Lecture II: Applications of Mathematical Programming in
Agricultural Economics
I.
Interregional and Spatial Economics
A.
A large section of the literature, but I only want to discuss two types:
1.
Arbitrage or regional supply and demand models.
If demand were
distributed identically across all areas of the country, but there was a
primary supply region (for example the orange juice market).
What
would the equilibrium look like?
What is the impact of profit on a
change in transportation costs?
What happens if Brazil enters the
market?
2.
Plant location models.
In the past most heavy industry was located
in the north, particularly in the area around the great lakes.
As the
population shifted south more industry shifted south.
Why?
Current
topics, the technology is being developed to condense most of the
water out of milk, reducing its shipping cost.
Will this cause the
dairies to move to Wisconsin?
If you were John Deere how do you
determine where to locate your warehouses?
B.
Leibnitz’s Rule
( )
(
)
( )
( )
( )
( )
( )
(
)
( )
( )
(
)
( )
(
)
( )
( )
,
,
,
,
B r
A r
B r
A r
V
r
f
x r dx
V
r
B r
A r
f
x r
V
r
f
B r
r
f
A r
r
dx
r
r
r
r
=
∂
∂
∂
∂
′
=
=
−
+
∂
∂
∂
∂
∫
∫
1.
In a market equilibrium
( )
( )
0
0
max
x
x
d
s
x
p
z dz
p
z dz
−
∫
∫
a.
( )
d
p
z
is the consumer’s inverse demand curve and
( )
s
p
z
is
the producer’s supply curve.
b. This amounts to maximizing the sum of consumer surplus and
producer surplus.
a.
Differentiating the sum of consumer surplus and producer
surplus yields
( )
( )
0
d
s
p
z
p
z
−
=
b.
Extending the problem
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AEB 6533–Static and Dynamic Optimization
Lecture 2
Professor Charles B. Moss
2
( )
( )
( )
(
)
(
)
(
)
(
)
1
2
1
2
1
2
1
,
,
0
0
0
1
2
1
1
1
2
1
2
2
1
2
2
max
. .
0
0
T
T
x
x
x
d
d
s
x
x
x
T
d
s
d
s
p
z dz
p
z dz
p
z dz
tx
s t
x
x
x
S
p
x
p
x
x
x
S
p
x
p
x
x
t
x
+
−
−
+
≤
∂
⇒
=
−
+
=
∂
∂
=
−
+
−
=
∂
∫
∫
∫
II.
Econometrics and Statistical Applications
A.
Historically, econometrics relied on closed form solutions made possible
by linear models of normally distributed random variables.
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 Fall '08
 Moss
 Supply And Demand, dynamic optimization, Mathematical Programming, general equilibrium analysis, Professor Charles, Professor Charles B. Moss

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