Unformatted text preview: Eco202 Equation Sheet
This study sheet includes the part of the course
labelled “The Core” in the textbook: The economy in
the short, medium and long run. In the past, this
material accounted for 5075 percent of the final
exam.
Please note that this is study sheet is just a brief
summary, and does not replace the textbook in any
way. Good luck! ↓ in  down down ↑  right/
down
(move
along
Md) up down ↓  left/ up down up spending • Increase in foreign price level
a.
P* up real exchange rate up (real
depreciation)
b.
e up increases export demand,
reduces import demand
c.
IS and NXcurve shift up Y, i
increase
d.
i up E down (appreciation) (move
along UIP) • Increase in expected future exchange rate (Ee
up, depreciation)
a.
UIPcurve shifts up/ right (E has to go
up for UIP to hold)
b.
UIP shift E up e up (real
depreciation)
c.
e up increases export demand,
reduces import demand
e.
IS and NXcurve shift up
d.
i up E down (appreciation), move
along new UIP, but not all the way
Increase in money supply
a.
LM shifts right Y increases, i
decreases
b.
i lower E up (move along UIP),
nominal and real depreciation 2. ISLM IN AN OPEN ECONOMY 1. ISLM IN A CLOSED ECONOMY • • The IS curve describes a relationship
between output and the interest rate; along
the IS curve the goods market is in
equilibrium.
The LM curve also describes a
relationship between output and interest
rate; along the LM curve the financial
market is in equilibrium. • distinguish between domestic demand and
demand for domestic goods
if demand for domestic goods > domestic
demand trade surplus a) with flexible exchange rates
•
demand in the goods market:
Yd = C(YT) + I(Y,i) + G + NX(Y,Y*,e)
• UIP: i t = it * + For the economy to be in equilibrium both
markets have to be simultaneously in
equilibrium: Ete+1 − Et
Et (b) with fixed exchange rates
•
fixed exchange rate nominal exchange
rate cannot change
•
i = i*, the domestic interest rate is fixed by
the foreign interest rate
•
money supply has to be such that LM
intersects IS at i = i*
•
no monetary policy possible A mathematical example :
Given : C = 100 + 0.6 (YT)
G = 200, T = 200, I = 100 – 10i
(M/P)d = 2Y – 200i ;
(M/P)s = 2000/4 = 500
IS: Yd = C+I+G
= 280 + 0.6Y – 10i
Yd = Y 280 – 10i = 0.4Y
Y = 700 – 25i (IS) LM: Ms = Md 2Y – 200i = 500
Y = 250 + 100i (LM) IS = LM 700 – 25i = 250 + 100i
i* = 3.6 Y* = 610
POLICY EFFECTS ON IS AND LM: The goods market gives the IS curve and the money
market the LM curve. The intersection determines the
equilibrium level of output and interest rate. IS LM Output Interest
Rate ↑ left/ down
(reduction
in
demand)  down in
taxes right/ up  up ↑ in right/ up
(increase
in
demand) spending • •
 up up Increase in money supply
a.
LM shifts right i decreases
b.
i lower E up but E can’t change
LM shifts back (MS down), i = i* • Increase in gov’t spending/ reduction in taxes:
a.
IS shifts up, moving along LM Y, i
increase
b.
i up E down but E can’t change
LM shifts right, i = i*
c.
Y increased “a lot”
move along
NX, trade balance worsened • Increase in foreign price level
a.
P* up real exchange rate up (real
depreciation)
b.
e up increases export demand,
reduces import demand
c.
IS and NXcurve shift up
d.
Rest like increase gov’t spending What happens if up ↓ • Given i* and E the UIP determines the exchange rate
E. down in
taxes What happens if e Depending on import and export demand net exports
may or may not be positive. Policy i up E down (appreciation) (move
along UIP) • in
money
in
money I. SHORT RUN • c.
left/ down Increase in gov’t spending/ reduction in taxes:
a.
Demand increases IS shifts up,
moving along LM Y, i increase
b.
i up E down (appreciation) (move
along UIP)
Increase in foreign income:
a.
Export demand increases IS and
NXcurve shift up
b.
IS shifts up, moving along LM Y, i
increase We’ve helped over 50,000 students get better grades since 1999! Need help for exams? Check out our classroom prep sessions  customized to your exact course  at www.prep101.com II. MEDIUM RUN IN A CLOSED
ECONOMY
• • The AD curve describes a relationship
between output and the price level; along the
AD curve the both goods and financial market
are in equilibrium.
