KEYNESIAN CROSs MODEL

The Great Depression of 1929

through 1933 was world-wide. The most severely hit
was the USA. where the stock market crash
for four years. It led to enormous
began on October 24, 1929 and continued
unemployment all over the world. In the United
States, the unemployment rate shot up from a low
of about 3 per cent in 1928 to a
high of about 25 per cent in 1933, and the real GDP fell
by about 30 per cent during
the period. Although the recession was not so
deep in most other countries, it was well
spread throughout the world. For example, during 1929-32, the real GDP fell 5.8.
15.7, 11.0, 22.5, 8.2, 8.0, 18.2 and 11.5 by
per cent in the United Kingdom.
Germany.
France, Austria, Netherlands, Spain, Czechoslovakia and
Karl Marx's
Hungary, respectively. Thus.
prediction of the collapse of the capitalism was well in sight. Further, it
provided sufficient proof for the inappropriateness of the classical theory of
output.
employment and price, which is characterised by the full employment equilibrium.
Since no theory is good unless it
explains the historical and current facts, Keynes was
prompted come out with an alternative theory, which later became the Keynesian
to
theory of income determination, which he outlined in his famous book "General
Iheory of Employment, Interest and Money"', published on February 4, 1936. This
marked the second revolution in macroeconomics.
Keynes is now regarded as the
1ather of macroeconomics. The
Keynesian model, as understood currently, has two
versions, which are (a) Fixed price model and (b) Flexible price model.
In order to clearly demonstrate the role of the fiscal policy in stabilising an
OIETWISe fiuctuating economy, the fixed price model is further presented in three
erSions, which are the: (i) Keynesian cross model, (ii) IS-LM model and (ii) Open
economy (Mundell-Fleming) model.
ne
present section deals with the first of these models. It is
the outset that: pertinent to note at

The Keynes
eynesian model in all its versions assumes some degree otf wage-price
g which reverses the classicalist Say's Law philosophy to the Keynesian's
296 Macrorcono

hUply, wliinh in

belief hal
demand
creates
i oW
Non a r k e t cleating cquiliai onatrat
at
possibility of
Uncploynent o tl u
(b) Monclary uolicy s t
lor the(a) Fiscal policy,
n active role he o t h e I W I S C licuating
eoti.
y
slabilisn
and trade policy
n

taken nmeTcly as a lact of lfe ul..

The wage-price
igidily was
ww% cplateA
Furlher, the KeyCsiat
later by the new Keynesuns only. ed price wvle
much
oulpul is dclemuncd by the auure
volume ol
postulates that
the
were cxpcctcd to supply any
quuantity
cts perditure
althe
demand and fims f
governinnents and inveslors demand
priceto meet the eonsumers,
on the current output
lalls short of the
Current income (i.c, if sale
pro spendiny
short ol the cOSIS ol producing i1), incomc us

current production lall to the

oulput and employment (vide thc fve
level of expenditure,
Via a reduction in
or outpul 1s purely demand dctermned
fixed r
wage rate). Thus, the real income Since
the
departure from the classical mocdet
Keynesian model marks significant
a
Could
be labeled as a revolution
in macrocconomics, As would be scen below K
consumption theory and a
new money demand functian
K.cynes
provided a new
functions (vide Chapter 9)
new labour demand-supply
Model
Description of the
The Keynesian cross model is very simple and the Simplest form of this model ca d
be expressed in just two equations:"
Consumption function: C-Co bY T,) (11.1)
Income identity: Y=C+1,+G (11.2)
where C consumption expenditure,
Y real income,
T= taxes net of transfer payments,
= investment expenditure and
G government expenditure
The subscript 0 (zero) indicates that the concerned variable is autonomous
(exogenous), for example, C% = autonomous consumption. The b is a parameter

