A Simple Model of Income Determination

SESSIONS 3 & 4

Objective

• To understand how different expenditure components (consumption, investment, govt. expenditure, tax) collectively determine the level of GDP.

• To understand how changes in those factors cause a change in the level of GDP.

3

Questions of Macroeconomics

• If I consume more, will GDP increase?

• If I save more, will GDP increase?

• If I invest more, will GDP increase?

• If GoI spends more, will GDP of India increase?

• If I consume more, will investment in India increase?

• If I save more, will investment in India increase?

4

Illustration

• Z = X + Y

• Under what condition does a rise in X cause a rise in Z?

• Under what condition a rise in X may cause a rise in Y as well?

• Can it so happen that a rise in X would cause a fall in Y?

• Effects depend on whether Z is fixed or flexible.

5

Some Preliminaries

• What is saving in macroeconomics?

Unspent income.

• What is investment in macroeconomics?

Expenditure on “Capital” goods.

• Should not be confused with “financial investment”.

• Caution:

• Saving has nothing to do with liquidity or money available in the financial market.

• Higher income does not lead to more “money”.6

A Simple Macro Model

Assumptions

• Short run, prices are fixed

- What is the immediate implication of fixed price for market adjustment?

- We can sense that if prices are fixed, it must be the output that changes to bring in demand-supply balance.

• There is a fixed available supply of labour and physical capital stock.

• Will not consider labour markets.

• The output is demand determined.

• What is meant by the assertion that the output is demand determined?

7

Demand Determined Output

• There is excess capacity; the economy is not able to

produce to the extent it can as there is lack of aggregate

demand.

• Factors of production are not fully employed; a feature

of recession (demand constraint economy).

• If aggregate demand can somehow be increased,

producers will respond to higher demand by raising

production, till economy hits full capacity barrier.

• Higher production means higher GDP, higher income

etc.

• Therefore this model (and subsequent ISLM) is

applicable only in recessionary condition.

Assumptions (contd)

• Will not consider financial assets.

• There is money but interest rates are fixed

• No foreign trade, hence need not worry about exchange rates and financial capital mobility.

• Output increases lead to employment increases.

- Why?

• The model is called “simple” as only goods market is considered.

9

The Circular Flow

• Total of incomes and total of expenditures on

final goods and services both measure GDP.

• If we equate income and expenditure (i.e. two

flows) we can get an equilibrium situation.

10

A Macro Economic Identity

• Income has three parts:

• What we consume by spending

• What we save by not spending

• What we do not get to see since government takes it

as direct income taxes

• Therefore: Y = C + S + T• Y : Income, Output

• Expenditure has three parts:

• Total Expenditure, E = C + I + G(for the time being we are ignoring net exports NX)

13

Macroeconomic Equilibrium

• INCOME = EXPENDITURE

• Y = E

• Y = C + I + G

• Alternatively,

• C + S + T = C + I + G

• S + T = I + G• If we assume that there is no govt., T = G = 0

• Above condition reduces to S = I

• Income-expenditure balance can also be stated in terms of Saving-Investment balance (leakage = injection).

14

Saving-Investment Balance

• Y = C + I + G

• Saving of the entire economy (total saving) =

Total income – expenditure by households –expenditure by govt. = Y – C – G

• However, Y – C – G = I

• Therefore National Saving = Investment

• We can also rewrite above as:

• [(Y – T) – C ] + [T – G] = I• Household (private) saving + Govt. (public) saving =

investment.

• SP + SG = I15

Quick Summary

• There are 3 ways to represent macroeconomic

equilibrium.

• Aggregate Supply = Aggregate Demand

• Income = Expenditure (Y = AE)

• Saving = Investment (S = I)

• They all are equivalent and each is reducible

to the other.

16

Some assumptions about how people decide on their expenditure magnitudes

• C : determined by the “consumption function” which

positively relates consumption to income (disposable

income) and has a slope less than one.

• Intuition: when income increases people consume

more, but not the entire incremental amount.

