1. GDP in an Open Economy with
Government
Lecture 6
2. Outline
• Government contribute to spending in the same
way as any other component of autonomous
sending
• Taxes affect private consumption via their effect
on disposable income
• Net exports are negatively related to domestic
income
• A necessary condition for GDP to be in
equilibrium is that AE = Y
• The size of the multiplier is negatively related to
the income tax rate and the MPI
207/14/14
3. Intro
• Adding government sector is to study fiscal
policy
• Aggregate desired spending (AE) can be
divided into autonomous spending and
induced spending
307/14/14
4. Government Spending and Taxes
• Government spending and taxes affect the
equilibrium GDP in 2 important ways
– Government spending is part of autonomous
spending in our model
– In deriving disposable income, taxes must be
subtracted from national income and government
transfer payments must be added
407/14/14
5. Government Spending
• Government Consumption Spending
– Government consumption
• (salaries, stationery, defence expenditure, etc)
– Transfer payments
• Indirectly affects desired aggregate spending (as
private consumption)
507/14/14
6. • Tax Revenues
– Negative transfer payments in their effect on AE
– Tax payments reduce disposable income relative to national
income
– Transfers raise disposable income relative to national income
• It is the net effect of taxes and transfers (net taxes (T)) that
matters when calculating the effect of government policy on
AE
• Net taxes is the total tax revenues received by the government
minus total transfer payments made by the government
• Net taxes (T) are positive since transfer payments are smaller
than total taxes and personal disposable income is less than
national income
607/14/14
8. Tax and Spending functions
• For given tax rates, the government budget
surplus (public saving) increases as GDP rises
and falls as GDP falls
• Assume government spending is exogenous,
i.e. it does not vary with GDP
• We assume tax rates exogenous. The
government sets its tax rates and does not
vary them as GDP varies. This makes tax
revenues endogenous
807/14/14
9. GDP (Y) Govt Spending (G) Net taxes (T = 0.1Y) Govt Surplus (T – G)
500 170 50 -120
1,000 170 100 -70
1,750 170 175 5
2,000 170 200 30
3,000 170 300 130
4,000 170 400 230
9
T - G
-170
0
National income (GDP)
The budget surplus function
Increases as GDP increases.
The slope of the surplus
function is equal to the income tax
Rate of 0.1
The budget surplus function
Increases as GDP increases.
The slope of the surplus
function is equal to the income tax
Rate of 0.1
07/14/14
10. Net Exports
The Net Export Function
• Desired net exports are negatively related to
GDP because of the positive relationship
between desired imports and GDP (Net export
function)
1007/14/14
11. 11
GDP (Y) Exports (X) Imports (IM = 0.25Y) Net exports
0 540 0 540
1,000 540 250 190
2,160 540 540 0
3,000 540 750 -210
4,000 540 1,000 -460
5,000 540 1,250 -710
IM = 0.25Y
540
Real National income (GDP)
2,160540
0
Real National income (GDP)
X = 540 (X – IM) = 540 - 0.25Y
.
Net exports have a negative relationship with the level of GDP
0 2,000
07/14/14
12. Shifts in the Net Export Function
• The NEF is drawn on the assumption that
everything that affects NX, except domestic
GDP, remains constant
• A change in any of these factors will affect the
amount of NX that will occur at each level of
GDP and hence will shift the NEF
– Foreign GDP
– Relative international price levels
• Caused by inflation rates and the exchange rate
1207/14/14
13. Foreign GDP
• Other things being equal, an increase in
foreign GDP will lead to an increase in the
quantity of domestic-produced goods
demanded by foreign countries
– foreign GDP net export function
– Leads to parallel shift in NX
1307/14/14
14. Relative International Prices
• Domestic prices rise relative to foreign prices
either
– if domestic inflation rate exceeds the rate in
other major trading countries (with exchange
rates fixed) or
– if the cedi appreciates (with price levels
constant).
• This discourages exports and encourages
imports, causing the NEF to shift downwards
• And vice versa
1407/14/14
15. Equilibrium GDP
• Our theory of GDP requires that we relate each of the
components of aggregate spending to national income
• Personal income taxes cause personal disposable
income to differ from national income (by the
proportion of income taxation net of transfers)
• We assume disposable income is always 90 percent of
national income
• The marginal response of consumption to changes in
NI (∆C/∆Y) is equal to the MPC multiplied by the
fraction of NI (GDP) that becomes personal disposable
income (∆Yd/∆Y)
C = 100 + 0.72Yd
1507/14/14
16. • The aggregate spending function
AE = C + I + G + NX
• Equilibrium GDP is determined where desired
aggregate spending (private consumption,
investment, government consumption, and
net exports) equals national output
1607/14/14
17. 17
National
income
GDP (Y)
Desired
Private
Consumption
spending
(C = 100 + 0.72Y)
Desired
Investment
Spending
(I = 250)
Desired
Government
Spending
(G = 170)
Desired
Net exports
(NX = 540 + 0.25Y)
Desired aggregate
Spending
(AE = C + I + G + (X – M)
0 100 250 170 540 1,060
100 172 250 170 515 1,107
500 460 250 170 315 1,195
1,000 820 250 170 290 1,530
2,000 1,540 250 170 40 2,000
3,000 2,260 250 170 -210 2,470
4,000 2,980 250 170 -460 2,940
5,000 3,700 250 170 -710 3,410
07/14/14
18. • What is the marginal propensity not to spend
on national output or domestic output (c)?
0.47
• Marginal propensity not to spend (1 – c)?
1 – 0.47 = 0.53
1807/14/14
19. Injections and Leakages
• An equivalent equilibrium condition to AE = Y
for the determination of equilibrium GDP is
that injections (investment + government
spending + exports) must equal leakages
(saving + taxes + imports)
S + T + IM = I + G + X
S + (T – G) = I + (X – IM)
• That is, total government (national) saving is
equal to national asset formation
1907/14/14
20. Multiplier
• Marginal propensity to import is 0.25
• Tax rate is 0.1
• Marginal propensity to spend is 0.47
– 10 percent of GHC1 increase in autonomous spending
goes to taxes, leaving 90p of disposable income. With
a MPC of 0.8, 72p is spent. Of this 25p is spent on
imports, leaving a total of 47p to be spent on
domestically produced consumption goods
– Thus (1 – c) is 0.53, and the simple multiplier is 1/
(0.53) = 1.89
2007/14/14
21. Changes in Aggregate Spending
Fiscal policy
• Changes in Government Spending
– A change in government spending, in this model,
changes the equilibrium level of GDP by the size of the
spending change times the simple multiplier
2107/14/14
22. Fiscal Policy
• Changes in Tax Rates
– If tax rates change, the difference between disposable
income and national income changes and as a result,
the relationship between desired consumption
spending and national income also changes
– If government increases income tax rate, it collects
less out of every cedi of national income so
disposable income rises for every level of national
income
– This results in a non-parallel upward shift of the AE
line (i.e. an increase in the slope), hence a rise in
equilibrium GDP
– The lower the income tax rate, the higher is the
simple multiplier
2207/14/14
23. • Changes that would alter the slope of the AE
line are
– A shift in the MPC, a shift in the rate of income
tax, and a shift in the propensity to import
– A fall in MPSave, income tax rate, and propensity
to import will al make the AE line steeper and
increase the multiplier
– A rise in any of these 3 has the opposite effect
2307/14/14
24. Net exports and equilibrium GDP
– As with other elements of desired aggregate
spending, if net export function shifts upward,
equilibrium GDP will rise
– If net export function shifts downward,
equilibrium GDP will fall
2407/14/14
