Simple Keynesian ModelNational Income DeterminationTwo-Sector National Income Model

OutlineMacroeconomics [2.1]Exogenous & Endogenous Variables [2.3]Linear Functions [2.6]Aggregate Demand & Supply [3.2]National Income Determination Model OR Simple Keynesian Model [3.3]

OutlineNational Income Identities [3.4]Equilibrium Income [3.5 & 3.11] Consumption Function [3.6]Investment Function[3.7]Aggregate Demand Function [3.8]

OutlineOutput-Expenditure Approach to Income Determination[3.9 ]Expenditure Multiplier [3.9]Saving Function [3.10]Injection-Withdrawal Approach to Income Determination [3.10]Paradox of Thrift [3.13]

MacroeconomicsNational income, general price level, inflation rate, unemployment rate, interest rate and the exchange rate are the economic measures to be explained in the macroeconomic models / theories

Exogenous & Endogenous VariablesExogenous Variablethe value is determined by forces outside the modelany change is regarded as autonomousI, G, X ( Micro: Income/Population)Endogenous Variablethe value is determined inside the modelfactor to be explained in the modelY, C, M ( Micro: Price/Quantity)

Linear FunctionsA function specifies the relationship between variablesy is the dependent variablex is the independent variabley=f(x)

Linear Functionsy=f(x)y= cy=mxy=c+mxm, c are exogenous variablesy, x are endogenous variables

Linear FunctionsConsumption FunctionsC= f(Y)C= CC= cYC= C + cY

Linear FunctionsC, c are exogenous variablesC, Y are endogenous variablesY is independent variablesC is dependent variables

Linear FunctionsCan you express the 3 consumption functions graphically?

Linear FunctionsThe parameter C is autonomous consumptionIt summarizes the effects of all factors on consumption other than national income.What is the difference between a change in exogenous variable (autonomous change) and a change in endogenous variable (induced change)?

Linear FunctionsC= f(Y, W)If wealth is deemed as a relevant factor but is not explicitly included in the consumption function C=C+ cY a rise in wealth W will lead to a rise in the exogenous variable Cgraphically, the consumption function C will shift upwards

Linear FunctionsWhat happens if c ?What happens if Y ?

Linear FunctionsConsumption function can also be a relationship between consumption C and interest rate r.What do you think of the relationship between the variables, i.e., consumption C and interest rate r?Are they positively correlated or negatively correlated?

Aggregate Demand & SupplyAggregate Demandthe relationship between the total amount of planned expenditure and general price level (v.s. aggregate expenditure E)Aggregate Supplythe relationship between the total amount of planned output and the general price level

Aggregate Demand & Supply Price LevelNational OutputAggregate SupplyAggregate DemandEquilibrium: no tendency to change andthe values of the endogenous variables will remain unchanged in the absence of external disturbances

Aggregate Demand & SupplyPYASAD1AD2YfWhen AS is verticalA shift of AD will cause a change In P only but have no effect on Y

Aggregate Demand & SupplyPYASAD1AD2When AS is horizontalA shift of AD will cause a change in Y only but have no effect on P

Aggregate Demand & SupplyADASYfYe

Aggregate Demand & SupplyThe Upward Sloping ASWhen the economy is close to but below full employment level Y < Yf, the attempt to raise output by increasing aggregate demand will face supply side limitationsboth price and output will increase

Aggregate Demand & SupplyThe Vertical AS (slide 18)When full employment is attained Y = Yf, an increase in aggregate demand can only cause prices to rise

Aggregate Demand & SupplyThe Horizontal AS (slide 19)When output is far below Yf, the equilibrium output is determined by ADThe supply side has no effect on income level as firms could supply any amount of output at the prevailing price levelThe Keynesian Model analyses the situation of an economy with fixed prices and high unemployment Y < Yf

National Income Determination ModelAssumptions:National income Y is defined as the total real output QA constant level of full national income YfSerious unemployment, i.e., there are many idle or unemployed factors of production

