Cu m com-mebe-mod-i-multiplier theory-keynesian approach-lecture-1

SM/CU/MCOM/FIRST YEAR/MEBE/MOD-I/2017-18 MOOCS: subirmaitra.wixsite.com/moocs 1
2.1 Introduction:
If we plot the values of GDP of any country over a period of say, fifty years, we will find a
periodic fluctuation around some trend line. These systematic fluctuations in the level of aggregate
economic activity is known as business cycles consisting of booms or expansions and recessions or
contraction. The long run model of the economy cannot explain recession or boom when the economy
deviates from its long run path.
GDP
Time
Figure: 1
To understand what kind of forces is responsible for these fluctuations in real output relative
to trend, we develop ‘Keynesian Model’. The cornerstone of this model is the mutual interaction
between output and spending: spending determines output and income, and at the same time, output
and income also determine spending.
We shall first develop a very simple model of income determination known as Simple
Keynesian Model. This most important assumption of this model is that prices are constant. In the
short run, firms stand ready to supply whatever output their customers want at the given prices. Thus,
demand becomes the ruling force in this model. If demand is strong, real GDP exceeds potential. In
recession, when demand is weak, real GDP drops below potential.
2.2 Simple Keynesian Model:
The Simple Keynesian Model is a static model of the economy which helps us to determine
equilibrium real national income based on ‘effective demand’ principle.
Equilibrium Income: Cases of Open and Closed Economies, Multiplier theory-
Keynesian Approach
Lecture-1

2.2.1 Assumptions:
(i) One-sector model: The SKM is a one-sector model which includes only the goods
market.
(ii) Absence of monetary sector: There is no monetary sector in the SKM.
(iii) Static model: The SKM is a static model. The model solves for static equilibrium
level of real output, which is the value of real output that has no tendency to change
once it has been established.
(iv) Closed economy with or without Government: The SKM assumes a closed
economy (i.e. without foreign trade) with or without Government.
(v) Constant prices: In stark contrast to the quantity theory model, the SKM assumes
an exogenously fixed price level.
(vi) Short-run model: The model is a short-run model and determines the value of real
national output for a particular period of time, such as a year.
(vii) Fixed stock of capital and labour: The model assumes that both the stock of
capital and the labour force, which when fully utilised determine the maximum level
of real output the economy can produce, are constant.
(viii) Profit maximization: An underlying behavioural assumption of the model is that
firms act as profit maximisers. If demand for their output exceeds supply, firms
increase production, providing there are spare resources put to work. Conversely if
supply exceeds demand, firms reduce output.
(ix) Effective demand principle: The SKM is based on Keynesian ‘effective demand
principle’. According to this principle, since commodities are necessarily produced
for a market, the size of the market must regulate the level of commodity production.
Put differently, effective demand refers to that level of the value of aggregate output
which, if produced and paid out as income, will be matched by an equivalent amount
of expenditure.
2.3 Equilibrium Income (AD—AS Approach):
Equilibrium in the SKM requires that the supply of real national output, Y, equals the quantity
of national output which people wish to buy, E. The condition for static equilibrium in this model is
therefore
Y = E ..............(1)

where E is the ‘desired’ Aggregate Demand or, alternatively, ‘Planned Expenditure’. Alternatively,
we can interpret Y as ‘Aggregate Supply’ or ‘Actual Expenditure’ in the economy and rewrite the
above condition as
Actual Expenditure (Aggregate Supply) = Planned Expenditure (Aggregate Demand) …(2)
2.4 Simple Keynesian Model without Government and Foreign Trade:
We now discuss SKM without government and foreign trade. Thus the economy is closed one
without any government expenditure (G) as well as taxes (T).
2.4.1 Aggregate Demand (Planned Expenditure) in SKM without Government:
Aggregate Demand or planned expenditure in SKM without government is composed of real
consumption expenditure C, and real investment expenditure, I.
2.4.2 Consumption Function:
Although many factors affect consumption, aggregate disposable income is the most important
one. Consumption is assumed to vary directly with income (Y). Specifically, consumption is assumed
to increase as income increases, with the increase in consumption being less than the increase in
income. In equation form, the consumption function is
C = C0 + c Y (C0 >0, 0<c<l) ….......(3)
where C and Y represent real consumption and real income, respectively. The equation indicates that
consumption is a linear function of disposable income. In the equation, C0 and c are constants, called
parameters. Consumption C and income Y are variables.
The constant C0 is called autonomous consumption or ‘subsistence consumption’. When Y
= 0, C = C0. It is that level of consumption which people must have in order to subsist even if income
level falls to zero and it is exogenously given.
The parameter c, called the marginal propensity to consume or MPC, is the slope of the
consumption function. If ∆Y denotes a change in income and ∆C denotes the change in consumption
associated with the change in income, the MPC, equals ∆C / ∆Y. For example, if Y increases by
Rs.200 and, as a result, consumption increases by Rs.150, the MPC is 150/200 = 0.75. Thus
consumption increases as Y increases, but by a smaller amount. This implies that, the MPC, must be
between 0 and 1, an assumption which is in accord with the empirical evidence.
We can graphically represent (Fig:2) the consumption function. We know that ' C0 ' is the
intercept parameter and 'c' is the slope parameter. Once the intercept and slope are specified, a straight
line is completely determined. For example, if C0 =100 and c = 0.75, the function will start at C0 =
100 and have a slope c = 0.75. If there is a change in C0, the consumption function will shift so that