• C = C(Y – T) with 0 < C′ < 1

• This means that the slope of the consumption

function is throughout positive but less than one.

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• The slope is called the marginal propensity to consume or MPC.

• The consumption function is supposed to have a positive value when disposable income is zero. Why?

• Because people would dissave to survive.

• This expenditure may be called the subsistence consumption or autonomous consumption.

• One specific linear form may be: C = C0 + c (Y – T)

• Here we have 0 < c < 1 [c = mpc]

• C0 is called the autonomous consumption.

• Meaning of autonomous? Does not depend on current disposable income.

18

Consumption Function

• Private investment is assumed to be exogenously given (called autonomous spending) I.

• Investment is supposed to depend on expectations of future business prospects.

• Government spending G and direct taxes T are held constant as exogenous variables determined by macroeconomic policy considerations.

19

Other Expenditures

Determining Equilibrium Income

• The equilibrium condition:

Income = Planned expenditure

Y = C + I + G

Y = c (Y – T) + I + G

• How many unknowns?

• This equation has one unknown Y, with T, G and

I given exogenously.

20

GITYcY ) (

Can solve for Y

`

S, I

E C + I + G

C + I

C

Y

Y

I

I + GS

S + T

Y*

45

With autonomous

consumption, the

saving function

takes the form:

S(Y) = − C0 + sY

21

Shifts in Exogenous Variables

• Suppose autonomous investment increases (due to

better business prospect), then planned expenditure

C + I + G increases (shifts to a higher level).

• In the new equilibrium Y is higher than before.

• Why does this happen? How?

22

The Multiplier

• First visualize it geometrically.

• Can you work out the reasoning?

• Suppose investment increases by ∆I, then immediately Y increases by ∆Y, this induces consumption to increase by c∆Y, then it increases by c²∆Y and so on till Y = planned E is re-attained.

• The expansion is in the series ∆Y + c∆Y + c²∆Y + c³∆Y + ……

• Answer?

23

• Let’s assume C(Y – T) = mpc (Y – T)

• Y = mpc (Y – T) + I + G

• ∆Y = mpc ∆Y + ∆I

• ∆Y(1 – mpc) = ∆I

• ∆Y/ ∆I = 1/(1 – mpc)

• (1 – mpc) is the marginal propensity to save < 1

• Note: ∆Y/∆I >1 output will rise more than the

initial increment in investment Multiplier

24

The Multiplier

• Derive it Mathematically

Y = C(Y – T) + I + G, ∆I > 0

dY = C′dY + dI

dY(1 – C′) = dI

dY/dI = 1/(1 – C′)

• (1 – C′) is the marginal propensity to save < 1

25

The Multiplier

• What is the value of multiplier when mpc = 1?

• Recall that output can be expanded till the point

economy hits full capacity barrier.

• When mpc is close to 1, economy quickly gets out

of the recessionary condition with an additional

dose of expenditure.

• Lesson – In recessionary condition, higher

expenditure in any form is beneficial for

economy.

26

A Quick Quiz

An Increase in G

• If government decides to spend more (as it often does in recession), aggregate demand rises and a multiplier is set into motion exactly as before.

• dY/dG = 1/(1 – mpc) > 1

• Called the Govt. expenditure multiplier.

• As a fiscal policy measure government can spend more to increase output and employment in the economy.

• Increase in output is more than the initial dose of expenditure.

27

Adjustment for ΔG = 1

28

A Change In Taxes

• What happens if there is a tax cut?

• Disposable income rises, hence consumption rises,

aggregate demand rises, output rises, employment rises

till a new (higher Y) equilibrium is attained.

• What happens to the diagram?

31

The Tax Multiplier

• Y = mpc (Y – T) + I + G

• Effect of a tax cut: ∆T < 0

• ∆Y = mpc ∆Y – mpc ∆T

• ∆Y (1 – mpc) = – mpc ∆T

• ∆Y/∆T = – mpc/(1 – mpc)

• Since ∆T < 0, ∆Y/∆T > 0

• Alternatively,

• dY = C′dY – C′dT

• dY(1 – C′) = – C′dT

• dY/dT = – C′/ (1 – C′)

32

A Quick Quiz

• Between govt. expenditure multiplier and tax

multiplier, which one is larger?

