UNCWilmington
ECN 321
Cameron School of Business
Dr. Chris Dumas
Dept. of Economics and Finance
Deriving an OwnPrice Demand Curve
for a Linear Programming Model of Consumer Choice
Recall from your Principles of Microeconomics course that an
OwnPrice Demand
Curve
is the relationship between the per unit price of a good/service/activity and the
quantity of that same good/service/activity purchased by a consumer. In this course, we
have been studying consumer choice problems in product markets using the method of
linear programming. In linear programming problems of consumer choice that feature a
budget (or income) constraint, we can derive the OwnPrice Demand Curve of the
consumer for each good/service/activity that appears in the budget constraint. To derive
the OwnPrice Demand Curve, we perform a
Sensitivity Analysis
on the results of the
linear programming problem. Recall that a Sensitivity Analysis is an investigation of the
response of a model variable to a change in the value of a model parameter. The
per unit
price
of a good/service/activity appearing in the budget constraint is a model parameter,
and the
quantity
of the good/service/activity chosen by the consumer is a model variable.
The OwnPrice Demand Curve is the relationship between per unit price and quantity
chosen. Thus, we can find a consumer's OwnPrice Demand Curve by performing a
Sensitivity Analysis on the results of a linear programming model of consumer choice.
Because the OwnPrice Demand Curve is a result that is derived from a model, the Own
Price Demand Curve is a theorem (recall that a theorem is defined as any result that is
derived from a model).
Example Problem
In this problem, our goal is to find the graph of a consumer's OwnPrice Demand Curve
for product X. Recall that an OwnPrice Demand Curve for product X has the price of X,
which we will denote P
X
, on the vertical axis and X itself on the horizontal axis. So, we
are trying to find several (X, P
X
) points that we can graph to get a picture of the Own
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 Fall '08
 Dumas
 Microeconomics, Linear Programming, Optimization, Supply And Demand, brownies, Buffy, ownprice demand curve

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