Multiplier Effect

DEFINITION of 'Multiplier Effect'

The expansion of a country's money supply that results from banks being able to lend. The size

of the multiplier effect depends on the percentage of deposits that banks are required to hold as

reserves. In other words, it is money used to create more money and is calculated by dividing

total bank deposits by the reserve requirement.

INVESTOPEDIA EXPLAINS 'Multiplier Effect'

The multiplier effect depends on the set reserve requirement. So, to calculate the impact of the

multiplier effect on the money supply, we start with the amount banks initially take in through

deposits and divide this by the reserve ratio. If, for example, the reserve requirement is 20%, for

every $100 a customer deposits into a bank, $20 must be kept in reserve. However, the

remaining $80 can be loaned out to other bank customers. This $80 is then deposited by these

customers into another bank, which in turn must also keep 20%, or $16, in reserve but can lend

out the remaining $64. This cycle continues - as more people deposit money and more banks

continue lending it - until finally the $100 initially deposited creates a total of $500 ($100 / 0.2)

in deposits. This creation of deposits is the multiplier effect.

The higher the reserve requirement, the tighter the money supply, which results in a lower

multiplier effect for every dollar deposited. The lower the reserve requirement, the larger the

money supply, which means more money is being created for every dollar deposited.

multiplier effect definition

An effect in economics in which an increase in spending produces an increase in national income

and consumption greater than the initial amount spent. For example, if a corporation builds a

factory, it will employ construction workers and their suppliers as well as those who work in the

factory. Indirectly, the new factory will stimulate employment in laundries, restaurants, and

service industries in the factory's vicinity.

What is the multiplier effect?

The multiplier effect is a concept in economics that describes how an injection into an economy,

such as an increase in government spending, creates a ripple effect which increases employment

and the output of goods and services in the economy.

How does it work?

1. An injection occurs in the economy, such as an increase in government spending. 2. The injection increases the aggregate demand in the economy for goods and services.

3. The increase in demand for goods and services causes firms to employ more workers and expand output.

4. As firms are employing more workers, more people have disposable incomes and subsequently the aggregate demand increases in the economy.

5. The increases in aggregate demand causes firms to employ more workers and the effect continues as before.

Key terms

Aggregate demand – This refers to the total of all the demand in an economy. The equation for

aggregate demand is: Consumption (C) + Government Spending (G) + Investment (I) + (Exports

(X) – Imports (M)).

Economy – A system that provides goods and services.

Gross domestic product (GDP) – This is the total value of all goods and services produced in an

economy during a set period of time.

Injections – Injections increase the demand for domestically produced goods and services.

Injections come from investment, government spending and export sales.

The Multiplier Effect

By Tejvan Pettinger on November 2, 2011 in economics

The fiscal multiplier effect occurs when an initial injection into the economy causes a bigger

final increase in national income.

For example, if the government increased spending by £1 billion, there would be an initial

increase in Aggregate Demand of £1bn. However, if this injection eventually caused real GDP to

increase by £2 billion, then the multiplier would have a value of 2.0

Multiplier (k) = Change in Real GDP (Y)

Change in Injections (J)

Example of How the Multiplier Effect Works

If the government spent an extra £2 billion on the NHS this would cause salaries / wage to increase by £2 billion, therefore National Income will increase by £2 billion.

However with this extra income, workers will spend, at least part of it, in other areas of the economy.

For example, if they spent 50% of the extra income there would be another £1 billion injected into the economy. e.g. shopkeepers would earn money from increased sales.

This extra spending would cause an increase in output, therefore firms would employ more workers and pay higher salaries.

Therefore these workers will also increase their spending. This will lead to another injection into the economy, causing higher Real GDP

In other words, if you increase salaries in the NHS, it isn’t just NHS workers who benefit from higher incomes. It is also related industries and service industries who see some benefits.

AD = C + I + G + X – M

Injections can include:

Investment (I) Government Spending (G) Exports (X)

Negative Multiplier Effect

The multiplier effect can also work in reverse. If the government cut spending, some public

sector workers may lose their jobs. This will cause an initial fall in national income. However,

with higher unemployment, the unemployed workers will also spend less leading to lower

demand elsewhere in the economy.

