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A Basic Model of the Determination
of GDP in the Short Term
Chapter 16
LIPSEY & CHRYSTAL
ECONOMICS 12e
Learning Outcomes
• The macroeconomic theory that we now study explains
the deviation of actual from potential GDP, that is the GDP
gap.
• The determination of GDP in the short run depends on the
behaviour of key categories of aggregate spending:
consumption, investment, government spending, and net
exports.
Learning Outcomes
• Consumption spending depends on disposable income
and wealth.
• Investment spending depends on real interest rates and
business confidence.
• A necessary condition for GDP to be in equilibrium is that
desired domestic spending equals actual output.
A BASIC MODEL OF THE DETERMINATION OF GDP
What Determines Aggregate Expenditure
• Desired aggregate expenditure includes desired
consumption, desired investment, and desired government
expenditures, plus desired net exports.
• It is the amount that economic agents want to spend on
purchasing the national product.
• In this chapter we consider only consumption and
investment.
A BASIC MODEL OF THE DETERMINATION OF GDP
What Determines Aggregate Expenditure
• A change in personal disposable income leads to a change
in private consumption and saving.
• The responsiveness of these changes is measured by the
marginal propensity to consume [MPC] and the marginal
propensity to save [MPS], which are both positive and sum
to one.
• This indicates that, by definition, all disposable income is
either spent on consumption or saved.
A BASIC MODEL OF THE DETERMINATION OF GDP
• A change in wealth tends to cause a change in the
allocation of disposable income between consumption
and saving. The change in consumption is positively
related to the change in wealth, while the change in
saving is negatively related to this change.
A BASIC MODEL OF THE DETERMINATION OF GDP
• Investment depends, among other things, on real interest
rates and business confidence. In our simple theory
investment is treated as autonomous, or exogenous, as
is the constant term in the consumption function, called
autonomous consumption.
• The part of consumption that responds to changes in
income is called induced spending.
A BASIC MODEL OF THE DETERMINATION OF GDP
Equilibrium GDP
• At the equilibrium level of GDP, purchasers wish to buy
exactly the amount of national output that is being
produced.
• At GDP above equilibrium, desired expenditure falls short
of national output, and output will sooner or later be
curtailed.
A BASIC MODEL OF THE DETERMINATION OF GDP
Equilibrium GDP
• At GDP below equilibrium, desired expenditure exceeds
national output, and output will sooner or later be
increased.
• In a closed economy with no government, desired saving
equals desired investment at equilibrium GDP.
A BASIC MODEL OF THE DETERMINATION OF GDP
• Equilibrium GDP is represented graphically by
the point at which the aggregate expenditure
curve cuts the 450 line, that is, where total
desired expenditure equals total output.
• This is the same level of GDP at which the
saving function intersects the investment
function.
A BASIC MODEL OF THE DETERMINATION OF GDP
Changes in GDP
• With a constant price level, equilibrium GDP is
increased by a rise in the desired consumption
or investment expenditure that is associated with
each level of national income.
• Equilibrium GDP is decreased by a fall in
desired spending.
A BASIC MODEL OF THE DETERMINATION OF GDP
Changes in GDP
• The magnitude of the effect on GDP of shifts in
autonomous expenditure is given by the
multiplier.
• It is defined as K = Y/A, where A is the
change in autonomous spending and Y the
resulting increase in GDP.
A BASIC MODEL OF THE DETERMINATION OF GDP
• The simple multiplier is the multiplier when the
price level is constant.
• It is equal to 1/[1 - z], where z is the marginal
propensity to spend out of national income.
• Thus the larger z is, the larger is the multiplier. It
is a basic prediction of macroeconomics that the
simple multiplier, relating £1 worth of increased
spending on domestic output to the resulting
increase in GDP, is greater than unity.
UK real GDP growth, 1886-2014
Terminology of Business Cycles
Costumers’ spending and personal
disposable income UK 1948-2008
Calculation of average and marginal
propensity to consume
The Consumption and Saving Functions
450
2000
500
S
C
1500
250
0
-100
1000
500
-500
500
450
1000
1500
2000
Real Disposable Income
500
1000
1500
2000
Real Disposable Income
(i). Consumption Function [£ million]
(ii). Saving Function [£ million]
Consumption and savings schedules
(£millions)
The consumption and saving functions
•
•
•
•
Both consumption and saving rise as disposable income rises.
