1. UNIT  6
Income Determination in a Simple Keynesian Macroeconomic Model

2. Objectives Describe the consumption function and its major features
Explain the relationship between consumption and saving
Calculate the marginal propensity to consume and save
Determine equilibrium in a two-sector and four-sector economy
Explain the working of the multiplier
Distinguish between inflationary and deflationary gaps

3. 1. Production, Income and Spending
There are two major schools of thought in economics:
The classical school
The Keynesian school

4. Classical School
Classical theory was the only economic theory during the first part of the twentieth century.
The classical economists believed in the laissez-faire approach, which means leave the market alone. This policy was based on the view that the economy should be left to itself and it will return to full employment on its own.

5. Classical School Classical economists believed that:
Prices and wages will automatically adjust upwards or downwards, as the situation requires.
Production, which creates supply, also creates sufficient demand since people spend their income.
Say’s law: (Jean Baptiste Say)
Supply creates its own demand.
By this he meant that whatever was produced would create the income necessary to purchase the product.
The classical theory was widely accepted until the Great Depression that lasted from 1929 to 1939.

6. The Keynesian school
The unemployment during the Great Depression convinced J.M. Keynes that the economy does not return automatically to a level of full employment.
He published a book ‘The General Theory of Employment, Interest and Money’ which criticized the Classical theory.
Say’s Law is not valid because households do not spend all their income. Some of it is leaked out of the circular flow of income.
Say’s Law does not apply in all situations. Investment does not depend on income and investment is not always equal to savings.
Economic forces such as collective bargaining prevent the free movement of prices and wages. Also, wages do not adapt downwards.
The continued unemployment of the Great Depression convinced Keynes that attention had to be paid to the demand side of the economy. 

7. The Keynesian school (Continue)
He argued that the level of output and employment is determined by aggregate demand (expenditure) and that government expenditure should be increased if the other three expenditure components are inadequate to maintain production and employment at a satisfactory level.

8. The classical school versus the Keynesian school

9. The classical school versus the Keynesian school
The circular flow indicates that income is generated as goods and services are produced. The following questions arise:
Which of the two happens first? Does production lead to demand because people have incomes, or does production take place because there is a demand?
If the government wishes to influence the economy, on which side of the circular flow should it focus?

10. 2. Basic Assumptions of the Keynesian Model
The aim of the Keynesian model is to explain how national income (Y) is determined.
It is based on the fact that the GDP (also called national income or production) is equal to the components of total demand or total spending.
Y (GDP) = C + I + G + (X – M)
 Assumptions:
Wages and prices are fixed.
Financial markets cannot be analysed in this model.
Income can be consumed or saved.
There is a direct relationship between C and Y as well as S and Y.
I and G are autonomous.
X is autonomous but M is directly related to Y.
There is no economic growth.
Tax is imposed as a lump sum.

11. 3. Leakages and Injections

12. Total leakages (S + T + M)
 Leakages are withdrawals from the circular flow of income. A leakage is income that flows out of the circular flow and is not used to purchase goods and services.
Saving (S)
Taxation (T)
Imports (M)

13. Total injections (I + G + X)
Injections are autonomous additions to the circular flow of income that increase spending. If a curve is autonomous, we present it graphically as a horizontal line.
Investment (I)
Government spending (G)
Exports (X)

14. 4. Consumption Spending
Consumption spending (C) is the first component of aggregate demand and refers to the purchase of final goods and services by households.
Income (Y) is the most important determinant of consumption spending (C). How much we consume depends on our income.
In a simplified economy people can do two things with their income:
they can spend it, or
they can save it

15. The Consumption Function

16. Consumption function and saving function
Please note:
In the Keynesian analysis the C-function and the 45-degree line are used together. The 45 degree line divides the quadrant into two equal parts and illustrates all the points where consumption is equal to income (C=Y).
The consumption function shows the relationship between consumption (C) and disposable income (Y). The C-function has a positive slope and shows the direct relationship between C and Y. When income increases, consumption will also increase.
Consumption is positive even if income is zero. As long as we are alive, we have to buy goods and services.
When income increases consumption also increases, but the increase in consumption will be less than the increase in income because consumers will save part of the additional income.
The vertical distance between the 45-degree line and the C-function represent saving.

17. Consumption function and saving function
Please note:
Positive saving occurs where the 45-degree line lies above the C-function and this means people deposit money into their savings accounts.
Dissaving occurs where the 45-degree line lies below the C-function. This occurs when people use previous savings to finance consumption.
Zero saving occurs where the C-function intersects the 45-degree line. Disposable income is 300 and consumption is also 300.