The value of the Multiplier depends upon:

If people spend a high % of any extra income, then there will be a big multiplier effect. However if any extra money is withdrawn from the circular flow the multiplier effect will be very

small.

k = 1 = 1

1-mpc mpw

1. Marginal Propensity to Consume (mpc). This is a persons willingness to spend money, if a worker saved all his money there wouldn’t be an increase in GDP

2. Marginal Propensity to Withdraw (mpw). This is when money is withdrawn from the circular flow it includes mpt + mpm + mps

3. The Marginal Propensity to Tax (mpt) 4. The Marginal propensity to Import (mpm) 5. The Marginal Propensity to Save (mps)

The multiplier will also be effected by the amount of spare capacity if the economy is close to

full capacity an increase in injections will only cause inflation.

Multiplier Effect of a Tax Cut

A tax cut has no effect on government spending, but, it should effect Consumer spending (C) and I (investment)

For example, imagine the government cut VAT from 17.5% to 15%. This has two effects:

1. Firstly, if consumers maintain the same spending habits, they will have more disposable income left over to buy more goods.

2. Secondly, they may be encouraged to buy goods (especially expensive electrical goods) e.t.c because they are cheaper.

Therefore, in theory, a tax cut should boost consumer spending and this leads to an overall rise in AD.

This means firms will get an increase in orders and sell more goods. This increase in output, will encourage some firms to hire more workers to meet higher demand. Therefore, these workers will now have higher incomes and they will spend more. This is why there is a multiplier effect. Extra spending benefits others in the economy.

Crowding Out

Monetarists argue the fiscal multiplier will be limited by the crowding out effect. E.g. if the

government increase Aggregate Demand through higher spending or tax cuts then this increases

consumer spending. However, the rise in borrowing (and higher bond yields) leads to a decline

in private sector investment. Therefore, there is no overall increase in AD.

Keynesian View on Crowding out and Multiplier

However, in a recession, Keynesians argue that the private sector typically has a glut of non

productive savings, therefore, the crowding out effect is limited and there will be a positive

multiplier effect.

multiplier effect

An effect in economics in which an increase in spending produces an increase in national income and

consumption greater than the initial amount spent. For example, if a corporation builds a factory, it will

employ construction workers and their suppliers as well as those who work in the factory. Indirectly, the

new factory will stimulate employment in laundries, restaurants, and service industries in the factory's

vicinity.

Multiplier & Accelerator Effects

In this chapter we look at two ideas, the multiplier process and the accelerator effect, both of

which help to explain how we move from one stage of an economic cycle to another

What is the multiplier process?

An initial change in aggregate demand can have a much greater final impact on

equilibrium national income

This is known as the multiplier effect

It comes about because injections of new demand for goods and services into the

circular flow of income stimulate further rounds of spending – in other words “one

person’s spending is another’s income”

This can lead to a bigger eventual effect on output and employment

What is a simple definition of the multiplier?

It is the number of times a rise in national income exceeds the rise in injections of demand that

caused it

Examples of the multiplier effect at work

Consider a £300 million increase in capital investment – for example created when an

overseas company decides to build a new production plant in the UK

This may set off a chain reaction of increases in expenditures. Firms who produce the

capital goods and construction businesses who win contracts to build the new factory will

see an increase in their incomes and profits

If they and their employees in turn, collectively spend about 3/5 of that additional

income, then £180m will be added to the incomes of others.

At this point, total income has grown by (£300m + (0.6 x £300m).

The sum will continue to increase as the producers of the additional goods and services realize an

increase in their incomes, of which they in turn spend 60% on even more goods and services.

The increase in total income will then be (£300m + (0.6 x £300m) + (0.6 x £180m).

Each time, the extra spending and income is a fraction of the previous addition to the circular

flow.

The Multiplier and Keynesian Economics

The concept of the multiplier process became important in the 1930s when John

Maynard Keynes suggested it as a tool to help governments to maintain high levels of

employment

This “demand-management approach”, designed to help overcome a shortage of capital

investment, measured the amount of government spending needed to reach a level of

national income that would prevent unemployment.

Factors that affect the value of the multiplier effect

The higher is the propensity to consume domestically produced goods and services, the

greater is the multiplier effect. The government can influence the size of the multiplier

through changes in direct taxes. For example, a cut in the rate of income tax will increase

the amount of extra income that can be spent on further goods and services

Another factor affecting the size of the multiplier effect is the propensity to purchase

imports. If, out of extra income, people spend their money on imports, this demand is not

passed on in the form of fresh spending on domestically produced output. It leaks away

from the circular flow of income and spending, reducing the size of the multiplier.

The multiplier process also requires that there is sufficient spare capacity for extra output to be

produced.

If short-run aggregate supply is inelastic, the full multiplier effect is unlikely to occur, because

increases in AD will lead to higher prices rather than a full increase in real national output. In

contrast, when SRAS is perfectly elastic a rise in aggregate demand causes a large increase in

national output.

