NATIONAL INCOME DETERMINATION NOTES
We can use simple algebra to determine national income. National income
is at equilibrium when Ag. Demand equals Ag. Supply. In a simple closed
model of income determination without gov. expenditure
taxation, then
Y=C+I
Suppose the consumption function is of the form:
C=a+bY suppose investment demand equals I0 (Autonomous)
We get the following 3 equations for the determination of equilibrium
level of national income.
Y=C+I
C=a+bY
I=I0
Substitute C and I in the first equation we have: Y=a+bY+I0
Y-bY=a+I0
Y(1-b)=a+I0
Y=1/1-b (a+I0)
The last equation shows the equilibrium level of national income when
ag. Demand equals. Ag. Supply. Equilibrium level of income can be known
by multiplying the sum of autonomous consumption and expenditure with
the multiplier Suppose an economy has autonomous investment of 600 and
the consumption function is given by C=200+0.8Y. Find equilibrium level
of income The issues of consumption investment and savings will be
explored further in the subsequent lecture.
3.2 Consumption, Investment, Savings and Tax Functions
Consumption and Savings
We assume a closed economy that has three uses for the goods and
services it produces. These three components of GDP are expressed in the
national income accounts identity as:
Y = C + I + G
Households consume some of the economy‘s output; firms and households
use some of the output for investments; and the government buys some of
the output for public purposes. Aggregate demand is the total amount of
goods demanded in the economy. Output is at equilibrium when the
quantity of output produced is equal to the quantity demanded. Thus, the
national accounts identity can be expressed as:
AD = Y= C+I+G
In practice the demand for consumption goods increases with income. The
relationship between consumption and income is described by the
consumption function. Households receive income from their labor and
their ownership of capital, pay taxes to the government, and then decide
how much of their after tax income they will consume and how much to
save. Assuming that households receive income equal to the output of the
economy Y and that the government then taxes the households an amount T,
we can define income after taxes (Y-T), as disposable income. Households
divide their disposable income between consumption and savings. We
assume that the level of consumption is directly depends on the level of
disposable income. The higher is the disposable income, the greater is
consumption. Thus
The variable co, the intercept, represents the level of consumption when
income is zero. The coefficient c1 is known as the marginal propensity
to consume. It measures the amount by which consumption changes when
income increases by one shilling. In our case, the marginal propensity
to consume is less than one, which implies that out of a shilling
increase in income, only a fraction, c1 is spent.
After a household spends in consumption that
remains must be saved. More formally saving is equal to income minus
consumption. Thus S = Yd-C
The savings function relates to the level of income. Substituting the
consumption function in equation one we get a savings function as follows:
From equation 2 we see that saving is an increasing function of the
level of income because the marginal propensity to save, s= (1- c1 ), is
positive. In other words, savings increases as income rises. For
instance, suppose the marginal propensity to consume is 0.8, meaning
that 80 cents out of each extra shilling of income is consumed. Then the
marginal propensity to save s, is 0.2, meaning that the remaining 20
cents of each extra shilling of income is saved.
Taxes
Taxes play a major role in financing government expenditure. We shall
now analyze the effects of taxes on the equilibrium level of income
keeping gov. expenditure constant. Simplest kind of tax is the lumpsum
tax in which a given amount of revenue is collected
irrespective of the level of income. After taxes people consume less and
save less. However consumption will not fall by the full amount of taxes.
This is because part of the disposable income was being consumed and
part was being saved prior to taxation. Hence the decline disposable
income due to the lumpsum tax will partly cause a decline in consumption
and savings. Consumption will fall by the amount of tax multiplied my
MPC. If Yd is change in disposable income, T for tax, then the decline
in consumption (-ΔC)is given by
-ΔC=T.MPC
Since T= ΔYd
-ΔC=ΔYd.MPC
For example:
Suppose government imposed 500 lumpsum tax. The MPC is 0.75 then decline
in consumption
is 500 X 0.75=375.
If taxes were reduced consumption will increase by the amount of lumpsum
tax multiplied by
MPC ie +ΔC=ΔYd.MPC. Impositions of Taxes shift the consumption function
downwards while a reduction in taxes shifts consumption function
upwards. A fall in NI after imposition of taxes is not equal to the
amount of tax collected, but by a multiplier of it. The multiplier is
equal to: -b/1- b where b is the MPC. This is called the tax multiplier
Investment
Both firms and households purchase investment goods, Firms buy
investment goods to add to their stock of capital and to replace
existing capital as it wears out. Households buy new houses, which are
also part of investment. The quantity of investment goods demanded
depends on interest rate, which measures the cost of the funds used to
finance investment. We can distinguish between nominal interest rate,
which is interest rate as usually reported, and the real interest rate,
which is the nominal interest rate corrected for the effects of
inflation. If the nominal interest rate is 10 percent and the inflation
rate is 3 percent, then the real interest rate is
7 percent. Here it is important to note that the real interest rate
measures the cost of borrowing, and thus determines the quantity of
investment.
Thus I = I(r)
Investment function 1
The investment function slopes downwards, because as the interest rate
rises, the quantity of investment demanded falls.
Government Purchases
The government purchases are a third component of the demand for goods
and services. The governments buys guns, build roads and other public
works. It also pays salaries to civil servants. If government purchases
equal taxes then the government has a balanced budget. If G exceeds T
then the government runs into a budget deficit. If G is less than T then
the government runs a budget surplus. For our discussion we take
Government purchases and taxes as exogenous variables.
Thus G = Go
T = To
3.3 Determination of Equilibrium National Income
Using the above information we can obtain equilibrium in two ways
- Using goods market and service market
- Financial markets
Equilibrium in the market for goods and services
Using the relationships discussed above we can get the equilibrium level
of income or output as follow:
Y = C + I + G
C = co + c1Y
d
I = I (r)
G = Go
T = To
We can combine these equations to obtain equilibrium level of income.
Y = co + c1 (Y-To) + I(r) + Go
The above model of income determination is known as the Keynesian model
of income determination.
*Equilibrium in the Financial Markets
To obtain equilibrium in the financial markets, we consider savings and
investment. Savings represent the supply of supply of loanable funds
while investment represents demand for loanable funds .We can be able to
analyze the financial markets by examining the interest rate, which is
the cost of borrowing and the return to lending in the financial
markets. We can rewrite the national income identity
Y = C + I + G as Y-C-G = I
The term on the left hand side is the output that remains after the
demands of consumers and the government has been satisfied. It is called
national saving. In this form the national income accounts identity
shows that saving equal investment. Savings represent the supply of
loanable funds while investment represents the demand for these funds.
The quantity of investment demanded will depend on the cost of
borrowing. At equilibrium interest rate the households‘ desire to save
balances firms‘ desire to invest and the quantity of loans supplied
equals the quantity demanded.
The Expenditure Multiplier
This is the amount by which equilibrium output changes when autonomous
aggregate demand increases by one unit. Assuming the absence of the
government and foreign sector the multiplier is defined as
From the above equation you observe that the larger the marginal
propensity to consume the larger the multiplier. The multiplier suggests
that output changes when autonomous spending changes and that the change
in output can be larger than the change in autonomous spending.
