Economics 3921 International Finance
Review of the First Year Income/Expenditure Model.
You have the following information about an economy
C=100+0.8*Y d
I = 130
Consumption Expenditure Function
Investment Expenditure
G = 200
X = 100
Government Expenditure
Exports
IM = 100+0.2*Y d
Y d
= Y-T
T = 0.05*Y
Imports
Disposable Income (GDP – Taxes)
Tax Function
1, Translate each of the seven equations into every day language.
C = 100 +0.8*Yd - households spend $0.80 of every dollar of after tax income; they save $0.20 of every dollar of after tax income. If income is 0 households spend 100 and save -100.
I = 130 firms spend 130 on newly produced capital goods and services
G = 200 Governments spend 200 on newly produced goods and services
T = 0.05*Y the government tax system applied a tax rate of 5% to total income.
X = 100 the rest of the world buys 100 of newly produced goods and services
Households, firms, and governments may be buying goods and services produced in the rest of the world. As a consequence we must subtract what they are buying from the rest of the world to determine how much they buying from domestic firms.
IM – 100 + 0.2Yd Households spend $0.20 of after tax income on goods and services produced in other countries and households, firms, and governments spend 100 on goods and services produced in the rest of the world.
2. Find the equilibrium level of GDP.
Equilibrium occurs when total spending (AE) is exactly equal to what the domestic firms are producing(Y).
AE = C + I + G + X-IM
Step 1 Express AE as function of Y (not Yd) Yd = Y – T = Y – 0.05Y = 0.95Y
C = 100 + 0.8*Yd = 100 + 0.8*0.95Y = 100 + 0.76*Y
IM = 100 + 0.2*Yd = 100 + 0.2*0.95Y = 100 + 0.19*Y
C – IM = 0 + 0.57 *Y = 0.57*Y
AE = 0.57*Y + 430
Find equilibrium (where Y = AE)
Y = 430 + 0.57*Y
Y – 0.57*Y = 430 + 0.57*Y – 0.57*Y
0.43*Y = 430
Y = 430/0.43 = 1000
3. What is the government’s budgetary position (G-T)?
T = 0.05*1000 = 50
G = 200
G – T = 200 – 50 = 150 (government deficit)
4. What is the current account (X-IM) position (surplus or deficit)?
X = 100
IM = 100 + 0.19*Y = 290 (current account deficit of 190
5. How much saving is there? Is it sufficient to finance domestic private investment?(Find I-S)
S = Y – C – T = 1000 – 100 – 0.76*(1000) – 0.05*1000 (or S = -100 +0.19*Y)
S = 90
I = 130
Firms can borrow 90 of the 130 they need to finance investment from domestic households. They need to borrow 40 from other sources.
The governments need to borrow 150 so they can not provide the needed savings.
But the rest of the world can provided all the needed fund (190)
6. Now suppose that Government Expenditure rises by 100. How is the government spending financed? (there are three sources of finance – increased taxes, increased borrowing from domestic household, increased borrowing from the rest of the world).
Note the new equilibrium occurs when Y = AE = 530 + 0.57*Y or when Y = 530/0.43 = 1232.55
T = 0.05*1232.55 = 61.627 (11.627 of the 100 is financed by increased taxes)
S = S = -100 +0.19*Y = -100 +234.18 = 134.18(44.18 in extra saving)
IM (imports also rise by 44.18 = 0.19*232.55) which translates into lending from the rest of the world.
The 100 increase in government spending is paid for by 11.627 of newly generated taxes; by
$44.18 of lending by domestic households and $44.18 of lending by foreigners .
Note 11.627 + 44.18 + 44.18 = 100
7. Instead of assuming Government Expenditure increased assume that autonomous imports increase by 100(IM = 200+0.2*Yd). How are the increased imports financed? Is the government deficit affected?
AE = 330 + 0.57*Y (assuming the original AE held before the increase in imports.
New Equilibrium Y = 330/.43 =767.44
New S = 45.81; I – S = 84.19 needs to be borrowed by firms from either government or the rest of the world.
New T = 0.05*767.44 = 38.372; G – T = 161.62 so the government can not lend but must borrow.
New IM =200 + 0.19*Y = 200 + 145.81 = 345.81 and X – IM = -245.81
245.81 must be borrowed from the rest of the world to pay for imports. Firms borrow 84.19 and governments borrow 161.62 for a total of 245.81.
8. Finally, assume that the all information about the economy is as originally as provided except that I rises by 100 to 230. How does this change the way activities are financed?
When I increases equilibrium Y increases (to 1232.55). When Y increases taxes increase to 61.62 so the governments have to borrow less (11.62 less) . When Y increases S increases by 44.18.
When Y increases imports increase by 44.18 which is additional foreign lending Thus 100 increase in I is financed because governments borrow less household and the rest of the world lend more.
Suppose we are looking at a two country world. The two countries are identical but interdependent. Interdependency arises because of international trade. One country’s imports are the other countries exports. Thus the export function for country 1 is X
1
= 100+0.2*Y d2
.
Explain in words. Try to solve for equilibrium in the two country world.
The exports of country 1 are the imports of country 2 and the exports of country 2 are the imports of country 1
For country 1 AE = 0.57*Y
1
+ 130 +200 + 100 + 0.19*Y
2
= 230 + 0.57 Y
1
+ 0.19*Y
2
If country 1 is in equilibrium
Y
1
= AE
1
= 430 + 0.57 Y
1
+ 0.19*Y
2
Or subtracting 0.57*Y
1
from both sides of the equation
0.43* Y
1
= 430 + 0.19*Y
2
Dividing both sides by 0.43 yields
Y
1
= 430/0.43 + 0.19/0.43*Y
2
= 1000 + 0.4418*Y2
We can not find Y
1
without knowing Y
2
; the two countries are interdependent.
But we can repeat the steps above for country 2 and given that country 1 and country 2 are identical we have
Y
2
= 430/0.43 + 0.19/0.43*Y
1
= 1000 + 0.4418*Y
1
Assuming country 2 is in equilibrium we can find the equilibrium in country 1 by using the equilibrium condition for country 2 in the equilibrium condition for country 1; i.e
Y
1
= 1000 + 0.4418*Y
2
= 1000 + 0.4418*(1000 + 0.4418*Y
1
) = 1441.8+ 0.195* Y
1
So Y
1
= 1441.8/0.805 = 1791.05
Substitute this into the equilibrium condition of country 2
Y
2
= 1000 + 0.4418*Y
1
= 1000 + 0.4418*1791.05 = 1791.2
