1. Lecture 3: Simple Keynesian Model
National Income Determination
Three-Sector National Income Model

2. Outline The Consumption Function Three-Sector Model Fiscal Policy
Output-Expenditure Approach: Equilibrium National Income Ye
Injection-Withdrawal Approach: Equilibrium National Income Ye
Fiscal Policy

3. Introduction Why focus on the consumption function?
Largest component of nations’ GDP
Important to understand relationship between consumption and national income in order to explain large changes in national income from shifts in autonomous expenditure
In two-sector model, consumption is the only endogenous variable. Therefore, changes in exogenous expenditure that affect national income depend on how consumption related to national income

4. Keynesian consumption function
Basic x’tic is that current consumption is related to current (disposable) income
Here, MPC= APC= c
Consumption function may also have a constant term
C= a + cY
Graphical illustration
Calculate the APC and MPCs. Are these equal?

5. Constant consumption and autonomous expenditure
Recall: E= C + I
Define C= a + cY; I= I*
Aggregate Expenditure (E)= a + cY + I*
(grouping autonomous expenditures together: A= a + I*
Aggregate Expenditure (E)= A + cY
Compare with usual expenditure function (E= I* + cY)

6. Constant consumption and autonomous expenditure
All autonomous expenditure flows and constants on expenditure functions can be grouped together into a single autonomous expenditure term, A
A shift (upwards or downwards) in any component of A also leads to shift in A

7. Assigned reading
Read on determinants of consumption
Lipsey pp, 491

8. Three-sector models
Introducing a Government sector

9. Three-Sector Model
With the introduction of the government sector (i.e. together with households C, firms I), aggregate expenditure E consists of one more component, government expenditure G.
E = C + I + G
Still, the equilibrium condition is
Planned Y = Planned E

10. Definitions and terminology
Government expenditure is made up of two parts
Government expenditure on current production, G
Transfer payments, Q
Government also collects tax revenues, T
Government budget balance may be defined as revenues minus expenditures
T- (G + Q)
When positive, there is a government surplus i.e. more revenues
When negative, there is a government deficit i.e. more expenditures
When zero, there is a balanced budget

11. Brief digression: implications of deficit in government budget
A deficit requires an increase in borrowing
Borrowing from private sector (local and foreign)
Borrowing from central bank
Private sector
Selling of bills and bonds (longer term)
Bills and bonds are promises to pay a stated amount sometime in the future
Central Bank
Creation of new money
No limit (presumably) to how much government can borrow

12. Behavioural assumptions of g
Assumptions about the Government component of AE
Government expenditure on current production is assumed constant, G= G*
Transfer payments are also an autonomous expenditure flow, Q= Q*
These assumptions may be relaxed later
Deal with simple case of how national income responds to constant G and Q
Graphical Illustration
Additional assumptions
All transfer payments are made to households
Firms may also receive these payments in the form of subsidies
All taxes are direct taxes on personal and company incomes
No indirect taxes like VAT in present economy
Taxes are a constant proportion of national income i.e. T= tY where 0<t<1
No progressive or regressive tax structures

13. Introducing new propensities
Average propensity to tax, T/Y
Total tax revenue as proportion of total income
Marginal propensity to tax, ∆T/ ∆Y
Change in tax from one unit change in income
Given functional form of taxes i.e. T= tY
APT= MPT= t

14. Behavioral assumptions about the household sector
In the 2-sector model, all national income was paid out to households
Households decided to consume or save amounts
National income, Y= disposable income, Yd
Introduction of taxes and transfer payments drives a wedge between national income and disposable income
Yd= Y- T + Q
Taxes reduce disposable income
Transfer payments increase disposable income
In the absence of each, Yd= Y

15. Behavioral assumptions about the household sector
We continue to assume C= cYd
Households spend a fraction of disposable income and save the rest
Given that Yd= Y-T+Q,
C= c(Y-T+Q)
=cY – cT + cQ, but T= tY
=cY – ctY + cQ
= c(1 – t) Y + cQ // But what does this mean?

16. Behavioral assumptions about the household sector
First term :c(1-t)Y
If t is the proportion of income taxed, 1-t is proportion not taxed i.e. disposable income
c(1-t) is proportion of income that is consumed or spent or marginal propensity to consume out of national income
Second term: cQ
Proportion of transfer payments that is consumed or spent
So total consumption, C, is made up of proportions of consumption from disposable income and transfer payments.
Question: Is there an autonomous component of this consumption function?
Graphical illustration

17. Next class Equilibrium in the 3 sector model The Multiplier
Output Expenditure Approach
Withdrawals Injections Approach
The Multiplier
Limitations of the Keynes Theory of National Income