-
7/27/2019 Gravity Slides
1/19
.
Population, Output and Trade
Erzo G.J. Luttmer
University of Minnesota
Economics 4431V, January 23, 2013
1
-
7/27/2019 Gravity Slides
2/19
0 2 4 6 8 10 12 14
x 108
0
20
40
60
80
100
120
140
population
0 2500 5000 7500 10000 12500 150000
50
100
150
GDP (billions of USD)
2
-
7/27/2019 Gravity Slides
3/19
Rank-Size Plots
Observations
, = 1
Ordered,1
rank 1
2
rank 2
rank
Plot
-axis: , -axis:
usually on a logarithmic scale.
So ( ) means
observations larger than or equal to
Divided by , this gives the right empirical distribution
function.
3
-
7/27/2019 Gravity Slides
4/19
104
105
106
107
108
109
100
101
102
population
rank
101
100
101
102
103
104
100
101
102
GDP (billions of USD)
rank
4
-
7/27/2019 Gravity Slides
5/19
Lorenz Curves
Horizontal axis
= fraction of population with income up to
Vertical axis
= fraction of aggregate income earned by those with income up
to
Income distribution {}=1
=X
=1
, =
P=1 P=1
5
-
7/27/2019 Gravity Slides
6/19
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
percent of all countries
percentofwoldpopulationor
GDP
population
GDP
6
-
7/27/2019 Gravity Slides
7/19
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
90
100
population (billions)
share
ofworldGDP(%)
7
-
7/27/2019 Gravity Slides
8/19
0 1000 2000 3000 4000 5000 60000
100
200
300
400
500
600
foreign GDP (billions of USD)
exports+imp
orts(billionsofUS
D)
trade with US
North America
Western Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
8
-
7/27/2019 Gravity Slides
9/19
101
100
101
102
103
104
103
102
101
100
10
1
102
103
foreign GDP (billions of USD)
exports+im
ports(billionsofU
SD)
North AmericaWestern Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
9
-
7/27/2019 Gravity Slides
10/19
104
105
106
107
108
109
103
102
101
100
101
102
foreign population
exports+
imports(billionsof
USD)
North America
Western Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
10
-
7/27/2019 Gravity Slides
11/19
102
101
100
101
102
103
104
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
foreign GDP (billions of USD)
UStradesurplus/foreignGDP
North AmericaWestern Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
11
-
7/27/2019 Gravity Slides
12/19
A Simple World Economy
Definitions:
= value of output of country {1 }
(0 1) share of output that is tradable, in every country
=
X=1
= value of world output
= value of goods produced in country and consumed in country
Assume common budget shares:
=
X=1
= 1
12
-
7/27/2019 Gravity Slides
13/19
supply of country- output =
demand for country- output =
X=1
=
X=1
=
X=1
=
Market clearing requires = , and hence
=
In equilibrium, income shares must be budget shares.
Now
=
becomes
=
13
-
7/27/2019 Gravity Slides
14/19
Recall
=
This is symmetric, and hence
=
Bilateral trade is balanced in this simple economy.
country- imports =X
{1}\{}
= 1
X{1}\{}
=
1
or
IM
=
EX
=
1
Quadratic in
, but
tiny for most countries.
14
-
7/27/2019 Gravity Slides
15/19
Plot
(EX + IM)2
=
1
=
1
where
= ln
Write
EX + IM = 2
1
For most countries, 1 very, very close to 1.
15
-
7/27/2019 Gravity Slides
16/19
100
101
102
103
104
105
106
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
world GDP/country GDP
(exports+imports)/(2xGD
P)
North AmericaWestern Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
Hong Kong
Singapore
16
-
7/27/2019 Gravity Slides
17/19
101
100
101
102
103
104
101
100
101
102
103
104
GDP (billions of USD)
exports+imports(billionsofUSD)
North AmericaWestern Europe
South America
Asia and Oceania
Africa
Eastern Europe and FSU
Middle East and North Africa
17
-
7/27/2019 Gravity Slides
18/19
A Power Law Example
Suppose
=1
( + 1), N
Note that =
X=
X
=+1
and1
( + 1) =1
1
+ 1
Therefore
=
X=
=
X=
1( + 1)
= 1
or
ln() = ln()
18
-
7/27/2019 Gravity Slides
19/19
Note
X=
=X
=
1
+ 1=
for every N.
Income share of lower (100 )%, for any (0 100),
P=1 P=1
=P
=1 1+1P=1
1(+1)
= 0
Not so for 1
1+ where 1.
19
