SME
Human Geography · Problem type
Which city draws more migrants
Use this for “City A has 1,000,000 people 100 km away; city B has 4,000,000 people 300 km away. Which draws more migrants?”
Chart
This is an example. Type your own values to start a new problem.
IA
=
PA
÷
(
dA (km)
)
2
IB
=
PB
÷
(
dB (km)
)
2
PA and PB are the two cities’ populations, and dA and dB how far each city lies from the migrants’ home.
SA
Share drawn to A
calculated · %
Formulas
IA
=
PA
dA
2
100
=
1,000,000
100
2
IB
=
PB
dB
2
44.4444
=
4,000,000
300
2
SA
=
100
×
IA
IA + IB
69.2308
=
100
×
100
100 + 44.4444
Assumptions
•
Gravity model: a city’s pull grows with its population and falls with the square of its distance.
•
The pull is an index: only how it compares with the other city’s pull matters.
•
The share compares only A and B, as if each migrant chose one of the two.
•
Jobs, family ties, cost and borders change real flows; the model gives a first guess.
Step-by-step
WE KNOW
PA = 1,000,000, dA = 100 km, PB = 4,000,000, dB = 300 km
FIND
pull of A (IA), pull of B (IB), share drawn to A (SA)
Step 1 · Find pull of A (IA)
Use IA = PA ÷ dA²
City A’s pull: its population over the square of its distance.
IA
=
1,000,000
100
2
IA
=
1,000,000
10,000
IA = 100
Step 2 · Find pull of B (IB)
Use IB = PB ÷ dB²
City B’s pull: its population over the square of its distance.
IB
=
4,000,000
300
2
IB
=
4,000,000
90,000
IB = 44.4444
Step 3 · Find share drawn to A (SA)
Use SA = 100 × IA ÷ (IA + IB)
A’s pull as a percent of the two pulls together.
SA
=
100
×
100
100 + 44.4444
SA
=
100
×
100
144.4444
SA
=
10,000
144.4444
SA = 69.2308%
Check
Put the numbers back in. Both sides should match.
100
=
1,000,000
100
2
✓
44.4444
=
4,000,000
300
2
✓
69.2308
=
100
×
100
100 + 44.4444
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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