Unlike the classicalists. Keynes believed that investment expenditure was not quite
sensitive to variations in the rate of interest. The cross model equates this insensitivity

to zero and, thus, treats all investments as autonomous. Since here, as well as
all versions of the fixed price model,
the price is constant, it is immaterial as
whether
the various
variables are in nominal or in real terms. Note that the Keynesian
consumption function (11.1) hypothesizes that (current) consumption (and thus.
saving) has two parts, viz. autonomous and
induced, the latter varies directly with
(current) income, as explained in Chapter 5. Keynes, thus,
ignored the interest ta
a determinant of consumption, which happened to be the only factor deteriining

private consumption/saving in the classical model. Further, the said equation inata es
that
if income goes up by one unit, ceteris paribus, by b.
consumption would go up
 Classieal and Keynesian ixcd Price
Models 297
that
Thus, note that the arameter h denotcs the
Keynes lamous marginal
Tquation (11.2) is the equilibrium condition, which equatespropensity
income
nenditure. where the latter
cquals the sum of the
planne

ent and planned private

msunmptiom, planned
planned government expenditure.
he
solutuon of he above two-cquation model for inconne would
give:
(11.3)
ethe marginal propensity to consune IS less than unity (vide Chapter 5), b< 1.
1The last tem is referred to as the
and avondngly
autonomous expenditure
nesian or fiscal) multiplier k. As will be apparent from cquation (11.3), if
(or
emment expenditure goes up by one rupce, all other variables held constant. the
nomewould mcrease by rupces
c h cquals rupces five, if bh =0.8. Also,
anvestment or autornomous part ot private consumption expenditure increases by
nune onc, ctris paribus. real ncome goes up by R5. The higher the b (marginal
nrnensitn to consume). the larger is the multiplier (k), and vice versa. In this model,
inestment always drags saving along with it at an equal pace. The equilibrium
wqures income to be cqual to all expenditures (Y = C+ Ih + Gn), which means
ational sav ing (= Y-C- G) equals national investment (V%). When investment
nereases. sav ings fall short of investment and the restoration of equality requires
SaVing to go up. Further, corresponding to the consumption function, the saving
tanction is given by:
National saving =

private saving +
government saving.
This means.
S=( -To- ) + (7o-G) = Y-C%-b (Y- 7o)-Go

S-C%+ Gg)+ h To+ (1 - b)Y

This suggests that, given the exogenous variables and the marginal propensity
consume, saving can increase only if income goes up. Further, since increase in
n g must cqual increase in investment, income must increase by a multiplier equal

0 he question is how this much increase in income comes through. This

5 eplained a little later, after the geometric explanation of the model, through the

ample of an increase in autonomous expenditure, which amounts to the same as

NTse in investment, as investment in this model is all-autonomous. In the above
aton, marginal propensity to save (MPS) equals (1 - b) and thus MPC + MPS
-1 -)=1.
An important application of the above model is found in the balanced budget
plier. The said multiplier states that if the government expenditure goes up
e one, and at the same time tax revenue goes up by rupee one (leaving the
udget balance unchanged) equation (11.3) would indicate that the income would
go up exactly by rupee one. This is so for
and
1-b 1-b
298 Macroeconon2

and thus
Y

because it indicates that the go.

This result
is interesting can increas
K10
say. by
billion, simply by increasing its expenditu
incread

national
income,
same through an increa
increase in tax reven by }l
nt
equivalent
financing the this so hanns
billion and rather Simple model,
In this cause inecomeHowis
this is possible? d e t e r m i n e d , and while the

solely demand
(expenditure) government spends all its
spend only 80 per cen
consumers
).
revenues (MPC for
government=
rest they save). As G, increa
of the increase
income (the
in their by R10 billion
K50 (10 k =
10 X 1/(1 -

0.8) hil
income is up by
ceteris paribus.multiplier
just explained process; and as o increases by 10 billion inaugh
s down
0.8). giving a of R10
T10 billion
net increase
billion in
by 40 billion (10
X 0.8/(1
-

natior
Incidentally. note an important po1nt here. n e pure government
expendin
income.
multiplier is 1/(1 - b) (which is.
accompanied by increase taxes)
in
(i.e. not
throoh
balanced budget (government expenditure financed ough in-
than unity) while the
creased taxes) multiplier is unity.
This means that government expenditure financed
than the one financed through taxation
through public debt is more expansionary
taxes reduce disposable income of the private sector
This so happens because while
government bonds (or lending to government)
by them does not. The said
buying
observation contradicts the Barro-Ricardo Equivalence theorem, which in any way,

as argued in Chapter 10, is not really

valid due to its unrealistic assumptions. The
cross model could be described geometrically as in Fig. 11.2.

