Module 14 A Simple Model of Income Determination

The Development of Macroeconomics Models

The value of some variables are assumed to be determined by:

External Events	Exogenous
Effected by model	Endogenous

Exogenous variables can effect Endogenous variable however Endogenous variables cannot effect Exogenous variables

Inflation Equation	The next period’s price level is equal to this periods price level times one put the rate of inflation Pt+1 = (1+INF)Pt Price Level is exogenous and the inflation rate in endogenous
Keynesian Revolution	is the assumption the price level is exogenous in the short run.

Consumption Function

A schedule that shows the level of planned consumption at each possible level of income

Assumptions

1) Private Sector Economy

2) Closed Economy

3) No International Trade

4) No Government Sector

5) Private Households only

6) Private Firms only

7) Savings only by households

8) Investment only by firms

9) Potential Output Fixed

Level of Aggregate demand Depends on:

1) Consumption (C)

2) Investment (I)

Disposable Income (Yd)	Is income minus taxes plus transfers rather than total income (Y) Y > Yd
Consumption Function	Is the relationship between consumption and income being stable and systematic
Marginal Propensity to Consume (MPC)	Marginal Propensity to Consume – Change in consumption that accompanies a change in income Equal to the change in consumption divided by the change in disposable income that produced the consumption change C – Short Run – C = a+bYd C – Long Run – C = bYd

Simple Model

The value of MPC is given by the slope of the consumption function. Since consumption (C) is a straight line. The MPC must be constant. The APC must decline as Y increase

Where C intersects the 45^O line, C = Y_d and consequently savings (Y_d-C )= 0

The above (left of) the intersection point S < 0 (dissavings)

The below (right of) the intersection C < Y and therefore S > 0 (positive saving)

Short Run Linear Consumption Function C= a+bYd	C = Consumption ‘a = consumption amount that is independent of income ‘b = consumption amount that changes as income changes also is the marginal propensity to consume MPC and the slope of the function Yd = disposable real income (income – taxes = transfers)
Long Run Linear Consumption Function C=bY(no intercept)	Yd = disposable real income (income – taxes = transfers) C = Consumption

Average Propensity to Consume (APC)	Proportion of income consumed and is calculated by dividing consumption expenditure by the level of disposable income
Marginal Propensity to Consume (MPC)	Marginal Propensity to Consume – Change in consumption that accompanies a change in income Equal to the change in consumption divided by the change in disposable income that produced the consumption change C – Short Run – C = a+bYd C – Long Run – C = bYd

Short Run APC > MPC caused by the lag before consumption adjust to changes in income

Long Run APC = MPC

Multiplier Process

One Persons Expenditure is another Persons Income

EXPENDITURE	creates	INCOME
INCOME	creates	EXPENDITURE

The process will continue as long as additional expenditure and additional income are generated. It is always a multiple of the increase.

The eventual increase in aggregate demand will be some multiple of the initial increase in demand

Movement along the consumption function reflect changes in consumption © associated with changes in disposable income (Y_d) changes in price.

Shifts in the position of the consumption function occur because of changes in other factors leading to changes in consumption (C) and income (Y_d) relationship like

1) Incomes

2) Price of complementary or substitute goods

3) Tastes change

The Solution to the Simple Model

Y = Yd	National Income (Y) = disposable income (Yd) since there is no government sector
Y = C+I	National Income (Y) = consumption (C) + Investment (I)
E = C+I	C + I also equal aggregate expenditure (E)
C = bYd	Consumption (C) is a function of income. A proportional relationship at all levels of income so that APC = MPC = b
I = Io	Investment (I) is fixed exogenously (outside the economic system)

The Multiplier

Is the multiple of the I that will increase the aggregate demand and shows how many times greater the total increase in national output will be than the increase in aggregate demand, In order to work there must be sufficient unemployment or inflation will result

The larger MPC the larger the Multiplier

If MPC is 0 then Multiplier is 1

If MPC is 1 then Multiplier is ¥ (infinity)

Autonomous aggregate demand x multiplier = Y

Y = autonomous aggregate demand x

Y = gives the multiplier

Marginal Propensity to save (MPS) or 1- MPC since MPC + MPS = 1

Potential Output

Output that would be produced in the economy operating at natural rate of unemployment i.e. U = 6% and 94% = employed workers.

