Keynesian Economic Model
Topic Twenty-One

### The Macroeconomic Model

A macroeconomic model is an analytical tool designed to describe the operation of the economy of a country. These models are usually designed to examine the dynamics of aggregate quantities such as the total amount of goods and services produced, total income earned, the level of employment of productive resources and the level of prices.

### The Closed Economy

In building the macroeconomic model, we start with a closed or two-sector economy where there is no G and X-M in the model. In such an economy, GDP will be measured or represented by:

GDP = AD = C + I

where

C - consumption,

I – investments.

Note that usually GDP is:

GDP = C + I + G + X – M

where:

C - consumption by individuals;

I - investments or spending by the business sector;

G - spending by the government;

X - exports and;

M - imports

### The Three-Sector Economy

When we add the government sector we will now transform the two-sector economy to a three-sector economy where AD = AE = Y = C + I + G. Notice that when we add the governments sector, aggregate income increases and so the aggregate income or demand curve moves up above the two-sector AD curve. Now with the government sector added, we also have taxes which are like a leakage from the circular flow of income. Also notice that equilibrium will now be AD = C + I + G = C + S + T, where injections equal to leakages.

### Open Economy

The model of the closed economy was constructed above where it was assumed that there is no trade meaning no exports and imports. This was only for purposes of simplicity. Now we will introduce both trade and government sectors and this will transform the two-sector model of AD = AE = C + I into the four-sector or open economy as:

AD = AE = C + I + G + X – M

The addition of the government and trade sectors will shift the aggregate expenditures curve upwards as seen in the following graph. The economy will be in equilibrium when leakages equal injections. Let W represent withdrawals and I represent injections. The economy will be in equilibriums when W = I. W = S + T + M = I = I + G + X. We can see that when the trade sector is added, aggregate demand and supply increase and so the AD curves moves up from C + I to C + I + G then to C + I + G + X - M

### The Consumption Function

The consumption function describes the relationship between disposable income and consumption such as follows:

C = a0 + b1 Y

where:

C = consumer spending,
a0 = autonomous consumption, or the level of consumption that would still exist even if income was \$0
b1 = marginal propensity to consume which is the change in consumption as a result of 1-unit change in disposable income.

Y = real disposable income.

The b1 is referred to as the marginal propensity to consume or the slope of the consumption function and a0 is the intercept. The marginal propensity to consume (MPC) is the additional or extra amount of those products consumed resulting from a 1-unit increase in disposable income. Another term is that of the average propensity to consume (APC) which is the absolute amount of consumption divided by disposable income.

Determinants of Consumption

There are certain factors which affect consumption and which also affect the consumption function. These factors are as follows:

• Real incomes – if people’s money wages rise faster than prices, then real incomes will increase and this leads to a higher level of real purchasing power. This will cause the consumption function to shift upwards from C0 to C1 as can be seen in the following graph.
• Direct and indirect taxation – if there is a cut in direct taxation then, other factors remaining the same, consumers will experience an increase in their disposable income and spending power.
• Interest Rates – many consumers depend on credit in order to purchase a sizeable amount of their goods and services. When the rate of interest falls, this will cause cost of borrowing to fall which will tend to increase spending which is consumption. This will have the effect of shifting the consumption function upwards from C0 to C1.
• Consumer Confidence – consumer confidence plays a key role in economic decision making. Consumer confidence translates into how people feel about the economy. If there is a great deal of confidence in the economy, people will spend more and this will shift the consumption upwards.
• Inflation – inflation reduces the purchasing power of money. Because purchasing power will decrease, consumption will also decrease which will cause the consumption function to shift downward. On the other, when there is deflation which is the general decline in prices, this will cause the purchasing power to increase. This will in turn result in an increase in consumption which will cause the consumption function to shift upwards.

### The Savings Function

What is not consumed is saved and is shown as the savings function which is as follows.

S = a0 + b1 Y

S = saving;
a0 = autonomous saving or the level of savings that would still exist even if income was \$0
b1 = marginal propensity to save, which is the change in savings as a result of 1-unit change in disposable income.

Y = real disposable income

The Paradox of Thrift is an economic concept which was made famous by John Maynard Keynes. Thriftiness is usually regarded as a virtue. An increase in thrift on the part of an individual can result in higher saving and wealth. It is also regarded a public virtue because if people consume less, more resources can be devoted to producing capital goods which lead to increase in income, output and employment. Ac­cording to Keynes, thrift is a public virtue only if the propensity to invest is equally high as propensity to save. Otherwise, thrift is a public liability if the increase in the propensity to save is unaccompanied by increase in the propensity to invest. Therefore, an increase in the propensity to save unaccompanied by an increase in the willingness to invest, will lead to a fall in income which is what is referred to as the paradox of thrift.