B
A

45
o
YY Income

Fig. 11.2 Keynesian Cross Model

med

planne
in the
figure, the line C ransforCtheE
desired) expenditure denotes the consumption function,
total
ViCe
(or
function, and the 45° line
versa. The
total
distance OA =
autonomous consumption
=

mpti
transform autonorium1s
nomous

its (C%) a
expenditure.
given by point K, The4 slopes
Cn of both
t hthe
the C and E e s b The equ
1. The equr <
w h e r e

linesD.
=

the E line where income = ment) o.I f

or

crosses hthee 45° expenditure (or saving .

line, hence,
investment)

mno
del.
any

the name the cross

Keynesia
 aulonomous
alls eNpendiure nerease',
expenditue
lhe liie
a the wll ahufi up
the cross WOuld move to
point nd the mcoe to, say. ilhe
wuuld in
The
merease in income would be a
uliplier of ihe ee to, al
neease
The said multipliei is he host in theaulonomus
eyend.

shall
mporlt element of the
as we see later, the keynesian
magc
Ignores, eowding out effet and the linan
roblems
of overnment expenditure ng
does the multiplier work When the aulonoous
How
menl expenditure) mereases by, expenditure (investmen
and or govermm

I0
ay, 10) billion t n w iln
by
up by
up billon, Is the tolal
theincome goes which expenditure,
nereased by that amount, Now, sice ncone is
has increased the edetemines
up hy ? |9 billwm
i c o m e ,

goes up by 8 billion aSsuming h

orivate consiumplion 08), whuh caUses a 7
reasc in toal expendilure and, hence, in the mcome
billion inerease
by the s n e amount
third round, ?8 billion inereuse in income would
In the lead to a 14 billon
increase in private consumplion and, therefore, in incOme as well
by the
ame amount. The process would continue until the nlimulus
exlausts The ota
nerease in income would thus be given by rupees:

10 +8t 6.4 1 5.12,. billion

10 + 10(0.8) + 10 (0.8) 10(0.8)' . . billion
10/(1 0.8) billion
50 billion
Further,savings would inerease by R10 ( 2 t 161 1.28 ..) billion, just equal
to the increase in autonomous expenditure, so that the new cquilibrium is establrshed
exactly. The process is taken to work instantaneously in the Keynesian model, and
hence the said multiplier is called a "static
multiplier", This is the Keynesian
hlicer theory. In reality, the adjustments happen through time lags, which are
gnored here. Three relevant time lags are
(a) Gestation period, is the time lapse belween (aulonomous) spending and
production
to Outpul-1ncome gap, is the time lapse between receipts of revenues from output
to the
payments to the factors of production
Robertson lag, is the time lost between change in ineome and consequent
change in consumption expenditure
How the above
process affects the production? Initially, when the uutonomous
pnditure increases, the demand exceeds the production, and the additional de
e t through reduction in inventories of linished goods. Consequently, Ine
cory level falls below the desired Ievel. Subsequently, production will be m

short
plenish inventories. Quile the opposite holds when the demand
is
uf
production.
the
h e government expenditure or investment lalls, ccteris parihus,
total the irms thus
ahle toexpenditure
arc
less than the value of the output,
nol able
lot sell all of becomes
their production, and accordingly firms adddesired
the difference
level, li to
their stock desired level, Iirm
of invent When the inventory level is above its
their Ories. The and the process contnues
until the
balance production. production falls imodel,
the total demand and the outpul is re-cslublished. In a
slutic
s process stantaneous,
Processis is i but it may take some time if the model is dynianic
In this model, lirns supply all hat u
is governed solely by expenditure ias
Customers de output t the fixed price (set either by firms or through
a conlact
300 MacToeconomi