the new function is parallel to the old. If there is a change in c, the function will rotate about the
intercept, C0 and will be either steeper or flatter.
C0
Figure: 2
2.4.3 Investment Function:
Like consumption, investment depends on many factors, including interest rates. In the SKM,
however, investment is assumed to be an autonomous or exogenous variable -- a variable whose
value is determined outside the model. Thus, investment is a constant, I0 (I0 >0).
Since investment is assumed to be constant at the Ī level, the investment function is
I = I0 (I0 >0) ………(4)
where I represents real investment and Ī represents a given, positive level of investment. Suppose I0
equals Rs. 50. With investment on the vertical axis and income on the horizontal, the investment
function is plotted as the horizontal line in Figure: 3,indicating that investment does not vary with
the level of income.
C = C0 + c.Y
Income (Y)
Consumption (C)
Investment (I)
I = I0
Income (Y)
Figure: 3

2.5 Equilibrium Income in Simple Keynesian Model without Government:
The economy in the SKM is said to be in equilibrium when
Actual Expenditure (Aggregate Supply) = Planned Expenditure (Aggregate Demand)
i.e. Y = C + I ….(5)
 Y = C0 + c Y + I0
 Y = C0+ c.Y + I0
 Y = C0 + c.Y + I0 …..(6)
By rearranging we get:
YE = [{C0 + I0} / (1 – c)] ….(7)
where YE is the equilibrium level of income in the SKM without government -- that level of income
which makes actual expenditure (AD) in the economy same as planned expenditure (AS).
2.6 Graphical Illustration:
The aggregate supply-aggregate demand approach is developed graphically in Figure: .
Aggregate supply, the output of goods and services, is depicted by the 45° line. With the same scales
on both axes, output on the vertical axis equals output or income on the horizontal axis for all points
on the 45° line. The 45° line is not a 'true' aggregate supply curve. For example, it indicates that any
amount, from 0 to infinity, may be produced. This is not possible; production is limited by the nation's
resources and its technology. Nevertheless, in the development of the model, it is helpful to think of
the 45° line as an aggregate supply curve.
YE
Figure: 4
Aggregate demand represents society's demand for goods and services. With no foreign trade sector,
it consists of the demand for consumer goods and services, the demand for investment goods and
government purchases. Consequently,
AD = C + c.Y + I
Aggregate Supply (Y)
Aggregate Demand (AD)

AD = C + I
= (C0 + c.Y + I0 )
Graphically, the aggregate demand line is the positively sloped line AD whose intercept is
equal to (C0 + I0 ) and slope is equal to 0 < c < 1.
With the 45° line representing ‘aggregate supply’ or ‘actual expenditure’ and the AD line
representing ‘aggregate demand’ or ‘planned expenditure’, the equilibrium level of income is YE.
Income level YE is the equilibrium level since it is the only level for which aggregate supply equals
aggregate demand. At income levels greater than YE, aggregate supply (represented by the 45° line)
is greater than aggregate demand (represented by the AD line), and income has a tendency to fall. At
income levels less than YE, aggregate supply is less than aggregate demand, and income has a
tendency to rise.
When AS > AD, Y tends to fall because of the unplanned inventory accumulation
by the firms (Iu = ∆inv. > 0), as producers are unable to sell their products.
When AD > AS, Y tends to increase because of the unplanned depletion in
inventories by the firms (Iu = ∆inv. < 0) to meet increased demand.
When AD = AS, Y is at its equilibrium level.
Since income tends to fall when AS > AD and to rise when AD > AS, income
eventually gravitates to its equilibrium level => stable equilibrium.
2.7 Economic Explanation:
If the nation's income (output) equals the equilibrium income (output), firms will be able to sell
their entire output. Consequently, no incentive exists for them to alter their production and income
remains at the equilibrium level.
If the nation's output exceeds the equilibrium output, firms are unable to sell their entire output
and experience a buildup in their inventories. An incentive exists, therefore, for them to reduce
production. As a result, output falls until it equals the demand for goods and services. Similarly, if
the nation's output is less than the demand for goods and services, firms sell more than they are
producing and experience a depletion of their inventories. An incentive exists, therefore, for them to
increase production. As a result, output rises until it equals the demand for goods and services.
2.8 Equilibrium Income in Simple Keynesian Model with Government:
We now discuss SKM with government but without foreign trade. Thus the economy is closed
one but government plays an active role in the economy. Thus, government spends (G) as well as
taxes (T).

