Simple Keynesian Model National Income Determination Two-Sector National Income Model

Outline Macroeconomics [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]

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

Outline Output-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]

Macroeconomics National 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 Variables Exogenous Variable the value is determined by forces outside the model any change is regarded as autonomous I, G, X ( Micro: Income/Population) Endogenous Variable the value is determined inside the model factor to be explained in the model Y, C, M ( Micro: Price/Quantity)

Linear Functions A function specifies the relationship between variables y is the dependent variable x is the independent variable y=f(x)

Linear Functions y=f(x) y= c y=mx y=c+mx m, c are exogenous variables y, x are endogenous variables

Linear Functions Consumption Functions C= f(Y) C= C’ C= cY C= C’ + cY

Linear Functions C’, c are exogenous variables C, Y are endogenous variables Y is independent variables C is dependent variables

Linear Functions Can you express the 3 consumption functions graphically?

Linear Functions The parameter C’ is autonomous consumption It 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 Functions C= 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 C’ graphically, the consumption function C will shift upwards

Linear Functions What happens if c  ? What happens if Y  ?

Linear Functions Consumption 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 & Supply the relationship between the total amount of planned expenditure and general price level (v.s. aggregate expenditure E) Aggregate Supply the relationship between the total amount of planned output and the general price level

Aggregate Demand & Supply Price Level Aggregate Supply Equilibrium: no tendency to change and the values of the endogenous variables will remain unchanged in the absence of external disturbances Aggregate Demand National Output

Aggregate Demand & Supply AS When AS is vertical A shift of AD will cause a change In P only but have no effect on Y AD2 AD1 Y Yf

Aggregate Demand & Supply AD1 AD2 When AS is horizontal A shift of AD will cause a change in Y only but have no effect on P AS Y

Aggregate Demand & Supply AS AD Ye Yf

Aggregate Demand & Supply The Upward Sloping AS When 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 limitations both price and output will increase

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

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

National Income Determination Model Assumptions: National income Y is defined as the total real output Q A constant level of full national income Yf Serious unemployment, i.e., there are many idle or unemployed factors of production

National Income Determination Model (cont’d) Income / output can be raised by using currently idle factors without biding up prices Price rigidity or constant price level There are only households and firms (2-sector). No government and foreign trade

National Income Identities An identity is true for all values of the variables In 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 I E  C + I

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

National Income Identities Aggregate expenditure E is, by definition, equal to national income Y Y  E C + S  C + I  S  I

Equilibrium Income Equilibrium is a state in which there is no internal tendency to change. It happens when firms 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 Income What 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 Income Ex-ante Y > E  Excess supply planned output > planned expenditure  unexpected accumulation of stocks OR unintended inventory investment OR involuntary increase in inventories In national income accounting, this amount Y-E is treated as (unplanned) investment by firms

Equilibrium Income Ex-post Y= E Firms will reduce output Actual (Realised)= Planned + Unplanned Expenditure Expenditure Investment Actual (Realised) Output = Actual Expenditure Firms will reduce output

Equilibrium Income Ex-ante Y < E  Excess Demand planned output < planned expenditure  unexpected fall in stocks OR unintended inventory dis-investment OR involuntary decrease in inventories However, in national income accounting, this amount E - Y consumed is not currently produced

Equilibrium Income Ex-post Y= E Firms will increase output Actual (Realised)= Planned - Unplanned Expenditure Expenditure Dis-investment Actual (Realised) Output = Actual Expenditure Firms will increase output

Equilibrium Income Ex-ante Y= E  Equilibrium There is no unintended inventory investment OR dis-investment Ex-post Y=E

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

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

Consumption Function Autonomous Consumption C’ It exists even if there is no income. This can be done by dis-saving, i.e., using the past saving Then, saving will be negative when income is zero. It is totally determined by forces outside the model What happens to the 3 consumption functions if C’  ? Or C’  ?

Consumption Function C’ = y-intercept  In C’ C = C’ C = cY

Consumption Function Marginal Propensity to Consume MPC = c It is defined as the change in consumption per unit change in income MPC = C / Y It is the slope of the tangent of the consumption function For a linear function, MPC is a constant What does the consumption function C look like if MPC is increasing? Decreasing? It is assumed that 0 < MPC < 1 What happens to the 3 consumption functions if c ? or c  ?

Consumption Function MPC = slope of tangent  in MPC or  in c C = C’ C = cY C = C’ + cY

Consumption Function Average Propensity to Consume APC It is defined as the ratio of total consumption C to total income Y APC = C / Y It is the slope of ray of the consumption function When C = C’ OR C = C’ + cY, APC decreases when Y increases. When C = cY, APC = MPC = c = constant

Consumption Function APC = slope of ray C = C’ C = cY C = C’ + cY

Consumption Function Relationship between APC and MPC C = C’ Divide by Y C/Y = C’/Y APC = C’/Y APC  when Y  Slope of ray flatter when Y  Slope of tangent = MPC = c = 0

Consumption Function Relationship between APC and MPC C = cY Divide by Y C/Y = c APC = MPC = c Slope of ray=Slope of tangent=constant=c

Consumption Function Relationship between APC and MPC C = C’ + cY Divide by Y C/Y = C’/Y + c APC = C’/Y + MPC C’ +ve APC > MPC Slope of ray steeper than slope of tangent Slope of tangent constant Slope of ray flatter when Y  APC  when Y 

Investment Function Let’s look at the 2nd component of the aggregate expenditure E  C + I An investment function shows the relationship between planned investment I and national income Y It can be a linear function or a non-linear function