and customers).
Iherctore, there is no 1arantee
guarantee that
that the
between fims
income () cquals the
full employment level of output (y expenditure
.If
dr
determined
YYr. there is unemployment
full employment
p . there is
And. Y, is not possible due l0 constraints
on tne production, caused the
and technology. Thus, the Keynesian model is
available factor supplies tent
full employment cquilibrium, and also with en the
with both under-full and
emplovment until around 1928 and
massive unemployment
during 1929-11T
explained the Great Depression, which according to him d.was
is how Keynes o
The stock market boom ot the 1920s busted in 1o
the lack of effective demand.
and so wealth was eroded. As a result, banks could not recover their loaned amounts
unts
and many of them failed. There was no insurance on bank deposits and so the nuhli
could not get their depOsits back. In consequence, private consumption suffered and
investors lost confidence. Governments then were not aware of the fiscal poliey
miracle (vide the Keynesian multiplier theory) and were instead practicing balanced
budgets. The effectiveness of the monetary policy in countering the recession was
also not quite known. Further, money supply could not even be expanded as it was
constrained by the availability of gold under the then prevailing gold standard
Accordingly. the shortage of demand could not be remedied. The result was the
Great Depression.
Some important concepts are relevant at this point. When Y. < Y there is an
income (GDP) gap due to the shortage of effective demand, called the deflationary
(recessionary) gap. Recall the autonomous expenditure multiplier, the recessionary
gap can be met through an increase in the autonomous expenditure by the
amount
equal to (Y- Yk. If Y> Yp, there is excess demand, called the infiationary gap
which can be corrected by decreasing the autonomous expenditure by ( - lphi.
Thus, as stated above, the Keynes model suggests that the Great Depression could
have been avoided through an appropriate increase in the government expendirur
i.e.. pure fiscal expansion.
An important paradox, called the paradox of thrift, also deserves our attention
here This states that as the people become more thrifty the national savings decrease
rather than increase. This is true in the Keynesian cross model, basically becau
saving and investment, though equal, are independent of each other. Thus, as peopic
get thriftier, they save more and spend less; and as the total spending falls (note tndt
investment and govenment expenditure remain same as before, and increased saving
go into hoarding), firms are not able to sell all their outputs and so their invento
holdings increase. Consequently, firms cut on their production and so the outpu
real income falls. Fall in income leads to low savings, that is, savings come bus
to their original level so that savings still remains equal to investment. In this cas
increased thriftiness leads to no change in saving and not to a fall in saving as the
us
paradox of thrift suggests. However, if investment depended (positively) on inco
as per the profit/accelerator theory (vide Chapter 6), the said paradox would no
To show this, let us resort to
algebra. Let the Keynesian model be as roo
C= 150 + 0.8 (Y-
T,)
l 50 +0.1 Y
Increase in thrift means decrease in either antonas anes nt.an ar in the marginal progc
 Classical and Kynersan Fzsd Pra Mdels 301
=C-I-G
G 1 0 0 . T, = 80

oution of the above model for ? would give

Soluto
0.1 Y=[150 0.8 T, +50 G]
On substitution of the values for G, and To. we get. = 2360
Further substitution of the value of Y in I and C functions would give
I = 286 and C = 1974

Drivate saving is defined as S = - C - 7. which. on substitution. would give

S= 306
S-T= l - G = 386
Note that
Next. suppose people become thriftier, ceteris paribus. This means either
autonomous consumption decines or and the marginal propensity to consume (MPC)
falls. Let MPC fall from 0.8 to 0.7. ceteris paribus. Solution of the model. as above.
would give
Y-1. 220:1= 172: C= 948, S= 192 and S -T=I- G=272
A comparison of the two sets of results would indicate that the saving has fallen
from 306 to 192 due to just one change. viz, MPC falling from 0.8 to 0.7. hence
the paradox of thrift. Incidentally, note that there is a catch here. which is that the
increased saving does not result in more investment. Where does the saving go then?
There is no automatic relationship between saving and investment. Though saving
is a source for investment, saving could well go into hoarding. Households could
leave their saving as cash in lockers. Alternatively, they could put it in banks or and
in stocks and bonds of firms. If the banks kept these saving in their vaults instead
of lending to businesses, the saving still remains hoarded and not invested. Also. if
banks lent those savings to business or even the government, but the business and
govenment kept such loan proceeds and or the proceeds from bonds and stocks as
dle funds instead of using them to acquire capital items (like structures, equipment
Or inventory), the saving is still hoarded and not invested. Such a situation often

anises when the economy is facing a recession. Business is pessimistic and so it

Cs away from investment. If this happens, saving remains a private virtue but
aOes not become a social virtue. Please note that under the classical model of full

poyment, saving and investment are not independent (they are linked through
nterest rate), and hence the paradox of thrift does not hold in it.
1neabove two equations model (vide equations 11.1 and 11.2) could be expanded
through endogenising the follows:
tax revenue as
Consumption function: C Cg + b(Y- T) (11.1)
Tax function: T To + tY (114)
Income identity: Y= C+I, + Go (11.2)
S the solution of
the n of the first two equations into the last equation, and
resultant quation for income would give:
IC-bT+o+ G] (11.5)
1-b(1-t)
which reduces value of the Keynesian multiplier (6) to:
Equations' numbers repeated in the chapte.
are
retained the earlier ones if they are
 1-b1-)
This is less than the value of the said multiplier in the earlier tw
arlier two
for
1. h 0
cquations model
Thus, if b - 0.8 (as before) and r= 0.1. the new multiplieris
3.57
Since taxes are leakages from cxpenditure (vide Chapter 2), the
nversely with the tax rate. l he inverse of the multiplier is accordinl
the multiplier varies