18. Consumption function and saving function
Consumption (C) consists of two parts:
(a) Induced Consumption:
This refers to consumption spending that depends on income.
Graphically it is represented by the C-function.
(b) Autonomous Consumption:
Autonomous consumption is independent of income and occurs when disposable income is zero.
Graphically it is the area from the origin (0) to the intercept of the C-function on the Y-axis. 

19. The formula for the consumption function
C = Ca + (c)Y
Where:
C = total consumption spending
Ca = autonomous consumption
c = MPC (discussed below)
Y = disposable income
Example: 
Suppose Ca = 120 and c = 0.8, how much will consumption be if income is N$400?
 C = (0.8 x 400) =
= N$440

20. The Saving Function
The S-function has a negative intercept on the Y- axis since it indicates negative saving or dissaving.
Like the C-function, the S-function is positively sloped because households will save more at higher income levels.

21. Marginal propensity to consume (MPC)
Definition: The marginal propensity to consume (MPC) is the extra amount that households consume when they receive an extra dollar of income.
If the MPC is 0.8 it means that in this particular community people will spend 80 cents of every extra dollar of income they receive. 
Graphically the slope of the C-function is given by the MPC.
The positive slope of the C-function indicates that if income increases, consumption also increases but not with the same amount, because part of the income will be saved.
The MPC tells us which part of the extra income will be consumed.
Formula: C
MPC = Y

22. 5. Investment Spending
Total spending in a two-sector economy consists of consumption spending (C) and investment spending by businesses (I).
Definition:
Investment is the purchase of production and capital goods by businesses to earn an income.
Most businesses have to borrow funds for investment and have to pay interest on the loan.
The interest rate is an important element of any investment decision. The higher the interest rate, the lower the expected return on the investment and vice versa.
The level of investment (I) is, therefore, inversely related to the interest rate (i).
The relationship between investment and the interest rate is shown in the diagram below:

23. The investment function
The interest rate is measured on the Y-axis. It is done like that because the interest rate is a price - the price we pay when we borrow money.
The amount of investment is measured on the X-axis.
The Keynesian theory examines the relationship between investment and the level of income.

24. 5. Investment Spending
The Keynesian analysis assumes that investment is autonomous. Changes in investment are not related to changes in income.
The theory assumes that planned investment has a given value that is determined by factors outside the model.
Therefore the investment function is depicted graphically as a horizontal line.
The diagram shows that investment is measured on the Y-axis and income is measured on X-axis. In the Keynesian theory, all expenditure components (total demand) are measured on the Y-axis while income (production or total supply) is measured on the X-axis.

25. 6.The Simple Keynesian Model in a Closed Economy
The components of the two-sector economy are:
Y + C + I
To obtain the total spending or aggregate demand, add the amount of investment (I) autonomously to consumption (C).
When investment is added to consumption, the curve will become the C + I function and it will shift upwards parallel to the C-function.

26. Total spending in a two-sector economy

27. Equilibrium in a Two-sector Economy
A two-sector economy is an economy that consists of households and firms with no government and no foreign trade.

28. Equilibrium in a Two-sector Economy
Equilibrium method 1:
Y = C+I
Y = 400 and C+I = 400
Equilibrium method 2:
I = S
At an income level of 400, I = 50 and S = 50.

29. The Impact of Changes in Investment Spending: the Multiplier
All economies experience changes in total spending (or aggregate demand). Such changes will disturb the equilibrium and we have to be able to predict the effect this will have on the economy.
Example:
Suppose Game opens a new shopping centre in Windhoek at a cost of N$100 million. Also suppose that the MPC in Windhoek 0.8 and the MPS is 0.2.
The process will start with the original investment of N$100 million which will increase the income of the construction firm and its workers by N$100 million. 
Suppose these people save 20% of their additional income (N$20 million) and spend 80% of their income (N$80 million) on consumer goods. The N$80 million becomes income for the businesses that produce the consumer goods and their workers.
These people in turn spend 80% of the N$80 million (N$64 million) on consumer goods and save the remaining N$16 million.
This process of receiving income and then spending the money, which generates income for other people, continues until the original amount of N$100 million is held in saving by various individuals.
This is when the process stops and no more income will be created. Through this process, the initial investment of N$100 million results in an increase of N$500 million in income. Part of the process is summarised below.

30. The multiplier process
Spending rounds
Increased income and output
Increased consumption (Spend 80%)
Increased saving
(Save 20%)
Round 1: Original increase in investment
100.0
80.0
20.0
Round 2:
64.0
16.0
Round 3:
51.2
12.8
Round 4:
etc.
41.0
11.2
Total:
500.0
400.0

31. The multiplier process
This example shows that an increase in investment of N$100 million can result in a much larger increase in the national income. Economists call this result the multiplier effect.

