MACROECONOMIC EQUILIBRIUM & VARIABLES; THE DETERMINATION OF EQUILIBRIUM INCOME (CONTINUEDâ€¦â€¦â€¦..):The Accelerator

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Introduction to Economics ECO401

Lesson 10.3

MACROECONOMIC EQUILIBRIUM & VARIABLES; THE DETERMINATION OF

EQUILIBRIUM INCOME (CONTINUED...........)

THE KEYNESIAN MULTIPLIER AND ACCELERATOR

The Keynesian Multiplier:

Reverting to the 450 line approach, the term [1/(1-b)] is called the Keynesian multiplier ("k")

and is the factor by which equilibrium output, income or expenditure increase in response to

an increase in AD (caused by an increase in "a", G, I or X-M). The higher is b, the bigger is the

multiplier.

Mathematical representation of Keynes multiplier is as follows:

Y = C + I + G + NX

C = a + bY

Then,

Y = a + bY + I + G + NX

Y bY = a + I + G + NX

Y = a + I + G + NX = 1 (a + I + G + NX)

1____

1b

Keynes's intuition about the multiplier was as follows:

An increase in AD caused by an injection into the circular flow, e.g. higher government

spending on wages paid to government employees, would lead to higher money wages held

by government servants. Higher wages would translate into higher consumption expenditure

on goods and services in the economy, leading to higher money incomes of sellers of goods

and services. When firms see consumers more prosperous, they are incentivised to produce

more, thus their demand for labour goes up. This triggers a second rise of income increases in

the hands of workers (who are also consumers) leading to a further multiplied effect on

consumption, production and hiring. And so on. The multiplier effect would not be infinite as

there are leakages (saving, taxes, imports) from the circular flow of incomes each time the

workers receive wages from firms. The lower the leakages and the higher the marginal

propensity to consume, the higher will be the multiplier effect.

Keynes paradox of Thrift:

The reverse multiplier effect can be illustrated in the context of Keynes's paradox of thrift,

which highlights the negative impact of higher saving in an economy in recession. As noted

earlier, Classical economists thought the solution to the problem of low investment during the

Great Depression was high real interest rates caused by low savings. If the latter could be

increased, the real interest rate would fall and investment would pick up. However, Keynes

said that such thrift (or conservative saving behaviour) would accentuate the recession. As

people save more, they will spend less. Firms will therefore produce less, and labour hiring

will, as a result, fall, leading to a decline in incomes. This decline would also happen in a

multiplied fashion, causing a huge decline in national income. The paradox lies in the fact that

that saving, while usually considered good for any one individual, can actually be harmful to

the overall economy if everyone started saving.

The Accelerator:

The accelerator is a related concept which formalizes the investment response to output or

income changes in an economy. The key observation here is that when an economy begins to

recover from a slump, investment can rise very rapidly and, in percentage terms, the rise in

investment may be several times the rise in income. Since investment is an injection into the

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circular flow of income, these changes in investment will cause multiplied changes in income

and thus heighten a boom or deepen a recession. The formula for the accelerator is α = I/(ΔY),

or (ΔK)/(ΔY), noting that I = ΔK, where I is investment and K is capital (the stock of plants,

buildings or machinery in the economy).

The reason why investment increases by much more than a change in income is as

follows:

Suppose firms anticipate national income (and hence the demand for their products) to rise by

10% p.a. over the next 5 years. In response, firms will therefore normally look to undertake an

investment (such as buying a machine) which will enable them to meet this new demand for

the entire 5 year period. It is usually neither feasible nor possible to buy a machine that has a

one year life! Thus, it is easy to see why a given annual change in output (10%) might prompt

firms with a five year horizon to make an investment of over 50%.

Reverting back to the formula, the size of the accelerator, α, depends on the marginal capital

to output ratio: (ΔK)/(ΔY). This is the cost of extra capital required to produce a Re.1 increase

in national output. So if Rs.2 billion worth of capital is required to produce Rs.1 billion worth of

output, then (ΔK)/(ΔY) is 2. It is easy to see that, other things being equal the marginal capital-

output ratio and the accelerator are essentially the same. α is likely to be greater than 1.

