 60 + 0.6Y.At income 200, C = 60 + 0.6(200) = 60 + 120 = 180 and Y = C + S so , S = Y – C = 200 -180 = 20.

Changes in consumption when income change.

consumption

Y = CC = a + b Y

C Y

45°income

Note: b = C = 400

1000 1500

Y

500

400

Changes in consumption when income change.

consumption Y = C

C = a + b Y C

Y

45°income

Note: b = C

= 400

1000 1500

Y

500

ea

400

SAVINGS• Some part of income earned is saved.• two components of savings:

autonomous dissaving, S1 = – a induced saving, S2 = (1 – b)Ywhere,(1 – b) = Marginal Propensity to Save.

= S/Y = slope of saving function.

Dissaving and saving.

Autonomous dissaving, (- a), is the amount that households draw out from their wealth to consume when no income earned.

Induced saving, (1 –b)Y, is the amount of saving that is induced by earnings of disposable income.

Saving Function, S

Saving

Yd (output)

S = – a + (1– b)Yd

–a

0

(1 – b) is the slope of saving function = ΔS/ΔY

Consumption & Saving Function,

C,S

Yd (output)

S = – a + (1– b)Yd

– a

0

C = a + bYd

a45º

e

Y = C + S,When S = 0,Y = C at the breakeven, point, e.

Y = C

Y = AD

Note that:

MPC + MPS =1, thus MPS = (1 – MPC).If MPC = b and MPS = (1 – b),Then, b + (1 – b) = 1

APC, APSThe fraction of income that is used for

consumption is the: Average Propensity to Consume (APC): APC = C YAnd, the fraction of income that is used for saving

is the: Average Propensity to Save (APS): APS = S Y and, at any level of income, APC + APS = 1

MPC

INCOME,Y

CONSUMPTION, C C = a + bYd

∆C

∆Y

0 1600

1200

a

MPC = ∆C = 400

∆Y 600

is the slope of the consumption function.

1000

800

MPC, APC

INCOME,Y

CONSUMPTION, C C = a + bYd

∆C

∆Y

0 1600

1200

a

MPC = ∆C = 400

∆Y 600 APC = TC = 1200 TY 1600

1000

800

TC

TY

MPC, APC

INCOME,Y

CONSUMPTION, C C = a + bYd

0 1600

1200

a

MPC = ∆C = 400

∆Y 600 APC = TC = 1200 TY 1600

1000

800

TC

TY

TC

Saving

Yd ( output)

S = – a + (1– b)Yd

–a

0

MPS = (1 – b) = ΔS/ΔY

is the slope of saving function.

ΔS

ΔY

MPS, APS

Saving

Yd (real output)

S = – a + (1– b)Yd

–a

0

while, APS = TS/TY

ΔS

ΔYTS

TY

MPS, APS

TS

Saving

Yd (real output)

S = – a + (1– b)Yd

–a

0

while, APS = TS/TY

TS

TY

MPS, APS

TS

BREAK-EVEN INCOME is a situation when all the income is just nice

for consumption purposes while no saving at all.

thus, Y = C and S = 0.

S = - a + (1 – b)Y

C = a + bYe

C,S

Y45º

AS=AD

S < 0

S > 0

S = 0

Activity

INCOME(Y) CONSMPTN (C) SAVING(S)0 140

200 260400 20600 500800

1000

1. Use the given data to answer the following questions.

a) Fill up the blank with appropriate values.

b) What are the values of MPC and MPS?c) Write down the consumption function and saving function.d) What is the amount of break-even income?

ANSWER

INCOME(Y) CONSMPTN (C) SAVING(S)0 140 140

200 260 60400 120 + 260 = 380 20600 500 100800 120 + 500 = 620 180

1000 120 + 620 = 740 260

1. Use the given data to answer the following questions.

a) Fill up the blank with appropriate values.

b) What are the values of MPC and MPS? MPC = C = 260 - 140 = 0.6

Y 200 – 0

MPS = 1 – MPC = 1 – 0.6 = 0.4c) Write down the consumption function and saving function. C = 140 + 0.6Y S = - 140 + 0.4Y

d) What is the amount of break-even income? is a point at e, when S = 0, so Y = C. S = - 140 + 0.4YSince S = 0, 0 = -140 + 0.4Y 140 = 0.4Y Y = 140/0.4 = 350

S = -140 + 0.4Y

C= 140 + 0.6Ye

C,S

Y45º

S = 0

Activity 2

INCOME(Y) CONSMPTN (C) SAVING(S)0 140 140

200 260 60400 380 20600 500 100800 620 180

1000 740 260Calculate the APC and APS at each level of income.

