SME
Human Geography · Problem type
Land rent and distance from market
Use this for “Wheat yields 4 t a hectare, sells for $200 a tonne, costs $120 a tonne to grow and $0.50 a tonne per km to haul. What rent does land 100 km out earn?”
Chart
R(100) = 120
This is an example. Type your own values to start a new problem.
R ($/ha)
=
Y (t/ha)
×
(
p ($/t)
−
c ($/t)
)
−
Y (t/ha)
×
f ($/(t·km))
×
d (km)
dₘₐₓ
Edge of farming
calculated · km
R₀
Rent at the market
worked out (not typed) · $/ha
Formulas
R
=
Y
×
(
p
−
c
)
−
Y
×
f
×
d
120 = 4 × (200 − 120) − 4 × 0.5 × 100
dₘₐₓ
=
p
−
c
f
160
=
200 − 120
0.5
R₀
=
Y
×
(
p
−
c
)
320 = 4 × (200 − 120)
Assumptions
•
Von Thünen’s isolated state: flat, even land around one market, every farmer paying the same freight rate.
•
Rent is what a hectare earns after growing and hauling costs; below 0, the crop loses money there.
•
Freight is paid per tonne per kilometre, so rent falls in a straight line and reaches 0 at dₘₐₓ.
Step-by-step
WE KNOW
d = 100 km, Y = 4 t/ha, p = 200 $/t, c = 120 $/t, f = 0.5 $/(t·km)
FIND
rent per hectare (R), edge of farming (dₘₐₓ), rent at the market (R₀)
Step 1 · Find rent per hectare (R)
Use R = Y × (p − c) − Y × f × d
Each
hectare’s
crop
earns
its
profit
at
the
market,
less
the
freight
to
haul
it
d
kilometres.
R
=
4
×
(200
−
120)
−
4
×
0.5
×
100
R
=
4
×
80
−
4
×
0.5
×
100
R
=
320
−
2
×
100
R
=
320
−
200
R
=
120
$/ha
Step 2 · Find edge of farming (dₘₐₓ)
Use dₘₐₓ = (p − c) ÷ f
Rent reaches 0 where the freight per tonne uses up the profit per tonne.
dₘₐₓ
=
200 − 120
0.5
dₘₐₓ
=
80
0.5
dₘₐₓ = 160 km
Step 3 · Find rent at the market (R₀)
Use R₀ = Y × (p − c)
At the market there is no freight, so a hectare earns its whole profit: the line’s top.
R₀
=
4
×
(200
−
120)
R₀
=
4
×
80
R₀
=
320
$/ha
Check
Put the numbers back in. Both sides should match.
120 = 4 × (200 − 120) − 4 × 0.5 × 100 ✓
160
=
200 − 120
0.5
✓
320 = 4 × (200 − 120) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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