Interaction of accelerator and Multiplier:

It is obvious that the interaction of the accelerator and multiplier can set off a chain reaction in

the economy which can life output and income manifold. For e.g., if there is a rise in

government expenditure, this will lead to a multiplied rise in national income. But this rise in

national income will set off an accelerator effect: firms will respond to the rise in incomes (and

the resulting rise in consumer demand) by investing more. But this rise in investment will

constitute a further rise in injections and thus will lead to a second multiplies rise in income.

And so on...

The reason why such an interaction cannot raise output infinitely is because of two reasons i)

the economy runs into the full-employment constraint, i.e. there is a fixed number of workers in

the economy, and ii) output must grow at an increasing rate (something which is difficult to

sustain for very long) in order for investment to continue rising. This is because the accelerator

links investment to changes in output, not the level of output. So for e.g., if output rises in year

1 by Rs.3bn, in year 2 by Rs.2bn, and in year 3 by Rs.1bn, then with α = 2, investment will be

Rs.6bn, Rs.4bn, and Rs.2bn in years 1, 2 and 3 respectively. As can be seen, I falls even

though output is rising, leading to a reverse multiplier accelerator chain reaction to be set off

effect will be reversed. The key point to remember, again, is that investment is related to

"changes in income" not the "level of income", and therefore "changes in income" have to

increase in order for investment to increase. A mere increase in level is not important.

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END OF UNIT 10 - EXERCISES

What are the conditions for macroeconomic equilibrium in the economy.

i. Injections (governemnt spending, exports, investment) into the circular flow of

incomes must equal the withdrawals (saving, taxes, imports) from the circular flow;

ii. Aggregate demand must equal aggregate income must equal aggregate supply.

The two approaches are equivalent. Note, however, that the equilibrium of an economy, at least

in a Keynesian world, does not imply the full-employment equilibrium. It is possible for

inflationary and deflationary gaps to exist.

What are the major macroeconomic variables involved in the determination of national

income?

C, I, G, X, M, T, S, prices, exchange rate, interest rate and money supply. We focus on the first

seven in this part of the course, but will enrich our analysis with the remaining four later in the

context of the IS-LM approach to equilibrium determination and international finance

considerations.

What does the 45 degree line in expenditure-income space represent?

It represents all the points at which the economy is in equilibrium, i.e. the expenditure on

domestic goods and services is equal to the supply of domestic goods and services is equal to

the incomes distributed to factors used in the production of those goods and services

Are the following net injections, net withdrawals or neither? If there is uncertainty,

explain your assumptions.

i. Firms spend money on research.

ii. The government increases personal tax allowances.

iii. The general public deposits more money in banks.

iv. Pakistani investors earn higher dividends on overseas investments.

v. The government purchases US military aircraft.

vi. People draw on their savings to finance holiday trips abroad.

vii. People draw on their savings to finance holidays within Pakistan.

viii.The government runs a budget deficit (spends more than it receives in tax

revenues) and finances it by borrowing from the general public.

ix. The government runs a budget deficit and finances it by printing more

money.

Increase in injections (investment).

ii.

Decrease in withdrawals (taxes).

iii.

Increase in withdrawals (saving).

iv.

Fall in withdrawals (a reduction in net outflow abroad from the household sector).

Neither. The inner flow is unaffected. If, however, this were financed from higher

taxes, it would result in an increase in withdrawals.

vi. Neither. The inner flow is unaffected. The consumption of domestically produced

goods and services remains the same.

vii. Decrease in withdrawals (saving).

viii. Neither. An increase in government expenditure (or decrease in taxes, or both) is

offset by an increase in saving (i.e. people buying government securities).

ix. Net injections. An increase in government expenditure (or decrease in taxes, or

both) is not offset by changes elsewhere. Extra money is printed to finance the net

injection.

