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Lecture 4. Consumption Function. Consumption Function: It shows the relationship between disposable income and consumption. What is disposable income? If we subtract tax from total income then we get disposable income.

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consumption function
Consumption Function
  • Consumption Function: It shows the relationship between disposable income and consumption.
  • What is disposable income?
  • If we subtract tax from total income then we get disposable income.

So consumption function shows how consumption changes when income changes.

C= f(Y) which implies that consumption is a function of disposable income.

Here M= Total income

T= Tax

M-T= Disposable income =Y

slide3

Here the equation for consumption function is

C= a + b Y where

a= intercept = autonomous consumption ( the consumption we will have when we do not have any income)

b= slope = MPC = ΔC/ ΔY

So the slope of the consumption function (b) is called the marginal propensity to consume (MPC), which shows the change in consumption due to the change in income.

MPC is always between 0 and 1. So 0< MPC <1. Why?

The reason is that if our income increases then we will consume some amount and save the rest.

So ΔC< ΔY. This implies that MPC cannot be greater than 1.

slide4

Example:

  • Suppose initially income is Y1=100. Now income increases to Y2=200. So the change in income is ΔY= 200-100= 100.
  • This increase in income causes an increase in consumption. Initially consumption was C1=80 and then with income increase it increases to C2= 160. So the change in consumption is ΔC= 160-80=80
  • So MPC= ΔC/ ΔY = 80/100= 4/5
savings function
Savings Function
  • It shows the relationship between savings and disposable income. That is it shows how savings changes as disposable income changes.
  • S=f(Y)
slide6

Here the equation for savings function is

S= -a + d Y where

-a= intercept = dissavings(when we do not have income we still have to consume goods and services and we do this by borrowing )

d= slope = MPS = ΔS/ ΔY

So the slope of the savings function (d) is called the marginal propensity to save (MPS), which shows the change in savings due to the change in income.

MPS is always between 0 and 1. So 0< MPS <1. Why?

The reason is that if our income increases then we will consume some amount and save the rest.

So change in savings will be less than change in income that is ΔS< ΔY. This implies that MPS cannot be greater than 1.

relationship between consumption and saving

45°

Relationship between Consumption and Saving

C

Saving

Consumption

Schedule

Consumption

Dissaving

Disposable Income

Saving

Dissaving

Saving Schedule

S

Saving

Disposable Income

slide8

We know that

Y= C+ S

  • So we will have

MPC+ MPS=1.

  • So we can write

MPC = 1- MPS

slide9

Total consumption

Total savings

APC =

APS =

Total income

Total income

  • Average Propensity to Consume (APC): The ratio of consumption and income is known as average propensity to consume. If we divide the total consumption by total income then we get APC.
  • Average Propensity to Save (APS) : The ratio of savings and income is known as average propensity to save. If we divide the total savings by total income then we get APS.
apc aps mpc and mps

(2)

Consump-

tion

(C)

(1)

Disposable

Income (Y)

(4)

Average

Propensity

to Consume

(APC)

(2)/(1)

(5)

Average

Propensity

to Save

(APS)

(3)/(1)

(6)

Marginal

Propensity

to Consume

(MPC)

Δ(2)/Δ(1)

(7)

Marginal

Propensity

to Save

(MPS)

Δ(3)/Δ(1)

(3)

Saving (S)

(1-2)

APC, APS, MPC and MPS
  • $370
  • 390
  • 410
  • 430
  • 450
  • 470
  • 490
  • 510
  • 530
  • 550

$375

390

405

420

435

450

465

480

495

510

$-5

0

5

10

15

20

25

30

35

40

1.01

1.00

.99

.98

.97

.96

.95

.94

.93

.93

-.01

.00

.01

.02

.03

.04

.05

.06

.07

.07

.75

.75

.75

.75

.75

.75

.75

.75

.75

.25

.25

.25

.25

.25

.25

.25

.25

.25