National Income Determination

For more, see any Macroeconomics text book

Determination of equilibrium Y and P• Equilibrium output and prices are determined by

aggregate demand (AD) & aggregate supply (AS)

AD shows the combination of the price level and level of output at which the goods and money markets are simultaneously in equilibrium

AS describes, for each given price level, the quantity of output firms are willing to supply

• AD-AS can be used to understand the policy options available a) to reduce unemployment, b) to smooth out output fluctuations, and c) to maintain stable prices

2

Classical System Vs. Keynesian System

• (Classical) Macroeconomic system is based on the writings of all the major economists before Keynes (1936)

• In this system, the equilibrium level of national income, Y, occurs at full employment level, given the flexibility of the wage rate– AS curve is vertical

• On the other hand, Keynes assumed unemployment and hence so what matters for equilibrium is AD curve– AS curve is horizontal

3

AD and AS

• In Keynes equilibrium national income/output is determined by aggregate demand

• But in classical system aggregate demand has got nothing to do with the determination of national income

• But we use both AS and AD to understand the equilibrium level of prices and output in the economy

• When a change shifts either AS or AD, we can determine how price and output shift

4

Aggregate Demand

Aggregate demand is the total amount of goods demanded in the economy

Following notations used:AD = Aggregate DemandY = OutputC = ConsumptionI = InvestmentG = Government purchases of goods and servicesE = ExportsM = ImportsNX = Net exports (Export – Import)S = Savings

Aggregate Demand…

Output is at its equilibrium level when the quantity of output produced is equal to the quantity demanded

That is,

Y = AD = C + I + G + NX

Aggregate Demand…

When Y ≠ AD, there is unplanned inventory investment (IU) or disinvestments

That is,IU = Y – AD

If IU > 0, firms cut back productionIf IU < 0, inventories are drawn down

Consumption

Chief component of aggregate demand

Refers to household spending

For simplicity, set I, G, NX equal to 0

Consumption function

• It defines the relationship between consumption and income

• Consumption increases with income, that is, demand for consumption goods is not constant, it increases with income

• Consumption function is given as

10,0; cCcYCC

Consumption function …Intercept C represents factors affecting consumption other than

income – wealth such as ownership of assets

c defines Slope of consumption curveIndicates the extent of rise in consumption with incomeAlso known as marginal propensity to consume (MPC)

MPC = ΔC/ΔY = c (0< c < 1)

MPC is less than 1, indicating that for an unit increase in come, only a faction of it, c, is spent on consumption

Saving (S)• Saving is that part of an individual’s income which is

not spent• In a simple economy

Y = C + S

= (1-c) Y = sYWhere s = (1- c)

YcCcYCYCYS )1(

Saving Function• Saving function relates the level of savings to the

level of income

• This shows the magnitudes of saving at different levels of Y

• S = sY, where, 0 < s < 1‘s’ is called the marginal propensity to save (mps)

Saving Function• Saving function, S = sY, shows that saving is an

increasing function of the level of income because the mps (s = 1-c) is positive

• Saving increases as income rises

• At equilibrium level of income, saving equals planned investment.

Marginal propensity to save (MPS)

• MPS is the increase in savings per unit increase in income

• MPS = ΔS/ΔY = s (0< s < 1)

• This implies that saving is an increasing function of Y but the increase in s is less than that in Y

Relation between MPC & MPS

• MPC + MPS = 1

Y = C + SΔ Y = Δ C + Δ S

1 = Δ C / Δ Y + Δ S / Δ Y 1 = MPC + MPS

Average Propensity to Consume(APC) & Average Propensity to Save (APS)

• APC = C/Y • APS = S/Y

Y = C+ S1 = C/Y + S/Y

1= APC + APS

Question

Savings function of an economy is S = – 400 + 0.3 Yd. If saving is Rs. 500, the

consumption in the economy is• Rs. 2700/-• Rs. 1500/-• Rs. 1720/-• Rs. 3000/-• Rs. 2500/-