Investment Function Again, there can be 3 investment functions I = I’ I = iY I = I’ + iY Economists usually use the first one, i.e., I= I’ as investment is thought to be correlated with interest rate r, instead of Y I’ , i are exogenous variables I , Y are endogenous variables

Investment Function Autonomous Investment I’ It 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 Function Marginal Propensity to Invest i It is defined as the change in investment I per unit change in income Y MPI = I / Y MPI would not correlate with Yd It is the slope of tangent of I It is also determined by forces outside the model

Investment Function MPI = i =slope of tangent I’ = y-intercept API  when Y MPI =0 I = I’ I = iY I = I’ + iY

Aggregate Expenditure Function Given E = C + I C = C’ + cY I = I’  E = I’ + C’ + cY  E = E’ + cY

Aggregate Expenditure Function C, I, E I C Slope of tangent = c Slope of tangent=0 Y I = I’ C = C’+cY E = I’ + C’+ cY

Aggregate Expenditure Function Autonomous Change When C’ or I’   E’   shift upward When c   slope of E steeper  rotate Induced Change When Y   E   move along the curve

Output-Expenditure Approach National income is in equilibrium when planned output = planned expenditure We have planned expenditure E=C+I Equilibrium income is Ye=planned E A 45°-line is the locus of all possible points where Y = E When E = planned E, Y = Ye

Output-Expenditure Approach Y = E Planned E=C +I C, I, E Planned E < Y Unintended inventory investment Actual E = Y Y=planned E Planned E>Y Unintended inventory dis-investment Actual E =Y Y Y Ye Y

Output-Expenditure Approach Y = planned E Y = I’ + C’ + cY Y = E’ + cY (1-c)Y = E’ Equilibrium condition Y = E’ 1 1-c

Output-Expenditure Approach If 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 < 1 1/(1-c) > 1 E’   Ye by a multiple 1/(1-c) of E’ 

Expenditure Multiplier 1/(1-c) Assume c=0.8, E’ = 100 The 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 =0.8 The sum of GP is E’ * multiplier

Saving Function We have Y  C + S [slide 27] Saving function can simply be derived from the consumption function S = Y – C if C = C’ + cY S = Y – C’ – cY S = -C’ + (1-c) Y S = S’ + sY S’= -C’ s = 1 - c S’ < 0 if C’ >0 S’ = 0 if C’ = 0

Saving Function S S S = sY S = (1-c)Y S = S’+ sY S =-C’+(1-c)Y Slope of tangent = s =1- c Y > Y*  S+ve Y Y Y* S’ Slope of ray = slope of tangent Slope of ray < slope of tangent

Saving Function Autonomous Saving S’ Since 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 Function Marginal Propensity to Save MPS = s It is defined as the change in saving per unit change in disposable income Yd OR income Y (in a 2-sector model) MPS = S/ Y It is the slope of tangent of the saving function MPS is a constant if the consumption / saving function is linear

Saving Function Average Propensity to Save APS It is defined as the total saving divided by total income APS = S/Y It is the slope of ray of the saving function

Saving Function Average Propensity to Save APS (cont’d) 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 Function Y = C + S Differentiate wrt. Y Y/Y=C/Y + S/Y  1= MPC + MPS  1 = c + s [slide 61] S = S’ + sY Divided by Y S/Y = S’/Y + s APS=S’/Y+MPS [slide 66]

How to determine Ye? Y = E C, S, I, E Planned Y = planned E +ve S Planned I C -ve S Planned C Y Y<C Y*=C Ye Y>C

Y = E Y = C  S =0  No Dis-saving  Y < E  Unintended Inventory Dis-investment  Actual I =Planned I – Unintended I E = C + I Y < C Y < E Planned I C Planned C Planned Y < Planned E Ye

Y = E Y > C  S +ve  Saving  Y > E  Unintended Inventory Investment  Actual I =Planned I + Unintended I E = C + I Planned I C Planned C Ye How about Y*<Y<Ye? Planned Y > Planned E

Injection-Withdrawal Approach Remember 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 = I’ sY = I’ – S’ S’=-C’ s=1-c (1-c)Y = I’ + C’ = E’ Equilibrium condition [slide 57] Y = E’ 1 1-c

Equilibrium Income No 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 Income Write 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=C Y=E Y<C Y>C E=C+I C=C’+cY E’=C’+I’ S = S’ + sY C’ I=I’ I’ S’=- C’

Planned Y=Planned E Unintended Inventory Investment E=C+I S=S’+sY Unintended Inventory Disinvestment E’=C’+I’ Unintended Inventory Investment Unintended Inventory Disinvestment I’ I=I’ Planned S=Planned I

Paradox of Thrift This is an example of the “fallacy of composition” “Thriftiness, while a virtue for the individual, is disastrous for an economy” Given I = I’ Given S = S’ + sY OR S = -C’ + (1-c)Y Now, suppose S’  Will Ye increase as well?

A rise in thriftiness causes a decrease in national income but no increase in realised saving. S=S” +sY S= S’+ sY Excess Supply I=I’ Ye

Paradox of Thrift If 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 S’ Ye will remain the same if I’ increase as much as S’ Ye will decrease if I’ increase less than S’

I  > S S=S” +sY S= S’+ sY I=I” I=I’ Ye

I  = S S=S” +sY S= S’+ sY I=I” I=I’ Ye =Ye

I  < S S=S” +sY The reduction in Ye is less than the case when I does not increase S= S’+ sY I=I” I=I’ Ye What about the case if I is an induced function of Y?