2.8.1 Aggregate Demand (Planned Expenditure) in SKM with Government:
Aggregate Demand or planned expenditure in SKM with government is composed of real
consumption expenditure C, and real investment expenditure, I and real government purchases, G.
Consumption and investment functions have been discussed above. But the presence of government
makes certain changes in the C function.
2.8.2 The Consumption Function in SKM with government:
In the presence of a government, imposing taxes on income, consumption is assumed to vary
directly with disposable income (YD). Specifically, consumption is assumed to increase as disposable
income increases, with the increase in consumption being less than the increase in disposable income.
In equation form, the consumption function is
C = C0 + c YD (C0 >0, 0<c<l) ….....(8)
where C and YD represent real consumption and real disposable income, respectively. The equation
indicates that consumption is a linear function of disposable income. In the equation, C0 and c are
constants, called parameters. Consumption, C, and income, Y, are variables.
Disposable income (YD) is equal to income plus transfers (TR) less taxes(T):
YD ≡ Y + TR – T …….(9)
The constant C0 is called autonomous consumption or ‘subsistence consumption’. When YD
= 0, C = C0. It is that level of consumption which people must have in order to subsist even if income
level falls to zero and it is exogenously given. The parameter c, called the marginal propensity to
consume or MPC, is the slope of the consumption function. We can graphically represent the
consumption function same as in Figure:2.
2.8.3 Government purchases:
Like investment, real government purchases are also exogenously given. Government
expenditure includes such items as national defense expenditures, salaries of government employees
etc. G is a policy variable, whose value is determined by the Government. In a democratic country
like ours, G is decided after prolonged discussion in the Parliament. Hence we can write:
G = G0 ……..(10)
2.8.4 Taxes and Transfers:
Transfers (or transfer payments) are those payments that are made to people without their
providing a current service in exchange. Typical transfer payments are social security benefits and
unemployment benefits. In the SKM, transfers are assumed to be exogenously given
i.e. TR = TR0 ……(11)
Taxes are compulsory payments to be made by the citizens of a country. Taxes may or may
not depend on the income. For example,

(i) If the taxes are lump-sum, T = 𝑇̅ (𝑇̅ >0) ……(12)
(ii) If taxes are function of income: T = T(Y), 0< TY <1 ……(13)
(iii) If taxes are proportional to income: T = t. Y, 0 < t < 1 …..(14)
(iv) If taxes are partly lump-sum and
partly proportional: T = 𝑇̅ + t.Y (𝑇̅> 0; 0 < t < 1) .…(15)
Note that ∂T/ ∂Y = TY represents the change in T due to one unit change in Y which is the
tax rate. Under proportional income tax, ∂T/ ∂Y = t where ‘t’ is the fixed tax rate such that 0 < t <
1. Obviously, T and t are decided by the Government and is therefore exogenously given.
2.8.5 Equilibrium Income in Simple Keynesian Model with Government:
The economy in the SKM is said to be in equilibrium when
Actual Expenditure (Aggregate Supply) = Planned Expenditure (Aggregate Demand)
i.e. Y = C + I + G ….(16)
 Y = C0 + c YD + I0 + G0
 Y = C0 + c.( Y + TR0 –T0) + I0 + G0
 Y = C0 + c.(Y + TR0 – t .Y) + I0 + G0
(assuming proportional taxes) …..(17)
By rearranging we get:
 YE = [ 1 / {1 – c(1-- t)}]{ C0 + c.TR0+ I0 + G0} ….(18)
where YE is the equilibrium level of income-- that level of income which makes actual
expenditure(AD) in the economy same as planned expenditure(AS).
Alternatively, the AD equation can also be written as:
 AD = { C0 + c.TR0 + I0 + G0} + c.(Y – t .Y)
= 𝐴̅ + c (1 – t) Y …..(19)
where 𝐴̅ = { C0 + c.TR0 + Ī + G0} is the autonomous part of AD.
The equilibrium condition:
Y = 𝐴̅ + c (1 – t) Y
=> YE = [ 1 / {1 – c(1-- t)}]. 𝐴̅ ……(20)
If the nation's income (output) equals the equilibrium income (output), firms will be able to
sell their entire output. Consequently, no incentive exists for them to alter their production and
income remains at the equilibrium level.
If the nation's output exceeds the equilibrium output, firms are unable to sell their entire output
and experience a buildup in their inventories. An incentive exists, therefore, for them to reduce