The AS curve describes a relationship
between output and the price level; it is
derived from the labour market and firms’
price setting behaviour (A) DYNAMICS OF ASAD WITH FLEXIBLE depreciation and adjustment for growth in the number
of effective workers EXCHANGE RATES • Steady State
In the steady state output per worker is constant,
hence worker per capita must be constant demand for domestic goods = domestic
demand – imports + exports ∆k * = sf (k *) − (δ + n + g ) k * = 0 Y = C(YT) + I(Y,i) + G + NX(Y,Y*,e) •
•
• e – real exchange rate = price of foreign goods
in domestic goods
UIP must hold
Changes in p cause a change in the real
exchange rate NX curve shifts IS/ AD
curves shift
Medium run: Y=Ybar, prices adjust change
in real exchange rate w ww.prep101.com Key difference to closed economy:
Fall in price level causes a depreciation of the
real exchange rate (e up) increase demand for
domestic goods IS and AD shift right i.e. in the steady state output per effective worker
growth is zero, independent of the savings rate
Total output grows at rate (n+g):
Y = ANy ∆Y/Y = ∆(ANy)/(ANy) =
∆A/A + ∆N/N + ∆y/y = g + n + 0 = (g+n)
Output per worker grows at rate g:
Y/N = Ay ∆(Y/N)/ (Y/N) = ∆(Ay)/(Ay)
= ∆A/A + ∆y/y = g + 0 = g (B) DYNAMICS OF ASAD WITH FIXED EXCHANGE
note: the natural level of output (Ybar) is the
point on the AS at P = Pe RATES •
• fixed exchange rate implies i = i*
money supply/ LM curve determined by IS
and i*
changes in price level change the real
exchange rate 1:1 because the nominal
exchange rate cannot adjust What happens if
AS
Increase in
markup (1+µ)
[i.e. everything
that improves
firms market
power]
Increase
bargaining
power (z up)
[or something
else that
increases z]
Increase in
structural
change
[or something
else that
decreases z]
Increase in
money supply
Increase in
gov’t spending AD P Y up  up down up  up down • Key difference to closed economy:
Interest rate predetermined no independent
monetary policy (LM fixed by i* and IS)
Fall in price level causes a depreciation of the real
exchange rate (e up) increase demand for
domestic goods IS and AD shift right IV. THE SOLOW MODEL
•
down  down up
•
•  up up up  up up up III. MEDIUM RUN IN AN OPEN
ECONOMY
The medium run in an open economy differs from the
medium run in a closed economy only by the
aggregate demand relationship, the supply is
unchanged. As in the ISLM framework the key
difference is the distinction between demand for
domestic goods and domestic demand. •
• Aggregate production function Y =
F(K,AN)
AN – effective labour or efficiency units
Constant returns to scale, decreasing
marginal products
A grows at rate g, N grows at rate n
Output per effective worker Y/AN = y =
F(K/AN, 1) = f(k) The Golden Rule
•
Find the savings rate that maximizes
steady state consumption
•
consumption = output – savings = output –
depreciation (in steady state)
•
maximize distance between f(k) and
(δ+n+g)k
•
find k** such that f’(k**) = δ+n+g Fundamental Solow equation K t +1 = (1 − δ ) K t + sF ( K t , AN ) / AN kt +1 = (1 − δ )kt − ( g + n)kt + sf (kt )
kt +1 − kt = ∆kt = sf (kt ) − (δ + n + g ) kt
i.e. the change in per effective worker capital is equal
to savings/ investment per effective worker minus To maximize consumption the slopes of the 2
curves need to be equal
f’(k) = (δ+n+g) Our Course Booklets  free at prep sessions  are the “Perfect Study Guides.” Need help for exams? Check out our classroom prep sessions  customized to your exact course  at www.prep101.com VI. TWOPERIOD BORROWING
1. CONSUMPTION CHOICE WITHOUT INVESTMENT
1st period saving/ borrowing = (Y1– C1)
2nd period repayment = (1+ i)*(Y1– C1) w ww.prep101.com 2nd period budget: C2 = Y2 + (1+ i)*(Y1– C1) point A – initial equilibrium/ endowment
point B – optimal allocation without investment
but international borrowing (part 1) note:
current account period 1 = (Y1– C1) [=savings]
current account period 2 = i*CA1 + (Y2– C2)
[=interest payment + savings] How to solve?
2 conditions:
1.
2. C2 = Y2 + (1+ i)*(Y1– C1)
(optimality)
C1 = C2 Combine: C1 = Y2 + (1+ i)*(Y1– C1)
(1+ i)*Y1] / [2+i] (budget)
C1 = [ Y 2 + C1 = C2 , Saving/ Borrowing = (Y1– C1) = [Y1 – Y2] /
[2+i]
international borrowing makes country better off
2. CONSUMPTION CHOICE WITH INVESTMENT
• Closed economy with investment: Invest such
that consumption in both periods equal
• Marginal product of capital could be very high/
low inefficient
• If MP high borrow money this period and pay
back next period
better off, because return (MP) higher than
interest rate
• If MP low lend money rather than invest and
collect interest payments next period
better off, because return on lending (interest
rate) higher than on investing (MP) point C – outcome with only domestic investment,
marginal product of capital is higher
than
interest rate (slope production/ investment function
steeper than (1+i))
inefficient borrow money to invest
until MP = (1+i)
point D – optimal investment: marginal product =
(1+i)
point E – resulting consumption point
This economy borrows from abroad to take
advantage of domestic investment opportunities
economy better off
note:
current account period 1 = (Y1– C1 – I1)
current account period 2 = i*CA1 +
(Y2– C2)
How to solve?
Separation between in investment and consumption
decision:
1.
Find optimal investment level: MP = (1+i)
2.
Use afterinvestment income and period 1
(=Y1–I1;Y~1 in the graph) and afterinvestment income in period 2 (Y~2 in the
graph) and borrow along budget line with
slope (1+i).
i.e. use point D, rather than point A, and
repeat exercise from part1
Investment and consumption decision are
independent! Our Course Booklets  free at prep sessions  are the “Perfect Study Guides.” ...
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This note was uploaded on 04/10/2010 for the course ECO ECO202 taught by Professor Masoudanjamshoa during the Spring '10 term at University of Toronto.
 Spring '10
 MasoudAnjamshoa
 Macroeconomics

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