INCOME(Y)

CONSMPTN (C)

SAVING(S)

0 140 140200 260 60400 380 20600 500 100800 620 180

1000 740 260

APC APS

- -1.3 - 0.3

0.95 0.050.83 0.170.78 0.230.74 0.26

ANSWER:

The values for APC and APS at each level of income.

2. INVESTMENT Investment is defined as the spending or purchase of plants, machineries,

buildings and inventories by firms for the purpose of producing goods and services.

two(2) types of investment spending: i)   Autonomous Investment what firms may had intended to plan or desired or has been

fixed and does not depend on income.ii) Induced Investment actual investment expenditures used to produce newly produced

goods, and depends on the level of:

Investment depends on the level of: I = f ( i,) interest rate, future expected profitability, income, technology, capacity and business taxes.

1. Autonomous InvestmentAs assume by Keynes; - is a fixed investment that does not change with the change in

income, but ; there will be a shift in the autonomous horizontal function, up or

down when there’re other factors that affect it.

1. Autonomous Investment Function Investment

I1

Autonomous

Investment I0

Diagram: Autonomous InvestmentA shift in autonomous investment upward to I1 may cause

by an increase in expected profit or a fall in interest rate but does not depend on income.

Income

refers as a fixed investment that does not change with the change in income.

2. Induced Investment Functionreal interest rate (i)

I = f(i, e

)

I = f(i)

I’ I’’ Investment

Diagram: Induced InvestmentInduced investment has a negative relationship with real rate of interest.

If future profit is expected to increase, at any given level of real interest rate the investment function will increase and shift the curve to the right.

i1

i2

refers to an investment that changes with the interest rate, income or expected profitability etc.

2. Induced Investment Function investment

I = f(Y)

Income

Diagram: Induced InvestmentInduced investment has a positive relationship with aggregate income.

Example is capital investment by the purchase of new plants and equipments.

is the actual investment that is induced by changes in income.

Investment and Saving• Investment is an injection: could increase aggregate

expenditure (AD) and boost up economic growth (income).

Investment spending will multiply through the multiplier effect to increase income.

• Saving is a leakage: could lower aggregate expenditure (AD) and income.

Saving becomes an outflow of money (leakage) from an economy. It becomes a stock of money that is not spent.

• At equilibrium, Saving will be equal to Investment, ( S = I )

Equilibrium in 2 sector economy

C,I

Yd (output)

045º

C + I

Y2

Y=AD

e2

equilibrium; Y = C + I (in 2 sector economy)

Equilibrium in 2 sector economy

C,S,I

Yd (real output)

S = – a + (1– b)Yd

0I

Y2

e2S = I

In 2 sector econ; equilibrium; S = I

1) If investment is 150 millions, calculate the equilibrium income and sketch a diagram to show this.

I = 150 C = 140 + 0.6YAnswer:At equilibrium (in 2 sector economy);(Using Total Approach): Y = C + I Y = 140 + 0.6Y + 150 Y – 0.6Y = 290 0.4Y = 290 Y = 290/0.4 Y = 725

Y = AD

C + I

Y

C,I

e

Ye = 72545º

ANSWER:

3. GOVERNMENT EXPENDITURE

Government Expenditure

Income Diagram: Autonomous Government Expenditure

G1

G0

G will be autonomously fixed according to Government Budget Policy for each year.

4. NET EXPORT (X – M)

Export is an injection and could increase the national income through the foreign trade multiplier, but import is a leakage.

Thus, net export (X-M), means the real foreign sector minus the total import of goods and services into the economy.

FULL EMPLOYMENT Equilibrium

•full employment equilibrium is an ideal objective because at this level of income, there is no available and useful resource of the economy that is wasted.

•full employment means the full utilization of all available labor and capital resources so that the economy is able to produce at the limits of its potential gross national product.

NATIONAL INCOME EQUILIBRIUM with inflation

Real Output (National Income)

ExpenditureY1=C+I+G+(X-M)

Y=E

45°

Yfe=C+I+G+(X-M)

Yfe Ye1

Inflationary Gape1

ef

NATIONAL INCOME EQUILIBRIUM with unemployment

Real Output (National Income)

Expenditure

Y0 = C+I+G+(X-M)

Y=E

45°

Yfe=C+I+G+(X-M)

Ye0 Yfe

Deflationary Gape0

ef

MULTIPLIERSAny Injection will multiply positively, whileany Leakage will multiply negatively.