In short – the multiplier effect will be larger when

1. The propensity to spend extra income on domestic goods and services is high

2. The marginal rate of tax on extra income is low

3. The propensity to spend extra income rather than save is high

4. Consumer confidence is high (this affects willingness to spend gains in income)

5. Businesses in the economy have the capacity to expand production to meet increases in

demand

Time lags and the multiplier effect

It is important to remember that the multiplier effect will take time to come into full

effect

A good example is the fiscal stimulus introduced into the US economy by the Obama

government. They have set aside many billions of dollars of extra spending on

infrastructure spending but these sorts of capital projects can take years to be completed.

Delays in sourcing raw materials, components and finding sufficient skilled labour can

limit the initial impact of the spending projects.

Calculating the value of the multiplier

The formal calculation for the value of the multiplier is

Multiplier = 1 / (sum of the propensity to save + tax + import)

Therefore if there is an initial injection of demand of say £400m and

The marginal propensity to save = 0.2

The marginal rate of tax on income = 0.2

The marginal propensity to import goods and services is 0.3

Then the value of national income multiplier = (1/0.7) = 1.43

An initial change of demand of £400m might lead to a final rise in GDP of 1.43 x £400m =

£572m

If

The marginal propensity to save = 0.1

The marginal rate of tax on income = 0.2

The marginal propensity to import goods and services is 0.2

The value of the multiplier = 1/0.5 = 2 – the same initial change in aggregate demand will lead to

a bigger final change in the equilibrium level of national income.

Multiplier Effect

Multiplier effect is a macro-economic phenomenon in which an initial change in spending results

in a greater ultimate change in real GDP. The initial change is usually a change in investment but

other components of GDP such as government spending, net exports and a change in

consumption which is not caused by change in income can also have multiplier effect on the

GDP.

The ratio of ultimate change in GDP to initial change in spending is called the multiplier and it is

represented using the following formula:

Multiplier = Change in Real GDP

Initial Change in Spending

Reordering the above formula, we get,

Change in Real GDP = Multiplier × Change in Initial Spending

So if an increase of $50 billion in investment increases real GDP by a multiplier of 5, the real

GDP will increase by $250 billion [= 50×5]. In this example, the multiplier effect is positive but

it can also occur in other direction as well i.e. decrease in initial spending reducing real GDP by

multiple times of initial decrease in spending.

Multiplier effect occurs under the assumption that the economy has room to expand so that

increase in spending does not result solely in inflation.

Explanation

Since the money spent in an economy is received by others as income and assuming that an

average person is likely to change their spending in direct proportion to their income, therefore

an initial increase or decrease in spending will start a chain of increased or decreased spending

by a number of people. The ultimate change in GDP will be the total of the incremental changes

in spending of multiple people caused by the initial change in spending.

Consider the example given above where the initial change in investment is $50 billion. This

initial investment increases GDP by $50 billion is first stage. The initial investment is received in

the form of income by a number people. Provided that they consume 80% of their income and

save the rest, $40 billion [=$50×0.8] of the initial investment will be spent in second stage. The

amount spent in second stage is also received by other people as income. In third stage, $32

billion [=$40×0.8] will be spent. In forth stage, $25.6 billion [=$32×0.8] will be spent. If we

continue this process long enough and add all the amounts together or, we can simply use the

following formula to calculate the total of this convergent geometric series:

Change in Real GDP = Initial Change in Spending

1 − MPC

Change in Real GDP = $50 billion

= $250 billion 1 − 0.8

As you may have noted, the multiplier is related to percentage of total income spent by people

who directly or indirectly derive income from initial spending. This percentage is known as

marginal propensity to consume.

The Accelerator Effect

The accelerator effect is when an increase in national income results in a proportionately larger

rise in investment

Consider an industry where demand is rising at a strong pace.

Firms will respond to growing demand by expanding production and making fuller use of their

existing productive capacity. They may also choose to meet higher demand by running down

their stocks of finished products.

At some point – and if they feel that the higher level of demand will be sustained – they may

choose to increase spending on capital goods such as plant and machinery, factories and new

technology in order to increase their capacity. If this investment goes beyond what is needed

simply to replace worn out, fully depreciated machinery, then the capital stock of the business

will become larger.

In this sense, the demand for capital goods is being driven by the demand for the products that

the firm is supplying to the market. This gives rise to the accelerator effect - the principle states

that a given change in demand for consumer goods will cause a greater percentage change in

demand for capital goods.