33

The Balanced Budget Multiplier

• What happens if the government raises taxes and spends the entire amount? (incremental govt. expenditure is entirely financed by raising tax)

• What is the total effect on output? Does it rise or fall?

∆T = ∆G

Y = mpc (Y – T) + I + G

∆Y = mpc ∆Y – mpc ∆T + ∆G

∆Y = mpc ∆Y – mpc ∆G + ∆G

∆Y (1 – mpc) = ∆G (1 – mpc)

• ∆Y/ ∆G = 1 > 0 34

The Balanced Budget Multiplier

• Mathematically,

Y = C(Y – T) + I + G

dY = C′dY – C′dT + dG

dY = C′dY – C′dG + dG

dY (1 – C′) = dG (1 – C′)

• dY/dG = 1 > 0

35

If I save more, will GDP increase?

36

What happens if we bring in Net Exports?

• Y = C(Y – T) + I + G + X – M

• X – M = Net exports

• X is assumed to be exogenously given like G, T and I (why?).

• M is taken to be a positive function of Y.

• M = M(Y); 0 < M′ <1; M′ - marginal propensity to import.

• Reason for such assumption?

• As income rises people spend more part of their income on imports (like luxury consumption).

37

What happens if X increases?

• Can you visualize the diagram?

• What is the economic reasoning now?

• Assume that M = M(Y) = mpm Y

• Y = mpc (Y – T) + I + G + X – M

∆Y = mpc ∆Y + ∆X – mpm ∆Y

∆Y(1 – mpc + mpm) = ∆X

∆Y/∆X = 1/(1 – mpc + mpm) = 1/(mps + mpm)

• Called the foreign trade multiplier.

• Can you compare this multiplier with the earlier multiplier for a closed economy without trade?

38

What happens if X increases?

• Derive it mathematically

• Y = C(Y – T) + I + G + X – M

dY = C′ dY + dX – M′ dY

dY (1 – C′ + M′) = dX

dY/dX = 1/(1 – C′ + M′) = 1/(mps + mpm)

39

A Numerical Example

• A Keynesian economy is described by the following

relations.

• C = 500 + (0.5)YD ; I = 100, T = 80, G = 200

• Graph (with correct labels) equilibrium Income (Y)

and Expenditure (E).

• Solve for private saving and public (i.e. govt.) saving.

• Find the multiplier and total autonomous spending

(i.e. spending that are independent of current level of

income).

40

• Total demand = Aggregate Expenditure (E) = C + I + G

• Goods market equilibrium, Y = AE; So we have Y = E

• Remember that YD = Disposable income = Y – T

• Substituting in Y = C + I + G

• Y = 500 + (0.5)YD + 100 + 200

• Y = 500 + (0.5)(Y – 80) + 100 + 200

= 800 + (0.5)Y – 40

= 760 + (0.5) Y [= Autonomous expenditure +

Income induced expenditure]

• So, equilibrium output Y = 760/0.5 = 1520

41

• YD = 1520 – 80 = 1440 (disposable income)

• C = 500 + (0.5)(1440) = 1220 (equilibrium

consumption expenditure)

• Autonomous spending = 760, Income induced

spending, (0.5)Y = (0.5)1520 = 760

• Equilibrium expenditure, E = 1220 + 100 + 200 =

1520 (total demand)

• Multiplier = 1/[1 – mpc] = 2

• Private Saving, SP = YD – C = 1440 – 1220 = 220

• Public Saving, SG = T – G = 80 – 200 = – 120 (budget

deficit)

• Check that S = I holds; S = SP + SG = 220 – 120 = 100 = I

42

43

Y = E, Slope = 1

E = 760 + 0.5 Y

Y* = 1520

Y

E

Autonomous spending = 760

E* = 1520Slope = 0.5