Line C relates desired consumption to disposable income.
Its slope is the marginal propensity to consume (MPC).
Saving is all disposable income that is not spent on
consumption.
• The relationship between disposable income and desired
saving is shown by line S.
The consumption and saving functions
• Its slope is the marginal propensity to save (MPS).
• Any given amount of disposable income must be accounted for
by consumption plus saving.
• Consumption and saving schedules (Table) show the
numerical values of desired consumption and saving at each
level of income, and correspond to the C and S lines in the
figure.
The aggregate spending function in a closed
economy with no government (£million)
An Aggregate Expenditure Function
5000
AE
4000
3000
2000
1000
350
1000
2000
3000
4000
5000
Real National Income Function [GDP] [£m]
An aggregate expenditure function
• The aggregate expenditure function relates total desired
expenditure to national income.
• Here desired expenditure is the sum of desired
consumption and desired investment.
• It is assumed that desired investment is £250 million
while consumption is £100 million plus 0.8 times income.
• So when income is zero there is autonomous
expenditure of £350 million.
• The marginal propensity to spend is 0.8.
The determination of equilibrium
GDP (£million)
Equilibrium GDP
[ii]. Saving Function[S = I]
[i]. An Aggregate Expenditure Function[AE = Y]
500
3000
S
450
[AE = Y]
I
250
E0
Desired saving (£m)
2000
1000
350
0
450
1000
Y0
2000
3000
Real National Income [GDP] [£m]
0
-100
-500
1000
Y0
2000
3000
Real National Income [GDP] [£m]
Equilibrium GDP
• GDP is in equilibrium where aggregate desired
expenditure (AE) equals national output.
• In the figure equilibrium GDP occurs at E0 where AE
intersects the 450 line.
• If GDP is below Y0 desired AE will exceed national
output and production will rise.
Equilibrium GDP
• If GDP is above Y0 desired AE will be less than national
output and production will fall.
• When saving is the only withdrawal and investment is
the only injection, the equilibrium level of GDP is also
that where saving equals investment.
The Simple Multiplier
AE = Y
450
0
Real National Income [GDP]
The Simple Multiplier
AE = Y
AE0
e0
E0
450
0
Y0
Real National Income [GDP]
The Simple Multiplier
AE = Y
E1
AE1
e1
a
e’1
AE0
A
e0
E0
Y
450
0
Y0
Y1
Real National Income [GDP]
The simple multiplier
• An increase in the autonomous component of desired
aggregate expenditure increases equilibrium GDP by
a multiple of the initial increase.
• The initial equilibrium is at E0, where AE0 intersects
the 450 line. Here desired expenditure equals
national output.
The simple multiplier
• An increase in autonomous expenditure of A then
shifts the AE function up to AE1.
• Because desired spending is now greater that output,
production and GDP will rise.
• Equilibrium occurs when GDP rises to Y1.
• Here desired expenditure e1 equals output Y1.
The multiplier – A numerical example
The multiplier – A numerical example
A numerical example of the multiplier
• Assuming that the marginal propensity to spend out
of national income is 0.8 and there is an autonomous
expenditure increase of £100m.
• National income and output initially rises by £100m.
A numerical example of the multiplier
• Those receiving £100m in income then spend £80m.
• This £80m of income leads to further spending of
£64m.
• This £64m of income lead to a further increase in
spending of £51.2m.
• If we carry on this process it will converge to an extra
income and output totalling £500m.
• The multiplier in this case is 5.
UK Household savings as a % of
GDP (1955Q1 to 2009Q3)
Total UK Business Investment
(1955Q1 to 2009Q1)
A BASIC MODEL OF THE DETERMINATION OF GDP
The macroeconomic problem: inflation and unemployment
• Models of the short-term determination of GDP explain why
actual GDP deviates from potential GDP.
• Actual GDP above potential can be associated with inflation,
while actual GDP below potential is associated with
unemployment and lost output.
A BASIC MODEL OF THE DETERMINATION OF GDP
Key Assumptions
• For simplicity we aggregate all industrial sectors into one, so
the economy produces only one type of output good.
• We explain GDP determination through the major expenditure
categories: private consumption, investment, government
consumption, and net exports.