A good example might be the surge in capital investment in wind turbines due to the super-high

level of oil and gas prices and a rising market demand for renewable energy. In this case, strong

demand created a positive accelerator effect. But this can also go into reverse e.g. during an

economic slowdown or recession. World oil prices have collapsed and many wind farm projects

have been scaled back or postponed.

Similarly the sharp fall in UK motor car production is also leading to a reverse accelerator

effect with planned investment spending subject to severe cut-backs and many jobs lost.

The Capital Output Ratio

The accelerator model works on the basis of a fixed capital to output ratio

For example if demand in a given year rises by £4 million and each extra £1 of output

requires an average of £3 of capital inputs to produce this output, then the net level of

investment required will be £12 million.

One criticism of this simple accelerator model is that the capital stock of a business can rarely be

adjusted immediately to its desired level because of ‘adjustment costs’ and ‘time lags’. The

adjustment costs include the cost of lost business due to installation of new equipment or the

financial cost of re-training workers. Firms will usually make progress towards achieving an

optimum capital stock rather than moving smoothly from one optimal size of plant and

machinery to another.

A further criticism of the basic accelerator model is that it ignores the spare capacity that a

business might have at their disposal and also their ability to outsource production to other

businesses to meet a short term rise in demand.

The accelerator principle is used to help explain business cycles. The accelerator theory suggests

that the level of net investment will be determined by the rate of change of national income. If

national income is growing at an increasing rate then net investment will also grow, but when the

rate of growth slows net investment will fall. There will then be an interaction between the

multiplier and the accelerator that may cause larger fluctuations in the trade cycle.

The accelerator effect will tend to be high when

The rate change of consumer income and spending is strongly positive

The amount of spare productive capacity for businesses is low

The available supply of investment funds is high

multiplier

A number which indicates the magnitude of a particular macroeconomics policy measure. In

other words, the multiplier attempts to quantify the additional effects of a policy beyond those

that are immediately measurable. For example, a decrease in taxation will have more of an effect

than just the value of the reduced taxes. It will lead to greater disposable income which might

cause an increase in consumption, which in turn might increase employment in industries which

enjoy greater demand and so on. So the total effect of the implemented policy equals the effect of

the policy measure, times the multiplier. This is true of most macroeconmic policy measures,

because the actual effect of the measure cannot be quantified by the effect of the measure itself.

When money is spent in an economy, this spending results in

a multiplied effect on economic output. This lesson explains

the multiplier effect and the how to use the simple spending

multiplier to calculate it.

The Multiplier Effect

In the economy, there is a circular flow of income and spending. Everything is connected.

Money that is earned flows from one person to another, and most of it gets spent again - not just

once, but many times. What this means is that small increases in spending from consumers,

investment or the government lead to much larger increases in economic output. Economists use

formulas to measure how much spending gets multiplied. To illustrate this, let's take a look at a

very simple economy, featuring these four familiar faces:

Bob, the lawn service guy, who also does landscaping when his customers are interested

Lydia, a neighbor who works on an assembly line in a car factory

Frank, who is a farmer

Davis, who recently moved into the neighborhood and works at the hardware store

Lydia's factory has a great year, and as a result, she earns an additional $1,000 of income. Lydia,

very eager to satisfy her own needs and wants, spends $800 of it on new landscaping for her

yard. Since Bob is in the landscaping business, that means Bob earns an additional $800. Since

Bob also has needs and wants, he spends $600 of that $800 at Frank's farm store. This money is

additional income to Frank the farmer, and guess what he does with it? He goes and talks to

Dave and spends most of it, let's say $500, at the hardware store. As you can see, the initial

$1,000 round of spending actually led to three more rounds of spending, with smaller amounts

each time. In this case, $1,000 of spending from Lydia led to an increase in economic output of

$1,000 + $800 + $600 + $500 = $2,900.

When money spent multiplies as it filters through the economy, economists call it the multiplier

effect. Money spent in the economy doesn't stop with the first transaction. Because people spend

most of the extra income they get, money flows through the economy one person at a time, like a

ripple effect when a rock gets thrown into the water. I'm sure you can remember a time when you

were standing next to a pond or a lake, and when you threw a rock in, you gazed at the ripple

effect that took place around the rock as it entered the water. Spending in the economy is like

this.

The question we want to answer is this: how do we measure this ripple effect? Here's a real-

world example that happens more often than you might think. Let's say that the economy is in

recession, and consumers like Lydia have stopped spending money, so economic output has gone

down.

