1
I.
Basic Microeconomic Problem
A. The Microeconomic Problem
1. The typical definition of economics is the study of the allocation of scarce
resources to satisfy unlimited and competing human wants and desires.
Within this basic definition, we see the elements of a mathematical
programming model:
a. An objective function, or a measure of human wants and desires
which we will attempt to maximize.
b. Constraints or limits to simply giving humans all that they could
possibly want.
c. Implied in the definition is also the concept that we have choice
variables or instruments within our control to effect this
maxmization.
2. Within the consumer’s problem we define those elements:
Max
U x
s t x p Y
( )
. . '
≤
a. In this problem, the objective function is the consumer’s utility, the
constraint is income, and the choice variables are levels of different
commodities consumed.
b. How do we determine the optimum for this problem?
3. Similarly, the producer’s problem becomes
Max
y p
w x
s t y
F x
'
'
. .
( )

=
a. As in the consumer’s problem, we have an objective function which
is profit, constraints which is the production function, and choice
variables which are the levels of inputs and outputs.
b. Again, how do we determine the optimum in theory and in practice.
Moss, Charles B. “Applied Optimization in Agriculture.” In
Handbook of Applied
Optimization
edited by Panos Pardolous and Mauricio G. C. Resende, pp. 957–66.
New York: Oxford Press, 2002.
II. Agricultural Optimization Problems
A.
Food and Diet Problems
1.
The food and diet research can be characterized by two major focuses:
a. Least cost combination of foods to meet dietary needs.
Stigler’s
“Cost of subsistence”.
b. Least cost feed ration studies.
2. The basic application would involve minimizing the cost of a diet subject to
some nutritional constraint:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentAEB 6533–Static and Dynamic Optimization
Professor Charles B. Moss
2
min
..
x
cx
s
t A
xb
′
≥
2.
More advanced formulations of the diet problem have been developed in
the guise of the household production model.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Moss
 Operations Research, Optimization, Charles B. Moss, Professor Charles B., Dynamic Optimization Professor, Optimization Professor Charles

Click to edit the document details