Week 1 Intro & Facts of Economic Growth
Gross Domestic Product total income rents interests ,
profits
=
,
wages , ,
(GDP) value of all
goods & services
produced
standardized basket of traded
purchasing power /carity (PPP) & non-traded
goods (eg haircut
·
change rates differences
Echeaper
↳
market ex overstate between countries countries
in
poor
GDP of standard of
per calcita living
measure
GDP worker of
per measure
productivity
x measure
welfare/wellbeing
·
GDP Growth Growth
Exponential Yt-Yt-1 100% % "doubles
meaning every period
=
gt
=
Yt -
1
x 100
g
Linear Growth
Yt =
Yt -
1 + a
logscale- =
logyt- logyt-
Rule of 72
(doubling time
Instantaneous rowth rate
g Y
ig =
continuous version of Y
g 7
=
Yt-Yt-1 dY
" =
lim I
Xt >
-
0 Xt dt
derivative of of z"take derivatives"
z
growth rate
logs then
=
7
co3y
0 .
egz
logy)
=
0 7
take log,
log z 03
logi
=
+ .
= 3 0 .
+
075 differentiate
T
growth rate
,Production Function Y =
F (K L , , ) output perworker
·
assumes constant return to scale F(z-K ,
z .
)) =
z .
Y +
concave
4 Y/L
y
=
4k =
k/L
diminphing MP FR > 0 FIk > O factors
per worker
·
Cobb-Douglas Y =
Akd(19
-
worker Alt( Ak" f(k)
output per
= = =
=
y
=
xAk * 0
*2
Mk =
fl =
fRk =
<(x-1)k < 0
share of income MPK; K
capital
= = <
, Week 2
Capital & the Solow Growth Model
Accumulation
Assumptions competitiveomarket w MPL r MPK
= =
tech constant
population
·
Capital 1
(endogenous
·
depreciation
↳
↳ investment
Capital Accumulation Equation -K =
investment
depreciation
-
investment =
s .
Y s= constant fraction of income saved for investment
S
depreciation S K constant fraction of
capital depreciates
= .
=
in continuous time :
OK =
K = =
SY-SK
k =
k/L
logk logk-logh
=
= E -
E constant
↳ =
=> k =
Sy
-
Sk
is sf(k)-Sk
horcapital per worker change over time
=
Depreciation ,
output f(k)
investment ,
e
outputas Y SS - . . . . . . . .
-
-
-
depreciation Sk
slope
=
S
consumption
·
investment sf(k)
iTrestments
>>> <)/(
depreciation
capital per worker (k)
investment
consumption output
+ =
Gross Domestic Product total income rents interests ,
profits
=
,
wages , ,
(GDP) value of all
goods & services
produced
standardized basket of traded
purchasing power /carity (PPP) & non-traded
goods (eg haircut
·
change rates differences
Echeaper
↳
market ex overstate between countries countries
in
poor
GDP of standard of
per calcita living
measure
GDP worker of
per measure
productivity
x measure
welfare/wellbeing
·
GDP Growth Growth
Exponential Yt-Yt-1 100% % "doubles
meaning every period
=
gt
=
Yt -
1
x 100
g
Linear Growth
Yt =
Yt -
1 + a
logscale- =
logyt- logyt-
Rule of 72
(doubling time
Instantaneous rowth rate
g Y
ig =
continuous version of Y
g 7
=
Yt-Yt-1 dY
" =
lim I
Xt >
-
0 Xt dt
derivative of of z"take derivatives"
z
growth rate
logs then
=
7
co3y
0 .
egz
logy)
=
0 7
take log,
log z 03
logi
=
+ .
= 3 0 .
+
075 differentiate
T
growth rate
,Production Function Y =
F (K L , , ) output perworker
·
assumes constant return to scale F(z-K ,
z .
)) =
z .
Y +
concave
4 Y/L
y
=
4k =
k/L
diminphing MP FR > 0 FIk > O factors
per worker
·
Cobb-Douglas Y =
Akd(19
-
worker Alt( Ak" f(k)
output per
= = =
=
y
=
xAk * 0
*2
Mk =
fl =
fRk =
<(x-1)k < 0
share of income MPK; K
capital
= = <
, Week 2
Capital & the Solow Growth Model
Accumulation
Assumptions competitiveomarket w MPL r MPK
= =
tech constant
population
·
Capital 1
(endogenous
·
depreciation
↳
↳ investment
Capital Accumulation Equation -K =
investment
depreciation
-
investment =
s .
Y s= constant fraction of income saved for investment
S
depreciation S K constant fraction of
capital depreciates
= .
=
in continuous time :
OK =
K = =
SY-SK
k =
k/L
logk logk-logh
=
= E -
E constant
↳ =
=> k =
Sy
-
Sk
is sf(k)-Sk
horcapital per worker change over time
=
Depreciation ,
output f(k)
investment ,
e
outputas Y SS - . . . . . . . .
-
-
-
depreciation Sk
slope
=
S
consumption
·
investment sf(k)
iTrestments
>>> <)/(
depreciation
capital per worker (k)
investment
consumption output
+ =