### Theories of Consumption

There are four main theories of consumption. These are the absolute income hypothesis, the relative income hypothesis, the permanent income hypothesis and the life cycle hypothesis.

Absolute Income Hypothesis

Keynes’ consumption function has come to be known as the absolute income hypothesis. This hypothesis is based on the notion that consumption is a stable function of cur­rent income or current disposable income which is income after tax payment. His consumption function is such that 0 < MPC < 1 and MPC < APC. Therefore, the relation between consumption and income is based on his Fundamental Psychological Law of Consumption which states that when income increases consumption expenditure also increases but by a smaller amount. Therefore, there is a non-proportional relationship between consumption and income.

Relative Income Hypothesis

American economist J.S. Duesenberry put forward the theory of consumer behaviour which focuses on relative income of an individual rather than his absolute income as a determinant of his consumption. Another important departure made by Duesenberry from Keynes’s absolute income hypothesis consumption theory is that the consumption of a person does not depend on his current income but on certain previously reached income level. According to the relative income hypothesis, consumption of an individual is not the function of his absolute income but of his relative position in the income distribution in a society. In other words, consumption depends on a person’s income relative to the incomes of other individuals in the society. For example, if the incomes of all individuals in a country increase by the same percent­age, then a person’s relative income would remain the same even though his absolute income would have in­creased. According to Duesenberry, because his relative income has remained the same the individual will spend the same proportion of his income on consumption as he was doing before the absolute increase in his income.

Permanent Income Hypothesis

Like Duesenberry’s relative income hypothesis, Milton Friedman’s permanent income hypothesis states that the basic relationship between consumption and income is proportional. However, according to Friedman, consumption de­pends neither on absolute income nor on relative income but on permanent income, based on expected future income. Friedman divided the current measured income (i.e., income actually received) into two: permanent income (Yp) and transitory income (Yt). Thus, Y = Yp + Yt. Permanent in­come can be seen as the average or mean income which is determined by the expected income to be earned over a long period of time. On the other hand, transitory income consists of unexpected increase or decrease in income, for example, income re­ceived from lottery.

Life Cycle Hypothesis

The life cycle hypothesis explains individual behavior as an attempt to smooth out consumption patterns over one's lifetime somewhat independent of current levels of income. This model states that early in a person’s life, his consumption expenditure may exceed income as the individual may be making major purchases such as purchasing a new home. At this stage in life, the individual will borrow from the future to support these expenditure needs. However, in mid-life, these expenditure patterns begin to level off and are supported by increases in income. At this stage, the individual repays any past borrowings and begins to save for his retirement. Upon retirement, consumption expenditure may begin to decline while income usually declines dramatically. In this stage, the individual dis-saves or lives off past savings until death.

### Potential GDP and the GDP Gaps

Actual GDP represents what the economy is actually producing, while potential GDP is that level of output that the economy could produce if all of the factors of production are fully employed (full employment). The difference between these two concepts is what is referred to as the GDP gap. When the economy is operating below its potential, the gap is referred to as a recessionary gap. In this case, aggregate demand (AD) is less than full potential GDP which is Y = C+I+G+X-M.

In times of economic prosperity, the economy may operate in excess of its potential output. In this case, the economy is operating in an inflationary gap. In this case, aggregate demand (AD) is more than full potential GDP which is Y = C+I+G+X-M.

### Leakages or Withdrawals

When there are no leakages and injections into the system, the circular flow of income is very static. There will be stagnation in the economy. In such a case, consumption expenditures by households will exactly match the goods and services produced by firms. This can be described as an equilibrium position in the economy.

Withdrawals are items that take money out of the circular flow. Leakages or withdrawals from the circular flow of income can lead to a decline in incomes and eventually translate into economic decline. Savings (S) as well as taxes (T) are leakages from the circular flow and this should be balanced with injections. When the government imports (M), this is also considered a withdrawal or a leakage in that the government pays for imported goods – it is a withdrawal from the system.

### Injections

Injections into the circular flow of income are spending that puts money into the circular flow of income. Investments (I) are considered to be injections which can result in economic growth and development. When the government (G) spends its income, this is also considered to be injections which can also lead to the creation of employment which will result in economic growth and expansion. Exports (X) are also considered to be an injection in that it is income that is earned by the country and adds to the system.