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It is possible that as people get richer they will spend a smaller and smaller fraction of

each rise in income (and save a larger fraction). Why might this be so? What effect will it

have on the shape of the consumption function?

It is likely that the rich will feel that they can afford to save a larger proportion of their income

than the poor. The consumption function will slope upwards, but get less and less steep. This

means mpc will fall as incomes rise.

What effect will the following have on the mpc:

a) a rise in the rate of income tax;

b) people anticipate that the rate of inflation is about to rise;

c) the government redistributes income from the rich to the poor?

a) The mpc will fall. Note that here we are relating consumption to gross income. For any

given gross income, a rise in taxes will cause a fall in disposable income and hence a fall

in consumption.

b) The mpc will rise as people spend a larger fraction of any rise in income, for if they wait

to consume, their incomes will be worth less in the enxt period in urchasing power terms.

c) The mpc will increase, because the poor have a higher mpc than the rich.

What would be the impact of changing the determinant variables given in the first column

(below) on consumption and saving. Must saving always fall if consumption falls?

Determinant

Consumption

Saving

Income (rise)

rise

Assets held (increase in)

rise

fall

Taxation (fall)

rise

Cost of credit (lower interest rates)

rise

fall

Expectations (that prices will rise)

rise

fall

Redistribution of income (becomes more equal)

rise

fall

Tastes and attitudes (people want to consume more)

rise

fall

The average age of durables (increases)

rise

fall

Thus there are two determinants of consumption (namely income and taxation, which will not

cause saving to rise if consumption is caused to fall.

Why, if the growth in output slows down (but is still positive), is investment likely to fall

(i.e. be negative)?

Because firms will require a smaller increase in capital. They will thus buy fewer extra machines

and other equipment: i.e. investment will fall. The underlying concept is that of Keynes's

investment accelerator which relates induced investment to changes in output rather than the

level of output.

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Give some other examples of changes in one injection or withdrawal that can affect

others.

· A rise in government expenditure on infrastructure projects may encourage firms to invest,

or, on the other hand, may replace private investment.

· A rise in taxation will reduce savings and imports as well as consumption of domestic

goods and services.

· A depreciation of the exchange rate will lead to increased exports (an injection) and

decreased imports (a withdrawal). This could encourage increased investment in the

domestic economy.

· Higher savings will mean less total consumption, including less expenditure on imports.

Keeping Keynes's paradox of thrift arguments in mind, is an increase in saving ever

desirable?

Yes.

· If there is a problem of excess demand, an increase in savings will reduce inflationary

pressures.

· If investment increases over time, an increase in savings will allow these increases to be

financed without problems of rising interest rates or inflation, problems which would have

the effect of curtailing the investment.

The present level of a country's exports is £12 billion; investment is £2 billion;

government expenditure is £4 billion; total consumer spending (including on imports) is

£36 billion; imports are £12 billion and expenditure taxes are £2 billion. The economy is

currently in equilibrium. It is estimated that an income of £50 billion is necessary to

generate full employment. The marginal propensity to save is 0.25.

a) Is there an inflationary or deflationary gap in this situation?

b) What is the size of the gap? (Don't confuse this with the difference

between Ye and Yf.)

c) What would be an appropriate government policy to close this gap?

Injections (J) = £12bn + £2bn + £4bn = £18bn

Domestic consumption (Cd) = £36bn £12bn £2bn = £22bn

∴ Expenditure on domestic goods, E = Cd + J = £18 + £22 = £40bn

Multiplier = 1/mps = 1/0.25

a) Deflationary gap. If the economy is in equilibrium, then Y = E. Thus Ye = £40bn. But full

employment is achieved at an income of £50bn. There is thus a deflationary gap.

b) £2.5bn. This is the amount that must be injected (given a multiplier of 4) in order to

increase national income by £10bn from the current £40bn to the full-employment level of

£50bn.

c) Increase government expenditure by £2.5bn.