The components of GDP

It just so happens that you are working in Congress. You're on the committee that's working on a

bill to increase government spending. Why would you want to do that? Because the economy is

in recession, and government spending is one of the components of economic growth. You know

that if consumers like Lydia have stopped their spending, that maybe some government spending

will help increase the output of the economy. It will ripple through the rest of the economy, and

maybe Lydia can get the landscaping that she desperately wants after all. What you really want

to know at this point is: how much will output increase if government spending increases by $1

billion?

At first glance, you might think that output will increase by exactly the same amount as

government spending increases, but you'd be incorrect. When the government spends money,

firms profit. When firms profit, workers take home more income, which then gets spent. Because

of this multiplier effect, output goes up by a much larger number. We can find out how much by

using what economists call the simple spending multiplier.

The MPC and the MPS

The simple spending multiplier shows us how much economic output increases with an

increase in spending. Economists ask the question this way: how much did real GDP change

when a component of aggregate demand changed?

To understand the simple spending multiplier, you also need to understand how likely people are

to spend versus save any extra income they get, because this determines how big the multiplier

effect will be. Economists call these two other concepts the marginal propensity to consume and

the marginal propensity to save.

The marginal propensity to consume is the percentage of extra income that consumers spend.

Economists call it MPC for short. So, if the MPC is 80%, that means consumers are likely to

spend (or consume) 80% of any extra income they get.

The marginal propensity to save is the percentage of extra income that consumers save.

Economists call it MPS for short. It's basically the inverse of the marginal propensity to

consume. Because we're talking about a percentage of income, both of these percentages will

always add up to 100%, or 1.0.

The easy way to think of this is to say that whatever the MPC is, subtract this amount from 1 and

you get the MPS. The MPS is 1 minus the MPC. For example, if the marginal propensity to

consume is 0.8 (which is 80%), then that means the marginal propensity to save must be 0.2 (or

20%). When the MPC is 0.85, on the other hand, then the MPS must be 0.15, et cetera.

The MPS is actually one of the components of the simple spending multiplier, which is why we

need it right now.

Formula for the Simple Spending Multiplier

The formula for the simple spending multiplier is 1 divided by the MPS.

Let's try an example or two. Assume that the marginal propensity to consume is 0.8, which

means that 80% of additional income in the economy will be spent. What we want to know is:

what is the maximum amount that real GDP could change if government expenditures increase

by $1 billion?

First, we find the marginal propensity to save, which is always 1 minus the marginal propensity

to consume. The marginal propensity to consume is 0.8. So, 1 minus the MPC is going to be 1 -

0.8, which is 0.2.

So if an increase of $50 billion in investment increases real GDP by a multiplier of 5, the real

GDP will increase by $250 billion [= 50×5]. In this example, the multiplier effect is positive but

it can also occur in other direction as well i.e. decrease in initial spending reducing real GDP by

multiple times of initial decrease in spending.

Multiplier effect occurs under the assumption that the economy has room to expand so that

increase in spending does not result solely in inflation.

The multiplier effect

Every time there is an injection of new demand into the circular flow there is likely to be a

multiplier effect. This is because an injection of extra income leads to more spending, which

creates more income, and so on. The multiplier effect refers to the increase in final income

arising from any new injection of spending.

The size of the multiplier depends upon household’s marginal decisions to spend, called the

marginal propensity to consume (mpc), or to save, called the marginal propensity to save (mps).

It is important to remember that when income is spent, this spending becomes someone else’s

income, and so on. Marginal propensities show the proportion of extra income allocated to

particular activities, such as investment spending by UK firms, saving by households, and

spending on imports from abroad. For example, if 80% of all new income in a given period of

time is spent on UK products, the marginal propensity to consume would be 80/100, which is

0.8.

The following general formula to calculate the multiplier uses marginal propensities, as follows:

1/1-mpc

Hence, if consumers spend 0.8 and save 0.2 of every £1 of extra income, the multiplier will be:

1/1-0.8

= 1/0.2

= 5

Hence, the multiplier is 5, which means that every £1 of new income generates £5 of extra

income.

The multiplier effect in an open economy

As well as calculating the multiplier in terms of how extra income gets spent, we can also

measure the multiplier in terms of how much of the extra income goes in savings, and other

withdrawals. A full ‘open’ economy has all sectors, and therefore, three withdrawals – savings,

taxation and imports.

This is 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).

By adding up all the withdrawals we get the marginal propensity to withdraw (mpw). The

multiplier can now be calculated by the following general equation:

1/1- mpw

Applying the ‘multiplier effect’

The multiplier concept can be used any situation where there is a new injection into an economy.

