GDP in an Open Economy with Government

Lecture 6

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

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Intro

• Adding government sector is to study fiscal policy

• Aggregate desired spending (AE) can be divided into autonomous spending and induced spending

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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

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Government Spending

• Government Consumption Spending– Government consumption

• (salaries, stationery, defence expenditure, etc)

– Transfer payments• Indirectly affects desired aggregate spending (as

private consumption)

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• 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

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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

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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

-1700

National income (GDP)

The budget surplus functionIncreases as GDP increases.

The slope of the surplus function is equal to the income taxRate of 0.1

The budget surplus functionIncreases as GDP increases.

The slope of the surplus function is equal to the income taxRate of 0.1

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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)

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GDP (Y) Exports (X) Imports (IM = 0.25Y) Net exports0 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

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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

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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

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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

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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

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• 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

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National incomeGDP (Y)

Desired Private

Consumption spending

(C = 100 + 0.72Y)

Desired InvestmentSpending(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 2,0003,000 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

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• 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 = 0.531804/10/23

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 + XS + (T – G) = I + (X – IM)

• That is, total government (national) saving is equal to national asset formation

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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

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Changes in Aggregate SpendingFiscal 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

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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

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• 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

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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

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