Topics CHAPTER
Review for the Final
MACROECONOMICS
SIXTH EDITION
N. GREGORY MANKIW
PowerPoint Slides by Ron Cronovich
2007 Worth Publishers, all rights reserved
Demand and supply
D( p ) a P S ( p) b P
What is endogenous here? P and Q What are parameters here? and What is exogenous here? a and b
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Demand and supply
1 Q a 1 P b
dQ 1 da dP 1 db
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Real GDP
Real GDP is computed using base-year prices
Let pq denote vector inner product Let p0 and p1 be price vector at time 0 and time
1 respectively Let q0 and q1 be quantity vector at time 0 and time 1 respectively
Real GDP at time 1 is p0q1 Real GDP deflator at time 1 is 100* p1q1/p0q1
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Formula for computing growth rates
If real GDP after T years is p0qT then the
formula for the annual rate of real growth is
(1+g)T = p0qT/p0q0 Hence g = (p0qT/p0q0 )1/T 1 You can use this approximation when g is small g ln(1+g) = (ln(p0qT) ln(p0q0))/T
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CPI
The CPI is computed using base-year quantities
CPI at time 1 is 100* p1q0/p0q0 The chain-weighted CPI is computed by
p1 q0 100* p0 q0
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p1 q1 p0 q1
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Chapter 3
The simplest macro model Y = F(K, L) C = a + b (Y-T) I = I(r) G and T are exogenous
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Comparative statics
For example, L changes by dL Then dY = (F/ L)dL dC = bdY dI = dY dC = (1b) dY dI = (I/ r)dr dr = (I/ r)-1 (1-b) dY This is the initial effect on the real interest rate The long-run effect is determined by the aggregate
production function w = F/ L r =F/ K
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Chapter 4
The three definitions of money
Velocity and the quantity equation The Fisher equation The demand for real balances The classical dichotomy
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The quantity equation, the Fisher equation, and the demand for money
PY = MV dP/P = dM/M DY/Y since dV = 0 The Fisher equation i = dP/P + r
L(i,Y) = M/P Expected inflation can determine current prices
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Chapter 18
Cagan's model of expectations
The money multiplier process Open market operations Baumol-Tobin model of money demand
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Cagan's model and Baumol Tobin Model
p(t) = [1/(1+ )] [m(t) + p(t+1)]
Solve this model using recursive substitution
p(t) = [1/(1+ )] {m(t) + [/(1+ )]m(t+1) + [/(1+ )]2m(t+2)+...}
Y TC = i F N 2N
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Baumol-Tobin continued
iY The cost-minimizing value of N : N 2F To obtain the money demand function, plug N* into the expression for average money holdings:
*
average money holding
YF 2i
Money demand depends positively on Y and
F, and negatively on i.
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Chapter 5
Net exports
Change in net foreign assets Small open economy The real exchange rate The convention for the nominal rate is $/THB = e P/P* Purchasing power parity Absolute Relative
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Absolute PPP
Calculate consumption weights in each country.
Let these weights be the vector w and w* These weights have to add up to unity They can be different in the different countries Then P = wp and P* = w*p* Check if eP = P*
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The macro model in the open economy
Y = F(K,L)
C = a + b(Y-T) I = I(r*) G, T given NX = NX()
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Increase in labor supply
S = Y C G dS = dY - dC
dS dI = dS 0 = dNX dNX = dY b dY = (1 - b) (F/L) dL dNX= (NX/)d d = (NX/)-1 (1 - b) (F/L) dL
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Chapter 6: Flow model of unemployment
Initial state U(0) and E(0)
The system evolves: U(t+1) = (1 - f) U(t) + s E(t) E(t+1) = (1 - s) E(t) + f U(t) Long-run steady state sE = fU s(L-U) = fU U/L = s/(s+f)
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Chapters 7 and 8
growth Solow model
Y = F(K, L) y = Y/L = F(K/L, 1) = f(k) k(t+1) = f(k(t)) + (1-)k(t) Long run steady state k = f(k) + (1-)k f(k) = k
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Capital per worker is the state variable
Knowing k(t) implies that y(t) = f(k(t)) c(t) = (1 )f(k(t)) i(t) = f(k(t)) r(t) = f'(k(t)) w(t) = f(k(t)) k(t)f'(k(t))
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Labor force growth
L(t+1)=(1 + n)L(t) k(t+1) = f(k(t)) + (1 - n)k(t) Need new capital for two reasons Replace depreciated capital To keep up with new workers Steady state: f(k) =( + n)k Hence the steady-state real interest rate is
higher
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How to linearize
Define h(x) = f(x) + (1 - n)x
Then h(k) = k for the steady-state capital-labor
ratio k
Also h(x) h(k) + h'(k)(x - k) k(t+1) k = (f'(k) + 1 n)(k(t) k) This is a linear first-order difference equation
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Rule of 70
If a system grows at the percentage rate g, then
it takes 70/g periods to double.
If it grows at the rate g (this means it
shrinks), then it takes 70/g to be cut in half.
Since ln(f'(k) + 1 n) f'(k) n, this
system has half life 70/(f'(k) n)
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Exogenous technological progress
Say workers become more effect at the rate g
Thus the efficiency of a worker grows according
to E(t+1) = (1 + g) E(t)
Now define all variables in terms of effective
works: y(t) = Y(t)/E(t)L(t), k(t) = K(t)/E(t)L(t), and so on
Then k(t+1) = f(k(t)) + (1 n - g)k(t)
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Steady-state with exogenous growth
Steady state condition f(k) = ( + n + g)k
Real interest rate is higher Output per worker grows at rate g Real GDP grows at rate g + n This is the best model of economic growth, but it does not answer the question, "What causes technological progress?"
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The Golden Rule
The steady state depends upon the savings
rate, and that rate has been taken as exogenous.
Which savings rate maximizes steady state
consumption per effective worker?
This savings rate means that we are treating
current workers and all future workers in the same way, once we have achieved the steady state
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Golden Rule savings rate
The highest possible steady-state consumption
per effective worker occurs when
r = f'(k) = + n + g Notice that f(k) = ( + n + g)k and the Golden
Rule real interest rate implies that = rk/ f(k)
This means that you should save at the rate that
is equal to capital's share in the economy!
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Present-value prices
p(1) = 1 p(t)/p(t+1) = 1 + r(t+1) The present value of a stream of real income y(t)
and y(t+1)
W = p(t) y(t) + p(t+1)y(t+1)
W/p(t) = y(t) + y(t+1)/(1+r(t+1)) Present value of a nominal stream of income W = Y(t) + Y(t+1)/(1+i(t+1))
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Savings and spending decisions
U(c(t),c(t+1)) = c(t)c(t+1)
c(1) = W/2p(1) = W/2 in real terms c(2) = W/2p(2) = (W/2)*(1+r(2)), in real terms s(1) = y(1) c(1), in real terms s(2) = y(2) c(2), in real terms
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Overlapping Generations model
Generation 0 lives for only one period
Every other generation lives for two periods Preferences and endowments are given Generation 0 is given some initial money m This is a model of money as a store of value
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Equilibrium prices
Homogeneous second-order difference equation
p(t+2) + p(t+1) + p(t) = 0
Characteristic equation: 2 + + = 0 Roots 1 and 2 General solution p(t) = a(1)^t + b(2)^t
Determine the constants a and b from the initial conditions p(1) = 1 Consumption in Period 1 is equal to supply in period 1
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Main Lessons of Macroeconomics
Real versus nominal
The macro economy considers economic
phenomena in the aggregate
Dynamic economic analysis is the essence of
macroeconomic theory
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