Examples of such situations include:

1. When the government funds building of a new motorway

2. When there is an increase in exports abroad

3. When there is a reduction in interest rates or tax rates, or when the exchange rate falls.

The downward or 'reverse' multiplier

A withdrawal of income from the circular flow will lead to a downward multiplier effect.

Therefore, whenever there is an increased withdrawal, such as a rise in savings, import spending

or taxation, there is a potential downward multiplier effect on the rest of the economy.

When an autonomous component of Aggregate Demand changes, equilibrium output (Y) will

change. The change in output will be even larger than the initial change in Aggregate Demand.

This result for the change in Y to be greater than the initial change in Aggregate Demand is

known as the multiplier effect. For example, if the marginal propensity to consume (MPC) is

0.80 and autonomous investment increases by $200, equilibrium output will ultimately change

by $1,000, not $200!

The simple output

multiplier = 1/(1-

MPC).

Calculating the Size of the Multiplier Effect

The size of the multiplier effect is given by:

where the (simple) output multiplier is defined as 1/(1-MPC). For example, with

an MPC of 0.80, the simple output multiplier is 1/(1-0.80) = 5, so the $200 initial

increase in investment ultimately increases output by 5 x $200 = $1,000.

The simple output multiplier assumes there are no proportional taxes, all

expenditures are for domestically produced goods and services, and the

price level is fixed.

Income-induced

consumption is the

key to

understanding the

output multiplier.

How and Why the Multiplier Works

Consumption is based primarily on disposable income. When Aggregate

Demand rises, output and hence income rise. The rise in income allows people

to consume more goods and services. This is called "income-induced"

consumption and it raises Aggregate Demand even more.

TABLE 1

Round

Initial Change

in Investment

Change in

Output

Change in

Consumption

Let's work through an

example of the multiplier

process. Suppose the MPC

is 0.80. A University

decides to build a new

residence hall worth $100

million. Construction

workers earn $100 million

in income, and they spend

80 percent--or $80 million-

-dining out, going to the

movies, shopping, and

buying new cars. The

increased spending of $80

million becomes income to

the owners and employees

of the restaurants, movie

theatres, shopping malls,

and car dealers. In turn,

these people spend 80

percent of the new $80

million, or $64 million, on

other goods and services.

The $64 million becomes income to others in the community, and the

process continues. Table 1 shows the impact of the multiplier through

various rounds. When all the effects are totaled up, output will increase by

$500 million because the value of the output multiplier is equal to 1/(1-

0.8) = 5. Remember that the initial increase in Aggregate Demand for the

new residence hall was just $100 million.

1 $100 $100.00 $80.00

2 0 $80.00 $64.00

3 0 $64.00 $51.20

4 0 $51.20 $40.96

5 0 $40.96 $32.77

6 0 $32.77 $26.21

7 0 $26.21 $20.97

8 0 $20.97 $16.78

9 0 $16.78 $13.42

10 to inf. 0 $67.11 $53.69

Totals $100 $500 $400.00

The Output Multiplier with Proportional Taxes

One by one, we will relax the assumptions we made in calculating the simple

output multiplier. Let us start by introducing proportional taxes. A proportional

tax is a tax that varies with the level of income. An example is the income tax. If

income is taxed at a 20 percent rate, then t = 0.20, where t is the tax rate. Tax

revenue (T) is the total revenue collected from the tax. It is computed by the

formula:

T = t × Y.

Proportional taxes

reduce the size of

the multiplier.

The formula for the output multiplier when proportional taxes are present,

is:

If MPC = 0.80, and t = 0.25, then the output multiplier

is

1/(1-0.80(1-0.25)) = 1/(1-0.6) = 1/0.4 = 2.5.

Proportional taxes reduce

the size of the multiplier

because when there is, say,

$100 of new Aggregate

Demand, an MPC of 0.8,

and a 25 percent tax rate,

output increases in the first

round by $100 but

disposable income only

goes up by DI = Y - T =

$100 - (.25 × 100) = $75.

Consumers will spend 80

percent of that $75, or $60

in the first round. Taxes

diminish induced

consumption, which in turn

diminishes the impact on

output in the next round.

Total output now changes

by only $250, not $500.

Table 2 illustrates the

impact of the tax rate on

the multiplier effect of the

$100 million investment in

the residence hall.