this model called the

marginal leakage rate. In its inmplications for
1o the above two-cquation model. We may now
unemployment,
conclude milar
that in the ahovo
models. nesian
(a) Price is determined exogenously
(b) Output is detemined in the prouct market
by the
aggregate expenditure
(c) Employment-unemployment, not shown here, are determined in the factor
market (with production function) by the output level
determined in the
product market (vide Chapter 9)
(d) Interest rate. not shown here, is determined in the
inoney market bv the
demand for and supply of money. Inierest rate is thus a purely monetary
phenomenon in the model

The model is thus segmentable. In terms of the AD-AS curves, the model would
look like in Fig. 11.3.

AD

Pe -AS

ig 11.3 AD-AS curves in the Keynesian Cross Mode

n ne above graph, Y, is given by the total expenditure andTe by the fixedThu
price
oyment output. 1i
nature of the model.
Y, may or may not equal Yp, the füll
the Keynesian model
is consistent with both full
empio ll as the
full
employment equilibrium. employment a
luntary

Further, unemployment, 11
auy i n v e s t

p e n s i t y t o mve

If investment was
hypothesised as a function proj
c c t i o n

(positive) of
of income,
income, he marginal
the
would affect the Keynesian
the aggregate demand.
multiplier positively,
as investment, like
 Classical and Keynesian Fixed Price Models 303

rises
it arises because the fims hire less workers than the supply of workers
as
aracter

and they hire less not because the real

rate:
the ruling wage wage rate is above
st inal productivity of workers, but because they are unable to sell more
t h margina
to the lack of effective demand. While
their product due workers, operate on
of firms are off their labour demand (MPP of
their supply
curve, labour) curve (vide
Chapter fixed money wages) and, hence. the involuntary unemployment.
oads to be emphasised that unlike the classicalists, Keynes thought that the
ive behind. saving was not interest income and that savings need not flow auto-
could be hoarded). The Keynes' theory assigns the
mati lly into investment (it
of bringing savin = investment to income and not to the interest rate, as in
role
theclassics
This can explicitly if we derive the saving function under this
be seen

(S) is given by
model. Private saving
S Y-7-C, substitution for C gives,
= Y- T- Co - b (Y-T), substitution for T yields,
= Y- To - t Y- Co- b (Y- To-1 H, rearranging gives,

= -Co-(1-b) T, +(1 -b) (1 -1) Y

to save (MPS) =
(1 b) (1 1), which is positive
Accordingly, marginal propensity
- -

t are positive fractions. This means as income goes up, private saving
as both b and
increases and vice Marginal propensity
versa. (MPC)) in the model
to consume

and (11.4), is given by

represented by equations (11.1). (11.2)
C-Cot b (Y- T)
=
Cot b(Y- To-1 )
Co-bT% + b (I - 1)
Thus, MPC =b(1 - 1)

which equals =
i. It can easily be proved
In addition there is marginal tax rate (MTR)
that the sum of the three marginal terms equals one:
MPC + MPS +MTR =
b (l -1) +(1 -b) (1 -1) +1=
same as budget or fiscal surplus
Let us next look at government saving, which is
FS). It is given by (recall here T is net of transfer payments)
tY-G
FS T- G =

To +

varies positively with income,

The above equation suggests that fiscal surplus varies as
constant. Next let us
look at how fiscal surplus
, 0 and t
stay
tax rate alone change,
and (c) both
14gOvernment expenditure alone change (b)
rate change. In
the first case, the partial
expenditure as well as tax
&emment
derivative of FS with respect to G gives,
autonomous expenditure
dFS)=0+ -1=t (k) -1 (Recall k
=

dG dG
multiplier)

