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Copyright © 2008 Pearson Education Canada
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Chapter 22
Adding Government and Trade to the Simple Macro Model
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In this chapter you will learn
1. how government purchases and tax revenues are related to national income.
3. how to distinguish between the marginal propensity to consume and the marginal propensity to spend.
2. how exports and imports are related to national income.
4. why the presence of government and foreign trade reduces the value of the simple multiplier.
5. how government can use fiscal policy to influence the level of national income.
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Government Purchases
Net Tax Revenues
Government purchases of goods and services (G) are part of desired aggregate expenditures
- not including transfer payments (CPP, EI, OAS, GIS, Social Assistance, subsidies, grants, etc.)
Net taxes (T) are total tax revenues net of transfer payments (CPP, EI, OAS, GIS, Social Assistance, subsidies, grants, etc.)
22.1 INTRODUCING GOVERNMENT
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The Budget Balance
The budget balance is the difference between G and T.*
- if G < T: a budget surplus
- if G > T: a budget deficit
*(ignoring debt-service payments)
We assume net taxes are given by:
T = tY
where t is the net tax rate.
Implies that all taxes are related to the level of income.
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Provincial and Municipal Governments
When measuring the overall contribution of government to desired aggregate expenditure, all levels of government must be included:
- particularly important in Canada
- combined purchases of provincial and municipal governments are larger than those of the federal government.
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Government Expenditure Function
Desired government expenditure is treated as autonomous – completely unrelated to the current level of Y
We can write G = G
Were G is determined by – what governments do! the budget process!
election cycles!
Mostly just the provision of ‘goods and services’ (general government, health, education public safety, transportation, etc.)
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Government Expenditure Function (what does it look like?)
Desired Government Expenditures
G
Actual National Income
Y
G
0
200
150
100
G’
G’’
Shift up implies a Government spending increases
Shift down implies Government spending cuts
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Government Net Tax Function
Desired Net Taxes
T
Actual National IncomeY0
200
150
100
T = tY
-150
-100
Governments set the tax rate (t) but Y determines the total taxes paid (T)
Y0
T1 = tY1
T0 = tY0
Y1
Recall Net taxes (T = Tx less transfers)MFC2007MFC2007,MFC2007,MFC2007MFC2007MFC2007
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Changes in Taxes (the tax rate t)
Desired Net Taxes
T
Actual National IncomeY
T = tY
0
200
100
T’’ = t’’Y
Net tax increases
Net tax decrease
-150
-100
T’ = t’Y
Note: t’ > t > t’’
Y0
T0’’
T0
T0’
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T - G
Pu
blic
Sa
ving
0300 600 900
Actual National Income
The slope of the public saving function is equal to the net tax rate.
Y G T = 0.1 x Y T-G150 51 15 -36300 51 30 -21525 51 52.5 1.5600 51 60 9900 51 90 39
The Public Saving Function
As national income rises, the budget surplus (public saving) increases.
Public Saving is defined as T – G
Net tax revenue which the government does not spend
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Copyright © 2005 Pearson Education Canada Inc.
Summary
1. All levels of government add directly to aggregate expenditure.
2. Governments also collect taxes and make transfer payments.
3. Government purchases and taxation, taken together, imply the public saving function, T-G.
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22.2 INTRODUCING FOREIGN TRADE
Net Exports We make two central assumptions:
2) Canada’s imports rise as Canadian GDP rises
For imports, we assume: IM = mY
where m is the marginal propensity to import.
1) Canada’s exports are autonomous with respect to Canadian GDP
The export function is simply X = X
What determines the value of is X? A number of things including FOREIGN NATIONAL INCOMES
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Export Function (what does it look like?)
Desired Exports
X
Actual National Income
Y
X
0
200
150
100
X’
X’’
Shift up implies Exports increases
Shift down implies Exports decrease
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Import function (what does it look like?)
Desired Imports
M
Actual National IncomeY0
200
150
100
M = mY
Y0
M1 = mY1
M0 = mY0
Y1
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Changes in Imports (the marginal propensity to import m)
Desired Imports
M
Actual National IncomeY
M = m Y
0
200
100
M’’ = m’’Y
Increase in imports
Decrease in imports
M’ = m’Y
Note: m’ > m > m’’
Y0
T0’’
T0
T0’
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Thus, net exports are given by:
NX = X - mY
Ceteris paribus, changes in domestic GDP lead to changes in net exports:
- as Y rises, NX falls- as Y falls, NX rises
The relationship between Y and NX is shown by the net export function.