TABLE 2

Round

Initial Change

in Investment

Change in

Output

Change in

Consumption

1 $100 $100.00 $60.00

2 0 $60.00 $36.00

3 0 $36.00 $21.60

4 0 $21.60 $12.96

5 0 $12.96 $7.78

6 0 $7.78 $4.67

7 0 $4.67 $2.80

8 0 $2.80 $1.68

9 0 $1.68 $1.01

10 to inf. 0 $2.52 $1.51

Totals $100 $250 $150

The Output Multiplier with Imports

When domestic income rises, consumers wish to purchase more goods and

services. Some of the things they wish to consume are imports. When income

The propensity to

import tends to

lower the multiplier

effect.

rises, demand for foreign goods and services also rises. This lowers demand for

U.S. goods & services and thus dampens the multiplier effect. We define the

marginal propensity to import (MPI) as the change in imports divided by the

change in disposable income. For example, suppose the MPI = 0.05. If

disposable income (DI) rises by $100, imports will rise by $5.

Assuming no proportional taxes but including imports, the output

multiplier formula is:

With an MPC = 0.8 and MPI = 0.05,

the value of the output multiplier is

1/(1 - 0.8 + 0.05) = 1/0.25 = 4.

Like taxes, the propensity to import tends to lower the multiplier effect because

demand for domestically produced final goods and services falls.

An Interactive Example

Below are two interactive tables that compute the value of the output multiplier

and display the impact of the multiplier through ten rounds. Enter in values for

the MPC (it must be between 0 and 1), the tax rate (between 0 and 100), and

the initial change in Aggregate Demand. Then click the "Compute" button. The

"Reset" button resets all the numbers to their default values.

Output Multiplier

MPC (between 0 and 1):

Tax rate (as %):

Initial Change in AD:

Multiplier:

Rounds of the Multiplier

Round Initial Change

in AD

Change

in Y

Induced change

in Consumption

1

2

3

4

5

6

7

8

9

10

Total

A rising price level

also tends to

reduce the value of

the multiplier.

The Output Multiplier with Price Level Changes

Just for this section, we will relax the

assumption of fixed prices. The figure

titled "Multiplier with Price Level

Changes" assumes that the Aggregate

Supply curve is upward sloping instead

of perfectly horizontal. When the

Aggregate Demand curve shifts and

the Aggregate Supply curve is upward

sloping, the multiplier effect is smaller.

The economy moves from point A to

point C, instead of going to point B

when the Aggregate Supply curve is horizontal. The smaller effect results

because Aggregate Demand is partially dampened as the price level rises. With

an upward sloping Aggregate Supply curve, the impact of an increase in

Aggregate Demand goes towards higher output and prices. In the extreme case

of a perfectly vertical Aggregate Supply curve, the output multiplier is zero.

Temporary

expenditures flow

through the

economy, but they

do not have a

permanent effect

on the equilibrium

level of output.

The Multiplier Effect and a Temporary Change in Aggregate Demand

Recall that the multiplier effect is calculated by:

The dynamic impact of the multiplier depends upon whether the change in

Aggregate Demand is temporary (a one-time expenditure), or permanent (a

permanent period after period increase in Aggregate Demand). For example, if a

government repairs a road, the injection into the economy is temporary. When

the road is finished, the new government injections into the economy stop. The

expenditures on the road will flow through the economy, but they will not

continue indefinitely.

On the other hand, the construction of a new public school building or a

new jail is more permanent. The government expenditures continue even

after construction of the building is completed. New jobs for teachers,

staff, and administrators will be created and the government must continue

to pay income to these workers year after year. First, we examine the

multiplier effect when the initial injection of Aggregate Demand is

temporary.

Suppose the government spends

$100 to repair an existing road,

injecting $100 temporarily into the

economy. The multiplier effect

occurs over a period of time.

Assuming no taxes or imports and

an MPC of 0.8, an increase in

government expenditures of $100

ultimately increases output by a

total of $500, but the increase in

output will not occur all at once. As

the figure titled "AD/AS Response

to Temporary Change in AD" illustrates, initially, AD0 and AS intersect.

The one-time $100 increase in Government Expenditures in round 1 shifts

the Aggregate Demand curve to the right (AD1). After this expenditure,

Government Expenditures decline by $100 because the road repair project

is completed. The increase in income from the road improvement

increases consumption and output in round 2, but only by 0.8 × $100,or

$80. So output is actually $20 lower compared with the previous round.

The intersection of AD2 and AS gives the level of output in round 2. The

process continues in round 3, and again in round 4. Each time the

Aggregate Demand curve shifts to the left. Eventually, the Aggregate

Demand curve will exactly overlie the original AD0curve, and the

multiplier effect will be completed. A useful analogy is to think of a stone

thrown into a still lake. The initial impact makes the biggest splash and

then the impact ripples through the water in successively smaller waves.

