Economics 3070
Fall 2008
Problem Set 1
(Due Sept. 10
th
in class)
Chapter problems are from edition 2 of the textbook
1.
Ch 1, Problem 1.3
A firm produces cellular telephone service using equipment and labor.
When it uses
E
machinehours of equipment and hires
L
personhours of labor, it can provide up to
Q
units of telephone service.
The relationship between
Q
,
E
, and
L
is as follows:
EL
Q
=
.
The firm must always pay
P
E
for each machinehour of equipment it uses and
P
L
for
each personhour of labor it hires.
Suppose the production manager is told to produce
Q
= 200 units of telephone service and that she wants to choose
E
and
L
to minimize costs
while achieving that production target.
a.
What is the objective function for this problem?
The objective function is the relationship the production manager seeks to maximize or
minimize.
In this example, the production manager wants to minimize costs.
The
production manager’s costs are given by the following expression:
P
E
E
+
P
L
L
.
Thus, the objective function is: min
P
E
E
+
P
L
L
.
b.
What is the constraint?
The constraint will describe the restriction imposed on the production manager.
Since the
production manager is told to produce
Q
= 200 units of telephone service, the constraint is
200
=
EL
.
c.
Which of the variables (
Q
,
E
,
L
,
P
E
,
P
L
) are exogenous?
Which are endogenous?
Explain.
The exogenous variables are the ones the production manager takes as given when she
makes her decisions.
Since she takes the production target (
Q
= 200) as given,
Q
is
exogenous.
The prices of equipment (
P
E
) and labor (
P
L
) are also exogenous, since she
cannot control these prices.
The production manager’s only choices are the number of
machinehours of equipment (
E
) to use and the number of personhours of labor (
L
) to
hire.
Therefore,
E
and
L
are the endogenous variables.
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Economics 3070
Fall 2008
d.
Write a statement of the constrained optimization problem.
The statement of the constrained optimization problem is
(
)
L
P
E
P
L
E
L
E
+
,
min
subject to:
200
=
EL
The first line shows that the production manager wants to choose
E
and
L
to minimize
costs.
The second line describes the constraint:
the production manager must produce 200
units of telephone service.
2.
Ch 1, Problem 1.9
A major automobile manufacturer is considering how to allocate a $2 million
advertising budget between two types of television programs:
NFL football
games and PGA tour professional golf tournaments.
The table below shows the
new sports utility vehicles (SUVs) that are sold when a given amount of money is
spent on advertising during an NFL football game and a PGA tour golf event.
New SUV Sales Generated
(thousands of vehicles per year)
Total Spent (millions)
NFL Football
PGA Tour Golf
$0
0
0
$0.5
10
4
$1.0
15
6
$1.5
19
8
$2.0
20
9
The manufacturer’s goal is to allocate its $2 million advertising budget to
maximize the number of SUVs sold.
Let
F
be the amount of money devoted to
advertising on NFL football games,
G
the amount of money spent on advertising
on PGA tour golf events, and
C
(
F
,
G
) the number of new vehicles sold.
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 Fall '09
 Raisenen
 Economics, Supply And Demand, production manager, pga tour golf

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