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The NX function is drawn holding constant:
• foreign GDP
• domestic and foreign prices
• the exchange rate
72
48
24
0 300 600 900
96IM = 0.1Y
X = 72
72
48
24
0 300 600 900
-24
Y X IM = 0.1 x Y NX0 72 0 72
300 72 30 42600 72 60 12720 72 72 0900 72 90 -18
Imp
ort
s an
d E
xpor
tsN
et E
xpor
tsNX = 72 - 0.1Y
Y
Y
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net exports, (NX = X – IM)
is also referred to as the Balance of Trade
if then we have
NX = X – IM > 0 a trade surplus
NX = X – IM = 0 a trade balance
NX = X – IM < 0 a trade deficit
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1. An increase in foreign income leads to more foreign demand for Canadian goods:
- increases X and shifts NX function upward
Shifts in the Net Export Function
2. A rise in Canadian prices (holding foreign prices constant) or an appreciation of the Canadian dollar :
- decreases X
- IM function rotates up as Canadians switch toward foreign goods
NX function shifts down and gets steeper
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IM´
X
(X - IM)
X´
IM
(X - IM)´
Illustration of a rise in Canadian prices relative to foreign prices or an appreciation of the Canadian dollar.
This could be caused by:- Δ exchange rate (appreciation)-Δ price levels (increase relative to foreign prices)
Imp
ort
s an
d E
xpor
tsN
et E
xpor
ts
Actual National Income
Actual National Income
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Foreign Income - An increase in foreign income results in an increase
Canadian exports - NX function shifts up. (and the reverse)
Shifts in the Net Export Function - Summary
Relative International Prices - A rise in Canadian prices relative to foreign prices reduces Canadian exports (X shifts down). The IM function also rotates up since Canadians now spend a higher fraction of income on foreign goods. The NX (=X-IM) function shifts down and also
gets steeper. (and the reverse)
Other considerations: Barriers to trade – tariffs, quotas, regulations, etc.
Taste – trade promotion, ‘buy Canadian’Mad cow disease, lead paint on toys, etc.
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Appreciation of the Canadian dollar - A rise in the value of the Canadian dollar reduces Canadian exports (X shifts down). The IM function also rotates up since Canadians now spend a higher fraction of income on foreign goods. The NX (=X-IM) function shifts down and also gets steeper. (and the reverse)
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Recall the exchange rate is the number of Canadian $’s required to purchase one unit if foreign currency (1.06 Cdn $’s = 1 US $)If the value of the Canadian $ changes such that it requires fewer
Canadian $’s to buy one unit of foreign currency, then we say that the Canadian $ has appreciated in value. (a fall in the exchange rate)
Jan. 2002 Sep. 2007 1.60 Cdn $’s = 1 US $ 1.06 Cdn $’s = 1 US $
OR
If the value of the Canadian $ changes such that it requires more Canadian $’s to buy one unit of foreign currency, then we say that the Canadian $ has depreciated in value. (a rise in the exchange rate)
Jan 1997 Jan 2002 1.35 Cdn $’s = 1 US $ 1.60 Cdn $’s = 1 US $
A fall (rise) in the exchange rate implies an appreciation (depreciation) in the value of the Canadian $
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We can look at appreciation and depreciation from the Foreigner’s perspective
If the value of the Canadian $ changes such that it requires more foreign currency to buy one Canadian $, then we say that the Canadian $ has appreciated in value. (a fall in the exchange rate)
Jan. 2002 Sep. 2007 0.63 US $’s = 1 Cdn $ 0.94 US $’s = 1 Cdn $
OR
If the value of the Canadian $ changes such that it requires less foreign currency to buy one Canadian $, then we say that the Canadian $ has depreciated in value. (a rise in the exchange rate)
Jan 1997 Jan. 2007 0.74 US $’s = 1 Cdn $ 0.63 US $’s = 1 Cdn $
A fall (rise) in the exchange rate implies an appreciation (depreciation) in the value of the Canadian $
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22.3 EQUILIBRIUM NATIONAL INCOME
Desired Consumption and National IncomeWith taxation, YD is less than Y.
Example: If T = (0.1)Y, then YD = (0.9)Y.
C = 30 + (0.8)(0.9)Y
C = 30 + (0.8)YD
C = 30 + (0.72)Y
The MPC out of national income (0.72) is less than the MPC out of disposable income (0.8).
C = a + bYD where YD = Y - tY so that
C = a + b(Y-tY) or C = a + b(1-t)Y
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The simple consumption function with taxes is written as:
If t increase then the slope of the consumption function, b(1-t), decreases.
Y
a Slope = b(1-t’)
C
Note this will cause the slope of the AE line to decrease also.
Slope = b(1-t)
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C = a + b(1-t)Y
where t’ > t
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The AE Function – total desired expenditure on Canadian goods and services from all sources
Recall that the slope of the AE function is the marginal propensity to spend out of national income — we call this z.