National Income Determination Model (contd)Income / output can be raised by using currently idle factors without biding up pricesPrice rigidity or constant price levelThere are only households and firms (2-sector). No government and foreign trade

National Income IdentitiesAn identity is true for all values of the variablesIn a 2-sector economy, expenditure consists of spending either on consumption goods C OR investment goods I.Aggregate expenditure (AE OR E) is ,by definition, equal to C plus IE C + I

National Income IdentitiesNational income Y received by households, by definition, is either saved S OR consumed C.Y C + S

National Income IdentitiesAggregate expenditure E is, by definition, equal to national income YY EC + S C + I S I

Equilibrium IncomeEquilibrium is a state in which there is no internal tendency to change. It happens whenfirms and households are just willing to purchase everything produced Y = E (v.s. Micro: Qs = Qd) [slide 30-36] Income-Expenditure Approach [slide 37-60]planned saving is equal to planned investment S = I Injection-Withdrawal Approach [slide 61-74]

Equilibrium IncomeWhat is the definition of GNP (/ GDP) in national income accounting?The total market value of all final goods and services currently produced by the citizens (/within the domestic boundary) of a country in a specified period

Equilibrium IncomeEx-ante Y > E Excess supplyplanned output > planned expenditure unexpected accumulation of stocks ORunintended inventory investment ORinvoluntary increase in inventoriesIn national income accounting, this amount Y-E is treated as (unplanned) investment by firms

Equilibrium IncomeEx-post Y= E

Actual (Realised)=Planned+UnplannedExpenditureExpenditureInvestment

Actual (Realised) Output = Actual Expenditure

Firms will reduce output

Equilibrium IncomeEx-ante Y < E Excess Demandplanned output < planned expenditure unexpected fall in stocks ORunintended inventory dis-investment ORinvoluntary decrease in inventoriesHowever, in national income accounting, this amount E - Y consumed is not currently produced

Equilibrium IncomeEx-post Y= E

Actual (Realised)=Planned-UnplannedExpenditureExpenditureDis-investment

Actual (Realised) Output = Actual Expenditure

Firms will increase output

Equilibrium IncomeEx-ante Y= E EquilibriumThere is no unintended inventory investment OR dis-investmentEx-post Y=E

Equilibrium IncomeWhen there is excess supply, i.e., planned output > planned expenditure, firms will reduce output to restore equilibriumWhen there is excess demand, i.e., planned expenditure > planned output, firms will increase output to restore equilibriumIn the Keynesian model, it is aggregate demand that determines equilibrium output. Remember the horizontal AS [slide 19]

Consumption FunctionNow, we will look at the 1st component of the aggregate expenditure E C + I i.e. CEmpirical evidence shows that consumption C is positively related to disposable income YdYd = Y since it is a 2-sector modelRemember the 3 consumption functions [slide 9 & 11]

Consumption FunctionAutonomous Consumption CIt exists even if there is no income. This can be done by dis-saving, i.e., using the past savingThen, saving will be negative when income is zero.It is totally determined by forces outside the modelWhat happens to the 3 consumption functions if C ? Or C ?

Consumption FunctionC = y-intercept In CC = CC = cYC = C + cY

Consumption FunctionMarginal Propensity to Consume MPC = cIt is defined as the change in consumption per unit change in incomeMPC = C / YIt is the slope of the tangent of the consumption functionFor a linear function, MPC is a constantWhat does the consumption function C look like if MPC is increasing? Decreasing?It is assumed that 0 < MPC < 1What happens to the 3 consumption functions if c ? or c ?