### The Multiplier Effect

When variables such as I or C change, GDP will change by a larger amount than the change in I or C. This is called the multiplier effect. For example, assume that there is a project which involves the construction of a factory that will cost \$100.00 million. Workers in this industry will earn income that they will spend on other things. This will cause an increase in real GDP. With this new level of GDP, more incomes will be earned and spent which will cause further increases in incomes and GDP. Therefore the initial increase in spending of \$100.0 million would have resulted in an increase in GDP by much more than the initial \$100.0 million. This is what is referred to as the multiplier effect. The multiplier can be represented as: K = êY/ êI, the change in GDP (Y) resulting from the change in investment.

There are two types of multipliers which are the multiplier effect and the spending multiplier. To illustrate this, let us take a look at a very simple economy comprising of four companies:

Shannon who is the store owner; Derrick who works on an assembly line in a car factory; Joe who is a food mart owner and; Davis who owns a hardware store.

Derrick’s factory has a profitable year and so earns an extra \$1,000 of income. Derrick decided to spend \$800 on clothes. Since Shannon is a store owner, Derrick spends this \$800 at Shannon’s store so then Shannon will earn \$800. Shannon also decides to spend part of this \$800 she receives which is \$600 on things that she desires. She spent this on Joe’s food mart. This is additional income for Joe who then goes to Davis and spends \$500 on tools. As we can see, the initial \$1,000 spending leads to three more rounds of spending with smaller amounts each time. Total spending was \$1,000 + \$800 + \$600 + \$500 = \$2,900. When money spent multiplies in this manner, we refer to it as the multiplier effect. Money spent in the economy does not stop with the first transaction.

### Spending Multiplier

In the above case we know that income increased by a multiple of the initial spending. This was referred to as the multiplier effect. However, we did not know by how much but we can know by the following formula:

where, MPS stands for marginal propensity to save which is the percentage of any increase in income which households are going to save; and MPC stands for marginal propensity to consume and it is the percentage of any increase in income which households are expected to consume. By definition, MPS + MPC = 1 and MPS = 1 − MPC. This is known as the spending multiplier which can be differentiated from the multiplier effect.

As an example, suppose a large factory is to be built which will cost \$8 million. This \$8 million which is spent to build the factory will go as income to the workers who are constructing factory. When this \$8 million is spent by the workers to buy goods and services, it will multiply throughout the economy. The final amount the \$8 million will multiply to can be determined if we know the marginal propensity to consume which in this case is 0.8. Using the above multiplier formula of:

When we multiply this 5 by the initial amount spent to construct the factory which is \$8 million, this \$8 million will multiply to \$40 million (\$8 multiply by 5). It is important to note that higher consumption will lead to a higher multiple.

### The Multiplier Effect in an Open Economy

Just as with the case where we can calculate the multiplier in terms of how extra income gets spent or consumed, we can also measure the multiplier in terms of how much of the extra income goes in savings and other withdrawals. This is so because an open economy has all sectors, and therefore has three withdrawals such as savings, taxation and imports. This will be indicated by the marginal propensity to save (mps) plus the extra income going to the government - the marginal tax rate (mtr) plus the amount going abroad – the marginal propensity to import (mpm).

When all withdrawals are added, we get the marginal propensity to withdraw (mpw). The multiplier can now be calculated by the following general equation:

1/1- mpw

The multiplier concept can be used in any situation where there is a new injection into an economy. It is also important to note that the higher the leakages, the lower will be the multiplier. For example, if the MPS is 20 percent, then the multiplier will be 1/.20 = 5. Now if we add another leakage other than savings such as tax (which is the amount of tax for additional incomes) which is 0.20, then the multiplier will now become:

1/ (0.20 + 0.20) = 2.5

Therefore, the multiplier decreased from 5 to 2.5 when the additional leakage of tax was added. Therefore, the higher the injections and the lower the leakages, the higher will be the multiplier and the lower the injections and the higher the leakages, the lower will be the multiplier.

### The Quantity Theory of Money

In its simplest form, the quantity theory of money is expressed as:

MV = PT

where,
M = money Supply
V = velocity of Circulation (the number of times money changes hands)
P = average Price Level
T = volume of Transactions of Goods and Services

It is built on the principle of equation of exchange:

Amount of Money X Velocity of Circulation = Total Spending

If an economy had \$5.00 of money, and each dollar was spent four times a month, total monthly spending must be \$20.00. This equation of exchange is a foundation of the quantity theory of money which is a theory of the price level. This theory states that inflation is caused by rapid increases in the quantity of money in circulation, and that deflation is caused by decreases or very slow increases in the quantity of money in circulation.

An alternative way of viewing this is to recognize that as prices go up, the value of money goes down; since it takes more dollars to buy things, money is worth less than it used to be. The quantity theory states that an increase in the amount of money relative to goods decreases its value, and a decrease in the amount of money relative to goods will increase its value. Money is thus like any other commodity: increases in supply decrease marginal value.