AE = C + I + G + NX
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AE
Y
40o line (AE=Y)
AE = C + I + G + NX
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The slope of the AE function
IF C = a +bYD where YD = Y – tY
I = I G = G X = X and M = mY where NX = X - M
Then AE = C + I + G + NX
= a + bYD + I + G + (X - M)
= a + b(Y – tY) + I + G + (X - mY)
= a + [b(1 – t) -m]Y+ I + G + X recall b is the MPC
AE = C + I + G + NX
In this model, we get:
z = MPC(1 - t) - m
Clearly, t > 0 and m > 0 lead to a lower value of z.
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Equilibrium National Income
In words, equilibrium Y occurs where desired aggregate expenditure equals actual national income.
Whenever AE is not equal to Y, there are unintended changes in inventories and firms have an incentive to change production.
As before, output is assumed to be demand determined in this model:
equilibrium condition is Y = AE(Y)
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The addition of government and foreign trade does not change the logic of the equilibrium!
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An alternative (but equivalent) approach to determining the level of national income is based on the relationship between national saving and the accumulation of national assets. For more details, look for “The Saving-Investment Approach to Equilibrium in an Open Economy with Government” in the Additional Topics section of this book’s MyEconLab.
www.myeconlab.com
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22.4 CHANGES IN EQUILIBRIUM NATIONAL INCOME
The Multiplier with Taxes and Imports
Recall multiplier is equal to 1/(1-z)
Imports and taxes make z smaller
the simple multiplier is also smaller
z = MPC(1 - t) – m
In our complete model, the multiplier is
1 / (1- [MPC(1 - t) – m])
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Using realistic values of taxation and imports for Canada, the evidence shows that the value of the multiplier is closer to 1 than 2.
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Y1 Y0
e1
AE1e0 •
AE =Y
E0
E1
Y Y
AE
For example, suppose MPC = 0.9 , t = 0.3 and m = 0.4
Then z = 0.9 (1 - 0.3) – 0.4 = 0.23 and the multiplier is
1 / (1-z) or 1 / (1 - 0.23) = 1.30
AE
The value of z is determined by:
z = MPC(1-t) - m
z = AE / Y - slope of the AE curve
z increases as MPC increases and decreases as t and m increase. Try different values for MPC, t, m and recalculate the multiplier.How does the picture change?
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Net Exports
As with other elements of AE:
- if NX function shifts upward, equilibrium Y rises
- if NX function shifts downward, equilibrium Y falls
Exports are autonomous with respect to domestic GDP, but they depend on:
- foreign income
- domestic and foreign prices
- exchange rate
- tastes
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Fiscal Policy
Fiscal policy is the use of the government’s spending and tax policies.
Any policy that attempts to stabilize Y at or near Y* is called stabilization policy.
Fiscal policy represents an attempt on the part of the government to keep actual output as close as is possible to potential output. (lots of problems with this but lets do the theory anyway)
It is often clear in which direction fiscal policy could be adjusted, but less clear how much adjustment is necessary.
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e´1
Y1 Y0
e1
AE1
AE0
e0 •
•
AE =Y
E0
E1
•G
Y Y
AE
For example, suppose z = 0.62 ==> multiplier = 2.63.
G = -$100 million ==> Y = - $263 million.
Consider a decrease in government expenditures (G < 0).
Equilibrium national income will fall:
Y = G x simple multiplier
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AE0
Y0 Y1
AE1
•
•
E1
E0
e0
e2
AE=Y
The government may also attempt to change national income by changing the net tax rate.
- a lower t causes the AE function to become steeper
- a higher t causes the AE function to become flatter
AE
Y
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Governments can also combine an increase in government purchases with an increase in tax revenues in such a way that the budget is left unchanged. How do such balanced budget changes affect the level of national income? To see more details on this type of fiscal policy, look for “What is the Balanced Budget Multiplier?” in the Additional Topics section of this book’s MyEconLab.
www.myeconlab.com
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22.5 DEMAND-DETERMINED OUTPUT
Our simple macro model (Chapters 21 and 22) is based on three central concepts:
• equilibrium national income
• the simple multiplier
• demand-determined output
The second and third are closely connected to our assumption of a constant price level.
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e´1
Y1 Y0
e1
AE1
AE0
e0 •
•
AE =Y
E0
E1
•
AE
Y Y
AE
We say the economy is demand driven.
Recall: desired AE = C + I + G + NX
The level of desired spending (the position of the AE curve) determines the level of equilibrium national income, Y.
Any change in the AE curve (shift or change in slope) implies a different level of equilibrium Y
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2. When firms are price setters they often respond to shocks by changing output (and only later changing their price).
1. When output is below potential, firms can increase output without increasing their costs.
When is this a reasonable assumption?
In the next chapter, we allow a variable price level:- more complicated- more realistic
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