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ECON 103 Review: Final Notes
f19] solow growth model. Use n = population growth. Which is true in steady state?
In steady state,
∆ k
k
. Since y=f ( k ), then
∆ y
y
.
∆ k
k
K
L
K
L
∆ K
K
∆ L
L
∆ K
K
∆ L
L
∆ K
K
=n
∆ y
y
Y
L
Y
L
∆ Y
Y
∆ L
L
∆ Y
Y
∆ L
L
∆ Y
Y
=n
So, this one is true
∆ K
K
∆ Y
Y
=n ;
∆ k
k
∆ y
y
f20] depreciation δ =0.02|n=0.03| y=f ( k ) =
√
k∨¿ k
¿
=?∧ y
¿
In steady state, Δ k= 0
Δ k=s∗f
k
δ +n
∗k=s √
k −
δ+ n
k= 0
s √
k=
δ +n
k
1: square at beginning:
s √k
2
=[( δ +n ) k ]
2
s
2
k
( δ +n)
2
k
( δ+n)
2
k
2
( δ+ n)
2
k
k =
s
2
( δ +n )
2
= ≫ k
¿
s
δ+ n
2
2: use k = √
k √
k
, square at end:
s √k
( δ +n) √
k
δ +n
√k √k
( δ +n) √
k
√
k =
s
δ+n
= ≫ k
¿
s
δ + n
2
Plug in numbers k = 25 :
y=f
k = 25
√
25 = ≫ y
¿
fA21] Consider an economy that is in steady state. The economy is now hit by a tsunami that destroys a
large part of the economy’s capital stock. As a result capital per worker falls (ignore the effect on
population, that is, assume no people die from tsunami). Therefore, the economy finds itself below the
steady state level of capital per worker. Assume that technology, population growth, and savings
remained constant. The subsequent decades should see:
rising consumption per worker, capita per worker and investment per worker
fA22] Say the economy is in steady state. Assume now that, because of climate change and the resulting
change in weather patterns, the depreciation rate increases. The other pa rameters, s , n , and technology
remain constant. Comparing the new steady state , I know that:
both output per worker and capital per worker have fallen
fA23] same info… same constant…Comparing the new steady state with the original st.st, I know that:
investment per worker and consumption per worker have fallen
fA24] Consider the AD/AS framework seen in lectures. Say that, because of the uncertainty created by the
sequester consumers decide to reduce their consumption in SR EQ.
both output and prices fall
fA25] same info. What happens to LR EQ?
output returns to its full-employment level and prices are lower
fA26] same info… Central Bank decides to increase the money supply M.
SR EQ: both output and price level increases while nominal interest rate decreases
LR EQ: everything goes back to the original level. Only real interest rate moves. Nominal won’t move.
Fed prints more money = make inflation (as seen in QTM)
fB1] See Midterm: seigniorage
fB3] Solow Model predicts that an economy converges to its first steady state level of income per capita.
Does this mean that in the LR all countries will have the same level of income per capita? Explain.
If depreciation, population growth, and income are the same for a LOW country and a HIGH country,
then both economies will have same k* in the LR meaning same y* = f(k*) in LR
However, if for example, s is different, then one country will have a higher st.st and higher income level
s
low
< s
high
= ≫ k
low
¿
<k
high
¿
= ≫ f (
k
low
¿
)
< f (
k
high
¿
)
= ≫ y
low
¿
< y
high
¿
Ans: FALSE. The Solow Model predicts “conditional convergence.”
You can choose any of the factors to prove it. Here, we used savings rate but you can also use fertility
rate, education, etc and graph it.
fB4] Because HIV affects many people in sub-Saharan countries, fertility in these countries have decreased
tremendously, meaning that households in these countries have much fewer children. As a result,
population growth is now much lower. Explain the long-run effects on income per capita (or per worker)
and consumption per capita (or per worker).
Draw Solow Growth Model graph, new st.st:
↑ ( δ + n) k=steeper slope
(
δ+ n
1
)
k= ≫ k
0
¿
→ k
1
¿
Show investment and depreciation. Which has bigger impact? Ex: ( δ +n) k < s∗f ( k )= ≫ n ↓
(Note: unless mentioned,
don’t change: Δ s= 0 .)
Ans:
L ↓= ≫
K
L
↑=k ↑= ≫ f ( k ↑)= y ↑= ≫ s∗f ( k ) ↑=i↑= ≫ ( 1 −s)∗f ( k ) ↑=c ↑
Similar problem: Black Plague, losing huge chunk of labor force means K↑ k↓
Graph uses same st.st =>> show only movement away from k*
Note: changes to variables on axis results in movement along a curve while other factors shifts the curve
fB6] Why is AD curve downward sloping?
fB7] Output is below its full employment level (Y
FE
=Y
LR
.
How can policy makers determine if this is due to shock to AD or AS? Does it matter for policy if it is an
AD shock or an AS shock? Explain.
Need to look at price level to determine
If P↓ ¿ P
AD
SR
AD shock
Stabilize both P and Y by shifting AD to the right
Does NOT matter for policy
If P↑ ¿ P
AS
SR
AS shock
Stabilize either P or Y but not both
DOES matter for policy