Consumption FunctionMPC = slope of tangent in MPC or in cC = CC = cYC = C + cY

Consumption FunctionAverage Propensity to Consume APCIt is defined as the ratio of total consumption C to total income YAPC = C / YIt is the slope of ray of the consumption functionWhen C = C OR C = C + cY, APC decreases when Y increases.When C = cY, APC = MPC = c = constant

Consumption FunctionAPC = slope of rayC = CC = cYC = C + cY

Consumption FunctionRelationship between APC and MPCC = CDivide by YC/Y = C/YAPC = C/YAPC when Y Slope of ray flatter when Y Slope of tangent = MPC = c = 0

Consumption FunctionRelationship between APC and MPCC = cYDivide by YC/Y = cAPC = MPC = cSlope of ray=Slope of tangent=constant=c

Consumption FunctionRelationship between APC and MPCC = C + cYDivide by YC/Y = C/Y + cAPC = C/Y + MPCC +veAPC > MPCSlope of ray steeper than slope of tangentSlope of tangent constantSlope of ray flatter when Y APC when Y

Investment FunctionLets look at the 2nd component of the aggregate expenditure E C + IAn investment function shows the relationship between planned investment I and national income YIt can be a linear function or a non-linear function

Investment FunctionAgain, there can be 3 investment functionsI = II = iYI = I + iYEconomists usually use the first one, i.e., I= I as investment is thought to be correlated with interest rate r, instead of YI , i are exogenous variablesI , Y are endogenous variables

Investment FunctionAutonomous Investment IIt is independent of the income level and is determined by forces outside the model, like interest rate.I is the y-intercept of the investment function

Investment FunctionMarginal Propensity to Invest iIt is defined as the change in investment I per unit change in income YMPI = I / YMPI would not correlate with YdIt is the slope of tangent of IIt is also determined by forces outside the model

Investment FunctionMPI = i =slope of tangentI = y-interceptI = II = iYI = I + iYAPI when YMPI =0

Aggregate Expenditure FunctionGiven E = C + IC = C + cYI = I E = I + C + cY E = E + cY

Aggregate Expenditure FunctionI = IC = C+cYE = I + C+ cYC, I, EICYSlope of tangent=0Slope of tangent = c

Aggregate Expenditure FunctionAutonomous ChangeWhen C or I E shift upwardWhen c slope of E steeper rotateInduced ChangeWhen Y E move along the curve

Output-Expenditure ApproachNational income is in equilibrium when planned output = planned expenditureWe have planned expenditure E=C+IEquilibrium income is Ye=planned EA 45-line is the locus of all possible points where Y = EWhen E = planned E, Y = Ye

Output-Expenditure ApproachY = EPlanned E=C +IYC, I, EY=planned EPlanned E>YUnintended inventory dis-investmentActual E =Y

YePlanned E < YUnintended inventory investmentActual E = YYY

Output-Expenditure ApproachY = planned EY = I + C + cYY = E + cY(1-c)Y = EEquilibrium conditionY = E 11-c

Output-Expenditure ApproachIf C or I E E Ye If c E steeper Ye If we differentiate the equilibrium condition, Y/E = 1/(1-c)Given 0 < c < 11/(1-c) > 1 E Ye by a multiple 1/(1-c) of E

Expenditure Multiplier 1/(1-c)Assume c=0.8, E = 100The one who receive the $100 as income will spend 0.8($100) then the one who receives 0.8($100) as income will spend 0.8*0.8($100)The process continues and the total increase in income is $100+0.8($100) +0.8*0.8($100) +

Expenditure Multiplier 1/(1-c)The total increase in income is actually the sum of an infinite geometric progression which can be calculated by the first term divided by (1- common ratio)The first term here is E = $100 and the common ratio is c =0.8The sum of GP is E * multiplier

Saving FunctionWe have Y C + S [slide 27]Saving function can simply be derived from the consumption functionS = Y Cif C = C + cYS = Y C cYS = -C + (1-c) YS = S + sYS= -Cs = 1 - cS < 0 if C >0S = 0 if C = 0

Saving FunctionY*SYYSSS = sYS = (1-c)YS = S+ sYS =-C+(1-c)YSlope of tangent = s =1- cSlope of ray = slope of tangentSlope of ray < slope of tangentY > Y* S+ve