Determined by

• quality, quantity and work effort of the labour force
• quality and quantity of the capital stock
• state of technology

Typically increase each year because of:

• Increase in labour force
• Increase in capital stock
• Technology changes

Potential output fall because of

War or Natural disaster killing people and destroying capital stock

Labour Force

Tends to increase only slowly over time in the absence of

Change in immigration policies affecting entry

Retirement from the labour force

Improved educational standards

Major determinant is past birth rates, participation rates, and existing retirement practices.

Major impact is Tax Rate

– assumed that lower the Tax Rate will increase work effort and consequently growth rate of Potential Output (Q)

Capital Stock

Any year investment expenditure is very small relative to existing capital stock., variation in Investment (I) on Potential Output (Q) are marginal

Depreciation occurs at constant proportion

If investment expenditure < depreciation result in capitol stock will decrease

Technology Change

Implementation of more efficient way of procuring out form given resources

Major source of growth in Potential Output (Q)

Government policy incapable of affecting rate of technological progress in short run/

.

Investment Multiplier

Conditions for expenditure Multiplier to exist

1) Sufficient unemployment to allow the process to operation

2) Additional demand can be met by domestically produced goods and services

3) Rate of Interest does not change enough to cause reduction in investment and consumption expenditure

Common Misconceptions about Multiplier

Attempt to increase Y one using fiscal policies implies increasing Government Expenditure (G) and /or Decreasing Tax Rate (T) and FST Rate.

Attempt to increase Y by monetary policy(M) implies increasing

This would be the case the year policy change made, However whether it would result in an actual increase in Y over previous year depends on absence of offsetting factors for example

Decrease in exports due to an appreciation of the currency

Therefore possible for an expansionist policy to be accompanied by a reduction in Y form one year to the next.

M/C

I. When Y = 0, C = a

II. When Y = 0, savings = -a

III. When Y = Y₁, savings = 0

I. The MPC is constant

II. The APC is constant

III. Y = C + S only for income levels > Y₁

For the equation C= a +bY the MPC is ; thus the MPC is constant and equal to b. Thus I is correct.

The APC =

Since a is fixed must decrease as Y increases. Thus II is incorrect.

By definition Y = C + S independent of income level.

When Y = 0, C = a and S = -a

When Y = Y₁, C = Y, S = 0

When Y > Y₁, S is positive, measured by the gap between the 45% line and the consumption function. Thus III is incorrect.

From a linear consumption function the following data were observed.

C	Yd
20	0
100	100

The form of a linear function with a positive intercept is

Plugging in the data we have

Thus the equation of the function is C = 20 +.8Y

An electronics company invested $10m in new factories, i.e. caused an initial increase in income Y of $10m. Assuming there are sufficient unemployed resources to allow the complete multiplier process to occur, which of the following would the value of the marginal propensity to consume have to be for the total increase in income to be 20 million?

The value of the investment multiplier is and the increase in income .

If I = 10 and Y = 20 then

Multiplier effects of an autonomous increase in investment expenditure.

Round	C	I	Aggregate demand	Y
1	0	100	100	100
2	80	0	80	80
3	64	0	64	64
4	?
5				?

From the first 3 rows of data a Y of 100 produces a C of 80, i.e. (MPC) and this is verified when a Y of 80 produces a C of 64, i.e.

Thus a Y of 64 in row 3 will generate a C of 51 (64 × .8) in row 4 and a Y of 51 will produce a C of .41 (51 × .8) in row 5 and a Y of .41 in row 5.

Which of the following will be the total change in C and Y when the multiplier processes are complete?

Since the value of the MPC is .8 the value of the multiplier will be 5. Thus the total change in income, Y, will be

Of the 500, 100 is the increase in investment. Thus the increase in consumption will be 500 - 100 = 400.

If a consumption function is linear and the values of the APC and MPC are equal which of the following is correct?

A	The consumption function goes through the origin

B

There are unemployed resources in the economy

C

The value of the multiplier increases as Y increases

D

The value of the multiplier decreases as Y increases

The APC = and is constant and MPC = and is constant for a linear consumption function. Thus C and D are incorrect. The equation of a linear consumption function is C = a + bY; but if , the intersect on the consumption axis a must be 0. Therefore the consumption function must go through the origin.