Autonomous Spending

• Autonomous variables– Determined outside the model / system– In the present context, they are assumed to be independent

of income

In equation AD = C + I + G + NX

I, G, NX were autonomous variablesNow introduce G in the mode, and hence there is taxes TA and

transfer payment TR

Autonomous Spending …

• In the new situation, consumption depends on disposable income, YD

• Recall AD = C + I + G + NX

)( TRTAYcCC

or

TRTAYYD

Autonomous Spending …• In the new situation, after substituting for C,

NXGITRTAcCA

where

cYAAD

cYNXGITRTAcCAD

NXGITRTAYcCAD

)(

])([

)(

Autonomous Spending …• That means,– Part of aggregate demand is independent of the level of

income or Autonomous– AD also depends on the level of income Y. It increases with

income because of c

• What follows?– The new equilibrium is where the level of output and income,

planned spending matches production– That is where Y = AD

The economy will reach equilibrium by adjusting production (Recall IU = Y- AD)

Autonomous Spending …Equilibrium level of output is higher, the larger c and A

How is equilibrium achieved?Equilibrium in goods market is given byY = AD

And therefore, new equilibrium condition is

cYAY

Autonomous Spending …• Y is on both sides, collecting terms and solving for

equilibrium level of output or income, denoted by Yo

ImpliesLevel of output is a function of c, and autonomous spending, A

Higher A, given the MPC, higher is Yo

AcYo )1/(1

Question• How change in some component of A will change

output

For instance,If mpc = 0.9 and autonomous spending is Rs. 1000, what will be the

Y?

How did it happen?

AcY )1/(1

Multiplier• Mechanism known as multiplier

• Multiplier is the amount by which equilibrium output changes when autonomous aggregate demand increases by 1 unit

Multiplier ….• In the equation,

• 1/ (1-c) is the multiplier• Implies that – Cumulative change in aggregate spending is equal to a

multiple of the increase in autonomous spending

– That is we are talking about change in equilibrium output when autonomous demand increases by 1 unit

YoAcAD )1/(1

Government Sector• Popular expectation is:

Govt should do something if anything goes wrong with the economy.

• Why such expectations are formed?

• Govt affects level of equilibrium income– Govt purchases of goods and services (G)– Transfers (TR) and taxes (TA) affect the relation between

output and income Y, and the disposable income (income available for consumption and savings) YD

Government Sector …

• YD is the net income available for household spending

)( TRTAYcCcYDCC

So

TRTAYYD

Government Sector …

• Fiscal policy– Policy of the government with regard to the level

of government purchases, the level of transfers and the tax structure

Assume :– G and TR are constant– Govt imposes a proportional income

tax, collecting a fraction, t, of income in the form of taxes, that is, TA = tY

Government Sector …

• Consumption function now can be rewritten as

YtcTRcCC

tYTRYcCC

)1(

)(

Government Sector …

• In the above equation:– Presence of transfers raises autonomous

consumption spending by the mpc– Income tax lowers consumption spending at each

level of income– Mpc out of income now is c(1-t)

Ex: if mpc is .67; t = .3; what is the mpc out of income

Government Sector …

• Combining the aggregate demand identity with the above equations:

YtcA

YtcNXGITRcC

NXGIYtcTRcC

NXGICAD

)1(

)1(][

)1(

Government Sector …

• Determination of income :

YtcAY

So

ADY

)1(

Government Sector …• We can solve the above equation for Yo, the

equilibrium level of income

)1(1

)()1(1

1

)]1(1[

)1(

tc

AYo

GITRcCtc

Yo

AtcY

YtcAY

Government Sector …

• Implications for fiscal policy:

– Fiscal policy can be used to stabilize the economy– When the economy is in a recession, or growing

slowly, taxes should be cut increase the government spending

– When the economy is booming, increase taxes and reduce government spending

Investment (I)• Gross private domestic investment• Associated with business sectors adding to the physical stock

of capital, including inventories

• It is gross in the sense that depreciation is not deducted• It is domestic in the sense that this is investment spending by

domestic residents & not spending on goods produced within the country

• Investment may be assumed to be autonomous to be independent or dependent on the level of income (Y)

Investment function

• In particular,

(b> 0)• the parameter ‘b’ the component depending

on income, which is called marginal propensity to investment

bYII

InvestmentPart of investment is independent of incomePart is dependent on income, that is, bY

)}1(1{

1*

)}1({

)1(][

)1(

)(

tcbAYo

YtcbA

bYtcNXGITRcC

NXGbYIYtcTRcC

MXGICAD

External SectorExports are independent of incomeImports dependent on income, that is, mY

})1(1{

1*

})1({

])1([][

)1(

)(

mtcbAYo

YmtcbA

YmtcbXGITRcC

mYXGbYIYtcTRcC

MXGICAD