production. As a result, output falls until it equals the demand for goods and services. Similarly, if
the nation's output is less than the demand for goods and services, firms sell more than they are
producing and experience a depletion of their inventories. An incentive exists, therefore, for them to
increase production. As a result, output rises until it equals the demand for goods and services.
2.8.6 Graphical Illustration:
The determination of equilibrium income in SKM with government is shown graphically in
Figure: . Aggregate supply, the output of goods and services, is depicted by the 45° line. With the
same scales on both axes, output on the vertical axis equals output or income on the horizontal axis
for all points on the 45° line. The 45° line is not a 'true' aggregate supply curve. For example, it
indicates that any amount, from 0 to infinity, may be produced. This is not possible; production is
limited by the nation's resources and its technology. Nevertheless, in the development of the model,
it is helpful to think of the 45° line as an aggregate supply curve.
Aggregate demand represents society's demand for goods and services. With no foreign trade
sector, it consists of the demand for consumer goods and services, the demand for investment goods
and government purchases. Consequently,
AD = C + I + G
 = {C0 + c.TR0 + I0 + G0} + c.(Y – t .Y)
= 𝐴̅ + c (1 – t) Y
Graphically, the aggregate demand line is the positively sloped line AD whose intercept is equal to
A and slope is equal to 0 < c (1 – t) < 1.
YE
Fig: 5
With the 45° line representing ‘aggregate supply’ or ‘actual expenditure’ and the AD line
representing ‘aggregate demand’ or ‘planned expenditure’, the equilibrium level of income is YE.
AD = 𝑨̅ + c (1 – t) Y
Aggregate Supply (Y)
Aggregate Demand (AD)

Income level YE is the equilibrium level since it is the only level for which aggregate supply equals
aggregate demand. At income levels greater than YE, aggregate supply (represented by the 45° line)
is greater than aggregate demand (represented by the AD line), and income has a tendency to fall. At
income levels less than YE, aggregate supply is less than aggregate demand, and income has a
tendency to rise.
When AS > AD, Y tends to fall because of the unplanned inventory accumulation by the firms
( Iu = ∆inv. > 0), as producers are unable to sell their products.
When AD > AS, Y tends to increase because of the unplanned depletion in inventories by the
firms ( Iu = ∆inv. < 0) to meet increased demand.
When AD = AS, Y is at its equilibrium level.
Since income tends to fall when AS > AD and to rise when AD > AS, income eventually
gravitates to its equilibrium level => stable equilibrium.
2.9 Is equilibrium income = full employment income?
In the SKM with or without government, the equilibrium level of income may or may not
represent a full-employment level. That is, full-employment may or may not exist at the equilibrium
level of income. Unemployment may exist at the equilibrium level of income because, for the model
in question, the equilibrium level of income is merely the level where intended investment equals
saving or, alternatively, aggregate supply equals aggregate demand. Here, we assume that
unemployment exists so that increases in aggregate demand result in increases in production.
2.10 Existence of Equilibrium:
Once the equilibrium in the SKM is established one may question whether is exists or not.
The equilibrium exists if AD and AS curves intersect each other in positive quadrant so that YE > 0.
For this sufficient condition (with 𝐴̅ >0) is that AD must be flatter than AS. Since slope of AD is c
(1 – t) and that of AS is 1, the sufficient condition for the existence of equilibrium is c (1 – t) < 1
which always holds as 0 < c (1 – t) < 1 (Fig: 5). That equilibrium would not exist if c (1 – t) > 1
may be seen from the Fig: where AD is steeper than AS so that no intersection is possible in the
positive quadrant.
2.11 Stability of Equilibrium:
That equilibrium in the SKM is stable can be realized from the fact that a disturbance in the
equilibrium causing the income Y to be different from YE, generates such forces which brings back
the economy back to equilibrium once again. With 𝐴̅ > 0, the sufficient condition for this stability
is that AD is flatter than AS i.e. c (1 – t) < 1. Since 0 < c (1 – t) < 1 always, the SKM gives a stable
equilibrium. The economic interpretation of this stability is:
When AD < AS

 Unplanned accumulation of inventories by the firms (Δinv >0)
 Unplanned or unintended investment ( Iu) > 0
 Reduction in production by the firms,
 Y falls till Y = YE
Again when AD > AS
 Unplanned decumulation of inventories by the firms (Δinv < 0)
 Unplanned or unintended investment ( Iu) < 0
 Increase in production by the firms,
 Y increases till Y = YE
 Stable Equilibrium.

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