32. Definition:
The multiplier is a number that tells us how much income will change in response to a change in an autonomous expenditure such as investment spending.
The size of the multiplier directly depends on the marginal propensity to consume (MPC) and the marginal propensity to save (MPS).
The formula is as follows:
Multiplier = or
1-MPC MPS
Assume the MPC = 0.8:

33. Definition: 1 1 Multiplier = -------- = ----- = 5 1-0.8 0.2
1 1
Multiplier = = = 5  
Original investment = N$100 million
Multiplier = 5
Increase income = N$500 million (N$100 million x 5)
Thus:  Investment x Multiplier =  Income

34. 8. Government Spending
If the government sector is added, the model is referred to as a three-sector economy.
Y = C + I + G
Government spending is determined by the Ministry of Finance and set out in the annual budget of the government.
Government spending is therefore also autonomous in the Keynesian model and is depicted graphically as a horizontal line.

35. Government spending and the level of income
Government spending (G) is measured on the Y-axis and income (Y) is measured on the X-axis.
The horizontal line indicates that government spending is autonomous with respect to income and determined by factors outside the model.

36. 9. The Foreign Sector
If the foreign sector is added, the model is referred to as a four- sector economy.
Y = C + I + G + X – M
The foreign sector consists of two components, exports and imports. We normally subtract imports from exports and then refer to it as net exports.
Exports (X)
The demand for Namibia’s exports depends on factors such as economic conditions in other countries, exchange rates and our international competitiveness, and not on the national income level.
Exports are autonomous in relation to income and are shown graphically as a horizontal line.

37. Exports and the level of income
Exports (X) are measured on the Y-axis and income (Y) on the X-axis. The horizontal line indicates that exports are autonomous or independent of income.

38. Imports (M)
There is a strong positive relationship between imports and the level of income in a country.
The more income we have, the more goods we can import.
This creates a problem for economic theory.
Exports are autonomous in relation to income, and to make the analysis less complicated, we assume that imports are also autonomous.

39. Net Exports (X – M)
If exports are greater than imports, net exports will be a positive number.
If imports are greater than exports, net exports will be a negative number.

40. Net Exports (X – M)
The horizontal line (X–M)1 shows a positive level of net exports. This means that exports are greater than imports.
The line (X–M)2 shows a negative level of net exports, meaning that imports are greater than exports.

41. 10. Equilibrium in a Four-Sector Economy

42. Equilibrium in a four-sector economy
Equilibrium method 1:
Y = C+I+G+(X–M)
Total spending is equal to the national income. The equilibrium income is YE.
Equilibrium method 2:
Total leakages are equal to total injections.
S+T+M = I+G+X

43. Equilibrium in a four-sector economy
Equilibrium method 1:
Y = C+I+G+(X–M)
Total spending is equal to the national income. The equilibrium income is YE.
Equilibrium method 2:
Total leakages are equal to total injections.
S+T+M = I+G+X

44. Activity
State whether aggregate demand (expenditure) will increase (shift up), decrease (shift down) or remain the same in the following cases
Additional government spending of N$50 million to strengthen the armed forces.
An increase in Namibian exports to Europe.
An increase in taxes.
A decrease in investment due to the political situation.
An increase I households’ purchases of savings bonds with no change in consumption expenditures.

45. 11. The Deflationary gap
Keynes was of the opinion that an economy could be in equilibrium with a large percentage of the workforce unemployed.

46. 11. The Deflationary gap
The economy is in equilibrium at income level Y1, which is below the full employment income YF.
When equilibrium income is below full employment income, this difference is called a deflationary gap.
Problem: Unemployment
Government action and policy: Expansionary fiscal policy
To eliminate the deflationary gap and obtain full employment, the total spending should be increased to shift the curve upwards.
Increase government spending, or
Decrease taxes

47. 12. The Inflationary Gap
If spending exceeds the potential output of the economy, i.e. the full employment income level, it will accelerate inflation.

48. 12. The Inflationary Gap
The economy is in equilibrium at income level Y1, which is above the full employment income level YF.
The demand for goods and services is greater than the economy can produce with the available resources. Competition for scarce resources such as labour, raw materials and capital will push prices up.
Problem: Inflation
Government action and policy: Restrictive fiscal policy.
To eliminate the inflationary gap and curb inflation, total spending should be decreased and the curve should shift downwards.
Decrease government spending, or
increase taxes