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
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