Or, d(FS) substitution for k

-1. on
dG 1-b(1-)
fractions
1-bX1-1, <0, since both b and 1 are positive
1-b
 Thus, as government expenditure goes up. ceteris paribus, fisca
ICe versa Similarly. it is easy to see that the relationship betwee surpl us falls.5. and
autonomous tax (7,) would be given by (take partial derivative of fs. al surplhis and

dFS14 1 respect to T
dTo dTo 1-b1-1)
1-b
> 0, since both b and f are
1-hl-1 positive fractions
It shows that, as expected, incrcase in autonomous tax,
ceteris parihuw
increase in fiscal surplus. Further. the two results can be combined to detenleads to
effect of an autonomous tax financed
government expenditure on fiscal su
Is given by the sum of two above effects: This
d-bxI-)11-b =
(1-b)
>0, for both t and b are
1-h1-)1-b1-) 1-b(1-1) fractions positive
The said
policy thus raises fiscal surplus. In other words, government
financed through autonomous tax is more than expendtun
the fact that the fiscal
self-financing! This comes throueh
expenditure multiplier is larger than the fiscal (autonomous
tax muluplier, which
happens because, as seen hitherto, balanced budget multiplier
is
positive! A consequence of this is that fiscal policy is more effeotive with
to output if it is respect
applied through enhanced government expenditure than through a
cut in tax, both
being of equal size in terms of their impact on fiscal deficit. We leave
it to the readers
to check the effects of a
further such analysis.
on
change in tax rate on fiscal surplus and

Economic Fluctuations and Stabilisation Policies

The business cycles in the
Keynesian cross model could be caused, only, by some
disturbance in the product
market, that is, expenditure or
investors become pessimistic, autonomous investment falls, aggregate
and then demand
through the
muluplier process, income falls by a multiple of the fall in autonomous
Similarly, consumers' pessimism would reduce the autonomous investmel
all in the world income consumptin a
would reduce autonomous (vide
on A fall in exports ( haptet
government expenditure or a rise in autonomous tax, celeris
would similarly
reduce the total autonomous Pauause
u u
recession and fall in expenditure.
income, again through the
Such events woud Cvens

wOuld iriBger multiplier process. The reverse

recovery and prosperity. As stated above, the
the Great
Depression to the lack of effective demand; causedKeynesta
by
och market

Ctasn, bank lailures,

por business confidence, contagion ellect
ne s he
of the world's"
falling mcome adversely affecting the net nrou slca
Satting passively, if the expors. c thru
government had increased its expenditure (tinanceu
borrowing internally could hae

softened or even
or
externally-or even taxes or
monetIS
n), i
avoided the Great of the required ncr
in
government expenditure or Depression. The exient
xlent o BIVen level

depends on the size of the fiscaldecrease in taxes to raise ncOn a nua

of factors including the marginal multiplier, which, in turr
on
urns, depends
thod bywh
to consune and ne ethod
government finances the resultant propensity
fiscal deticit. Thus:
 Classical and Keynesian Fixed Price Models 305

Unlike the c l a s
sicalists, Keynes advocated an interventionist fiscal policy.

ieon (19;
Paul Samuelson (1939) has shown that the intcraction of the Keynesian multiplier

the
celeration principle (vide Chapter 6) could cause business cycles.
and del, the monetary policy has no role in stabilising the economy,
simple model,
In this of money nor ven the rate of interest enjoy any influence on
neither
the quantity which.alone is the sole
as

aggregato
demand, determinant of the output, employment
the
and
mployment. However, the fiscal policy is significant in this regard as any
unemployment.

in ernment expenditure and/or taxes exerts

significant effects on the real
change
rough the multiplier. Further, the effectiveness of this policy varies directly
multiplier or directly with the marginal propensity to consume
with the Keynesian
ndinversely with thetax rate and, as will be demonstrated later, inversely with
propensity toimport y if the economy is an open one (vide Chapter 12).
the marginal
above models, investmer does not depend on the interest rate and, thus, there
nthe
evenacrowding out of privat investment due to government expenditure.
Isnot
The recessions can be softened or even eliminated through an appropriate increase
in government expenditure and/or a cut in taxes. The only constraint to this would
come from the government budget constraint, which may go haywire unless the
gOvernment is able to raise funds through additional money supply and/or public
borrowings, which may be associated with their own problems. Nevertheless, the
Keynesians think that the Great Depression could have been softened if the various
govermments around the world had played active roles.
Incidentally, note that if taxes depend on income, as they do, the tax revenue
tM goes down during the recessions due to fall in income and it goes up during
the prosperity when income rise. Similarly, the transfer payments (social security,
unemployment compensation, etc.) are more during recession and less during
prosperity, fr they vary inversely with the income. Taxes and transfer payments
atiect disposable income and there by private consumption and investment. Thus,
both of these are counter eyclical in nature and dampen the effects of recession and
ospenity on the economy. Further, they are built in the system rather than come
iough any policy initiative. Accordingly, they check business cycles to some extent
matically and hence they are called the automatic stabilisers in the economy.
TUnately, they are not adequate to avoid the business cycles altogether and
hence we need
stabilisation policies.
Keynesian Cross Model-An llustration
The
working of the Keynesian cross model may be illustrated through hypo-
a
thtical
eica example. Note that the theoretical model is good only for analyzing the
now