Why does investment in construction and producer goods industries tend to fluctuate

more than investment in retailing and the service industries?

Because demand for the output of these industries (which are `investment' goods industries)

fluctuates much more as a result of the accelerator effect.

Give some examples of single shocks and continuing changes on the demand side.

Does the existence of multiplier and accelerator effects make the distinction between

single shocks and continuing effects more difficult to make on the demand side than on

the supply side?

Examples of single shocks include government expenditure on a specific project, a surge in

consumer spending in anticipation of a rise in taxes and a temporary movement in the exchange

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rate (a depreciation causing a rise in aggregate demand through increased exports and

decreased imports, and an appreciation causing a fall in aggregate demand). Examples of

continuing changes include a sustained increase in consumer or business confidence, which

builds over time, and changes in interest rates that then remain for a period of time. The

multiplier and accelerator will amplify single shocks on the demand side and the process will last

for several months. Aggregate demand will not go on and on rising, however, unless there are

continuing changes on the demand side, which then continue to be amplified by the multiplier

and accelerator. Thus the effects are somewhat less clear cut than with changes on the supply

side, but it is still possible to distinguish between single shocks on the demand side and

continuing changes (even if the single shocks do cause multiplier and accelerator effects).

Draw an injections and withdrawals diagram, with a fairly shallow W curve. Mark the

equilibrium level of national income. Now draw a second steeper W curve passing

through the same point. This second W curve would correspond to the case where the

mps is higher.

Assuming now that there has been an increase in injections, draw a second J line above the

first. Mark the new equilibrium level of national income with each of the two W curves. You can

see that national income rises less with the steeper W curve. The higher mps has a

W, J

Weconomy 2

Weconomy 1

Economies with different marginal rates of taxation

dampening effect on the multiplier. A higher tax rate has the same dampening effect as well by

reducing the size of the multiplier (by increasing the size of the term in the denominator).

Multiplier with taxes = 1/[1-{mpc(1-t)}];as t increases, (1-t) falls,, therefore 1-{.} rises, causing

the multiplier to fall.

What effects will government investment expenditure have on public-sector debt (a) in

the short run; (b) in the long run?

a) Increase. Unless financed by extra taxation, an increase in government expenditure (for

whatever purpose) will lead to an increase in public-sector debt.

b) Possibly decrease. If the investment leads to extra output and income, then the extra tax

revenue from the extra incomes and expenditure could more than offset the cost of the

investment, thereby leading to a fall in public-sector debt.

If cuts in interest rates are not successful in causing significant increases in

investment, how can they lead to economic recovery? What, in these circumstances,

determines the magnitude of the recovery?

They can lead to recovery if they cause consumers to borrow more. The increased spending

causes a multiplied rise in national income. The magnitude of the recovery depends on (a) the

amount of extra consumer spending; (b) the size of the multiplier; (c) whether there is any

subsequent increase in investment (through the accelerator effect).

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How do people's expectations influence the outcome?

People's expectations will reinforce whatever it is they expect (self-fulfilling expectations). If

firms expect a rise in government expenditure to lead to a) higher interest rates, b) a reduction in

private-sector investment and hence c) no expansion of the economy, they will reduce their

investment plans, thus bringing about the effect (i.e. economic stagnation) that they had

anticipated.

If the government increases spending by Rs.10bn and finances it totally from taxes, will

there be any expansionary impact on output?

Yes. The increase in spending is an injection of Rs.10 bn. The withdrawal, however, is less than

Rs.10bn, as saving (a withdrawal from the system falls). Why does saving fall? Because higher

taxes reduce disposable income and therefore given a fixed mps out of disposable income,

saving will fall. The concept is called balanced budget multiplier, i.e. the fact that tax-financed

spending (which has no effect on the fiscal balance) can still be expected to have a multiplied

(albeit much smaller) effect on equilibrium output and income.

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