Eventually, the water returns to its initial peaceful condition.

Because of the road repair

expenditures, equilibrium

output rises, but the impact

dampens out overtime. The

figure titled "Change in

Output from Temporary

Change in AD" shows the

change in equilibrium output in

each round. Notice that the

change in equilibrium output

asymptotically returns to zero.

Permanent

expenditures have

a lasting effect on

the equilibrium

level of output.

The Multiplier Effect and a Permanent Change in Aggregate Demand

If the government(or any private

investor) funds an on-going project

like financing a school, the impact

is much larger than that of a

temporary spending increase.

Suppose for simplicity that the

government spends $100 to

construct a new school and then

spends $100 each year to operate

the school. The government is

injecting $100 into the economy

permanently.

As the figure titled "AD/AS

Response to Permanent

Change in AD" illustrates, in

the first round, output increases

by $100 due to the initial

change in government

spending. The higher output

and, hence, higher income

induces $80 more consumption

spending (assuming an MPC of

0.8, and no imports or taxes). If the government expenditure is permanent,

total output rises in the second round by $180 ($100 of government

expenditures plus $80 for the induced consumption). In the third round,

consumption increases again by an additional $64 ($80 x 0.8), so output

increases by $100 + $80 + $64,or $224. The process continues with each

successive increase in output becoming smaller and smaller until the

incremental change in output is zero. However, the overall equilibrium

level of output in the community will be $500 (5 x $100) higher than

before the school was built and operated. The cumulative impact on the

equilibrium level of output is illustrated in the figure titled "Change in

Output from Permanent Change in AD."

Conclusion

The multiplier almost seems magical, in that the economy is getting something

for nothing. Not so. The multiplier process is the result of numerous businesses

and individuals increasing their production activities to take advantage of

potential profit opportunities.

Although the multiplier process can be a powerful force of economic

expansion or contraction, we must keep in mind that the process occurs

primarily in the short run. Imagine a city with a fully employed labor force

that builds a new high school out in the suburbs. The spending for the high

school creates multiplier effects as teachers and staff earn income and then

spend that income on other things in the community. If the teachers and

staff at the new high school, however, came from a city high school which

was closed, then the overall multiplier effect on the region is much smaller

(and may even be zero) because income in the community where the

school was closed is less. The multiplier effect has its greatest impact

when idle resources exist.

Multiplier is a pure number used to multiply a given change in investment to find

the resulting change in income

Multiplier – the multiple by which an initial change in aggregate spending will alter

total expenditure after an infinite number of spending cycles

The larger the size of the multiplier, the greater is the expected inflationary impact.

This is so, because the buildup of greater demand is dependent on the size of the

multiplier.

The value of the multiplier depends on the value of the MPC. The higher the MPC,

the higher is the value of the multiplier.

Multiplier – a term in macroeconomics denoting a change in an induced variable,

such as (GNP or money supply) per unit of change in an external variable, such as

(government spending and bank reserves)

Aggregate Demand – the total quantity of output demanded at alternative price

levels in a given time period

Consumption function – a mathematical relationship indicating the rate of desired

consumers spending at various income levels

Leakage – income not spent directly on domestic output, ex. savings, imports,

taxes

If leakages exceed injections, the economy contracts

The circular flow of income has several leaks in it. Income diverted into consumer

saving, business saving (retained earnings and depreciation), taxes or imports

reduces the value of the circular flow

Other autonomous spending injects income into the circular flow. These injections

come from investment, export sales and government spending

If injections exceed leakages, the economy expands

Investment – expenditures on new plant and equipment in a given time period, plus

changes in business inventories

Investment represents an injection into the circular flow that may offset the

leakage caused by consumer saving

Recessionary gap – the amount by which desired spending at full employment falls

short of full employment output

Recessionary gap is the amount by which the total value of goods supplied at full

employment exceeds the total value of goods demanded

Recessionary gap implies that desired saving exceeds desired investment

A recessionary gap may lead to a cutback in production and income. A reduction in

total income will in turn lead to a reduction in consumer spending. This additional

cuts in spending cause a further decrease in income, leading to additional spending

reductions and so on. This sequence of adjustments is referred to as the multiplier

process.

Recessionary gap is the origin of cyclical unemployment

Inflationary gap – the amount by which desired spending at full employment

exceeds full employment output

The existence of an inflationary gap implies that desired investment exceeds

desired saving