tions
needst of the relationships and for measuring the sizes of the relationships one
the
In rics techniques
y model using the historical data the variables involved and the
economet
y th
to estimate the model. Suppose an economy is characterised
on

Productfollowing
Market:estifmated ometric) structural model:
C=150+0.8 (Y- T)
T 100 +0.1 Y
306 Maaoeconomics

300
G
=

200,
= C+/+ G

Money M a r k e t :

04Y- 100 i
P
Ma 800. P= 1 (fixcd)

Function and Factor Market:

Production
Full employment
income =2100
The product market will
model is segmentable.
The above
real magnitudes,
which are consumption determine the
income Y. and other
tax revenue T. At the so detemined income level, the money ma stment
detem
The gap betwecn the
o determined incor
the internal rate
i.
mdicale it the cconomy fl nd the full
income. if any, would is at
employment
under-full employment
or over-full
Remember emplthatoyment
employment equilibrium
Jevel gets determined in the product market and the employment of labour output
Is then
per the production f.
ihe requirement of labOur as
determined simply by
other words. the labour market plays ne passive role. Recall from Chanter a
under price rigidity, fims surrender their labour demand function, and dem
much labour as required to produce the output demanded. To show
show this.
this, let
let n
us work
on the product market model first.
Substitution of the various equations in the income identity yields:
Y= 150+0.8 (Y - 100 -0.1 Y)+200+300
or, (1 - 0.8 + 0.08) 150 -80+ 500
=

Y [570] = 2035
or.
0.28
Further, at Y= 2035, tax revenue equals
T 100 + 0.1Y
100 +0.1 [2035]
=

= 303.5

The govemment budget surplus (BS) is given by:

BS T- G
=
303.5 300 3.5
Private consumption is
given by:
C= 150 + 0.8 (Y-7 )
=
150 +0.8 (2035 303.5) =1535
Private saving (S) is given by
S = Y- T- C
2035 303.5 1535 = 196.5
National saving =BS+S= 196.5 +3.5 200
wnch
equals the autonomous national investment
(l%= 200).
Marginal propensity to save =(1- t) (1 - b) = 0.9 X 0.2
Marginal propensity to consume = b{1 - )= 0.8 X 0.7 ).72
Marginal tax rate [ = =-
0.1 renaun
Ihus, if income and
the 7 2
a n d

goes
up by 100, tax revenue 10,
disposable income = 90 is used goesprivate
partly as increased up uy consumption
 Classical and Krynesian Fixed Prie Models 307

increased private saving = 18. Further, if govermment expenditure goes up

e TUee and it 15 financed by one rupee increase in autonomous tax, the increase

ascal deficit would

= (1-b)__0.1010.8) = 0.0714
1-b1-t) 1-0.8(1 0.1)
Thus. f G and To each go up by R100, ceteris paribus, fiscal surplus would go
y.14
= 3.571
The Keynesian multiplier =

0,28
The merginal leakage rate =571 =0.28
3.571 0 .28

To denermine the interest rate, we must move to the money market given the
cmeevel as determined in the product market. Thus,

0 . 4 Y-100 i
P
L M, =
800, P =1
800 04 (2035) 100 i
i= 0.14, or i = 14%
ITCE e
equilibriurm output (2035) falls short of the full employment output
0, e qznity of labour
employed will be below the full employment, causing
t l errgiasyment equilibrium. The defiationary gap equals:
21)-2S35 - 18.2
3571
, the uszl autonomous expenditure (i.e., C0 Iy Gg- Tg) increases
ehe, mploryment
utcez-ens. ievel of income would be attained. As Keynes argued,
eTnpiaryment equilibriurn is entirely due to the lack of effective demand.
DE in first dtermined in the product market itself and then at the
A I e , interest rate is determined in the money market, the above