Saving FunctionAutonomous Saving SSince S= -C + (1-c)Y

If C= 0 when C= cY S = (1-c)Y S = 0

If C +ve when C = C + cY S = -C + (1-c)Y S ve

If Y= 0 S = -C Dis-saving

Saving FunctionMarginal Propensity to Save MPS = sIt is defined as the change in saving per unit change in disposable income Yd OR income Y (in a 2-sector model)MPS = S/ YIt is the slope of tangent of the saving functionMPS is a constant if the consumption / saving function is linear

Saving FunctionAverage Propensity to Save APS It is defined as the total saving divided by total incomeAPS = S/YIt is the slope of ray of the saving function

Saving FunctionAverage Propensity to Save APS (contd)When S= sY APS = MPS = s = constant

When S=S+ sY APS < MPS as S ve APS ve when Y < Y*[slide 62] APS = 0 when Y = Y* APS +ve when Y > Y* APS when Y

Saving FunctionY = C + SDifferentiate wrt. YY/Y=C/Y + S/Y 1= MPC + MPS 1 = c + s[slide 61]

S = S + sYDivided by YS/Y = S/Y + sAPS=S/Y+MPS[slide 66]

CY = EY*=CYC-ve S+ve SHow to determine Ye?YePlanned Y = planned EPlanned CPlanned IYC, S, I, E

CY = EYePlanned CPlanned IE = C + IPlanned Y < Planned E

Y = C S =0 No Dis-saving Y < E Unintended Inventory Dis-investment Actual I =Planned I Unintended IY < CY < E

CY = EYePlanned CPlanned IE = C + I

Y > C S +ve Saving Y > E Unintended Inventory Investment Actual I =Planned I + Unintended IPlanned Y > Planned EHow about Y*

Injection-Withdrawal ApproachRemember the national income identity S I [slide 28]The equilibrium income happens when planned Y= planned E as well as planned S = planned I [slide 29]

Injection-Withdrawal Approach

S+ sY = IsY = I SS=-Cs=1-c(1-c)Y = I + C = EEquilibrium condition [slide 57]Y = E

11-c

Equilibrium IncomeNo matter which approach you use, you will get the same equilibrium condition.Can you derive the equilibrium condition if investment I is an induced function of national income Y, using the 2 approaches?

Equilibrium IncomeWrite down the investment function I first. Then write down the saving function S. Remember planned S = planned I when Y is in equilibrium {Injection-Withdrawal}

Write down the investment function I as well as the consumption function C. Together they are the aggregate expenditure function E. Remember planned Y = planned E when Y is in equilibrium {Output-Expenditure}

Injection-Withdrawal Approach

Output-Expenditure Approach

Y=EE=C+IC=C+cYI=IICE=C+IYCY=CS = S + sYS=- C

E=C+II=IIE=C+IS=S+sYPlanned Y=Planned EPlanned S=Planned IUnintended Inventory InvestmentUnintended Inventory InvestmentUnintended Inventory DisinvestmentUnintended Inventory Disinvestment

Paradox of ThriftThis is an example of the fallacy of compositionThriftiness, while a virtue for the individual, is disastrous for an economyGiven I = IGiven S = S + sY OR S = -C + (1-c)YNow, suppose S Will Ye increase as well?

I=IS= S+ sYS=S +sYYeExcess SupplyA rise in thriftiness causes a decrease in national income but no increase in realised saving.

Paradox of ThriftIf a rise in saving leads to a reduction in interest rate and hence an increase in investment (Think of the loanable fund market), national income may not decrease

Ye will increase if I increase more than SYe will remain the same if I increase as much as SYe will decrease if I increase less than S

I=IS= S+ sYS=S +sYYeI=II > S

I=IS= S+ sYS=S +sYYeI=I=YeI = S

I=IS= S+ sYS=S +sYYeI=IThe reduction in Ye is less than the case when I does not increaseWhat about the case if I is an induced function of Y?I < S