Consumption And Savings Functions By Prof. Tarun Das

Economic Environment and Policy (EEP) Session-5 Consumption and Savings Functions Dr. Tarun Das, Professor, IILM

Prof. Tarun Das, IILM

EEP Session-5

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Contents of this presentation 1. Consumption Function 2. Savings Function 3. Simple Keynesian Model 4. Various Models on Consumption

Prof. Tarun Das, IILM

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1.1 Consumption Function Consumption function shows the relationship between consumption (C) and income (Y) at different levels of income. C = f(Y) = α + β Y α > 0, β >0 α is minimum level of consumption for biological survival. Average Propensity to Consume (APC) is the average consumption expenditure per unit income. APC is the ratio of total consumption to income. Marginal propensity to consume (MPC) is the rate of change of consumption with respect to income. Prof. Tarun Das, IILM

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1.2 APC and MPC

APC = C/Y = Slope of the ray OA from origin to the consumption function=AB/OB MPC = dC/dY = slope of the C=α +β Y consumption function = β = AB/DB Consumption Function

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1.3 Properties of APC and MPC APC = C/Y = (α + β Y)/Y = α /Y + β MPC = dC/dY = β , For Linear consumption function MPC is constant. (1) Both APC and MPC lie between o and 1. (2) APC falls continuously as income rises. (3) C = APC . Y MPC = dC/dY = APC + Y . dAPC/dY (4) We know that dAPC/dY <0 and Y>0 So MPC < APC, or APC exceeds MPC. (5) If APC remains unchanged MPC=APC. Then Consumption Function passes through origin. (6) If income ⇒ infinity, APC tends to MPC.

Prof. Tarun Das, IILM

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1.4 Relation between APC and MPC

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General Consumption Function- Concave and Positively sloped

APC MPC Y O Prof. Tarun Das, IILM

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2.1 Savings Function Savings function shows the relationship between savings (S) and income (Y) at different levels of income. S = f(Y) = a+ b Y a< 0, b >0 ‘a’ is minimum level of income (equal to minimum level of consumption) above which savings are feasible. Average Propensity to Save (APS) is the average savings per unit income i.e. APS is the ratio of total savings to income. Marginal propensity to save (MPS) is the rate of change of savings with respect to income.

Prof. Tarun Das, IILM

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2.2 APS and MPS APS= S/Y = Slope of the ray OA from origin to the savings function = AB/OB MPS=dS/dY=slope of savings function=b=AB/BD Savings Function S = a+ b Y

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2.3 Properties of APS and MPS APS = S/Y = (a + bY)/Y = a/Y + b MPS = dS/dY = b (1) Both APS and MPS lie between o and 1. (2) APS increases continuously as income rises. (3) S = APS . Y MPS = dS/dY = APS+ Y . dAPS/dY (4) We know that dAPS/dY >0 and Y>0 So MPS > APS, or MPS exceeds APS. (5) If APS remains unchanged MPS = APS. Then Savings Function passes through the origin. (6) If income ⇒ infinity, APS tends to MPS.

Prof. Tarun Das, IILM

EEP Session-5

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2.4 APS and MPS APS = S/Y = Slope of the ray from origin to the savings function MPS = dS/dY = slope of the savings function = b General Savings Function

S MPS

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2.5 Relation between APC, MPC, APS, MPS

Y=C+S (1) Y/Y = C/Y + S/Y i.e. APC + APS =1

(2) dY/dY = dC/dY + dS/dY i.e. MPC+MPS =1 (3) Y=C+S = α + β Y +S So S = Y - α - β Y = - α + (1- β ) Y = a + bY Therefore, a = - α MPC Prof. Tarun Das, IILM

and b = 1- β , MPS =1-

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2.6 Relation between APC, MPC, APS, MPS (1) For all positive income level, APC, APS, MPC and MPS lie between 0 and 1. (2) APC + APS =1 (3) MPC+MPS =1 (4) At all levels of Y, APC>MPC and APS<MPS (5) As income rises, both APC and MPC fall And both APS and MPS rise. (6) For sufficiently large levels of income. APC=MPC and APS=MPS. Prof. Tarun Das, IILM

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3.1 Simple Keynesian Model Two SectorsHouseholds and Business Bodies Y = C + S Income Allocation Y=C+I Expenditure Approach Equilibrium condition C+S = C+I ⇒

Prof. Tarun Das, IILM

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3.2 Equilibrium Income and Output

Problem-1 Given C = 30+0.6Y and I =50, estimate equilibrium level of income (Ye). What are C, S, APC, APS, MPC and MPS at Ye? Answer: Y = C+I = 30+0.6Y+50 Y-0.6Y = 30+50 Or, 0.4Y=80 So, Ye =80/0.4 = 200 MPC=0.6, So, MPS = 1-0.6= 0.4 at all income. APC = 30/Y + 0.6 = 30/200 + 0.6 = 0.75 APS = 1-0.75 = 0.25 Equilibrium Ce =30+0.6*200 = 150 Equilibrium savings = Ye-Ce= 200-150=50=I Prof. Tarun Das, IILM

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3.3 Equilibrium Income and Output

Alternatively equilibrium condition requires that S=I S= Y-C = Y – 30 - 0.6 Y = 0.4 Y – 30 = I = 50 Or, o.4 Y = 80 So Ye = 80/ 0.4 = 200 Savings function S = -30 + 0.4 Y So MPS = 0.4, MPC = 1-MPS = 0.6 APS = -30/Y + 0.4 = 0.25 ay Ye=200 APC = 1- APS = 1 -0.25 = 0.75 Equilibrium consumption Ce=150 Equilibrium savings-investment Se= Ie= 50 Prof. Tarun Das, IILM

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4.1 Different Models on Consumption a) b) c) d)

Absolute income hypothesis Relative income hypothesis Permanent income hypothesis Life cycle income hypothesis

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4.2 Absolute income hypothesis Given everything else, Individual consumption depends on absolute level pf income. C = C(Y) dC/dY >0 MPC >0 d²C/d²Y <0 MPC falls as Y rises.

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4.3 Relative Income Hypothesis Duesenberry’s theorem “Keeping up with the Joneses: consumption of a family also depends on the demonstration effects of neighbors and relatives. C = C(Y/ Yr) Y = own income Yr = Income of close relatives and known families Prof. Tarun Das, IILM

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4.4 Milton Friedman’s Theory of Permanent Income Hypothesis C = Cp + Ct Y = Yp + Yt Cp = β Yp Where Cp = permanent consumption Ct = transitory consumption Yp = permanent income Yt = transitory income

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4.5 Modigliani Life cycle hypothesis Modigliani and Brumberg postulated that current consumption of an individual depends on the present value of his expected income or wealth during his life. C C

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Thank you Have a Good Day

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