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Lab 11
Agricultural and Resource Economics
(ARE 201)
This lab assignment is worth 100 points. Unless instructed differently, you are to
complete the assignment and have it to me by this Thursday at 5:00 p.m. Late lab
assignments will not be accepted without prior arrangement with me. Please let me know
if you need any help with this assignment. Good Luck!
Purpose of Lab:
This assignment will teach you how use marginal analysis in making business and
personal decisions and review the fundamentals of graphing.
Assignments:
Using Marginal Analysis in Making Business and Personal Decisions. Marginal
analysis is one of the most important skills that you will learn in this course. It can help
you make many different types of decisions. For example, a business manager can use
marginal analysis to determine if the business should hire another person. Among other
things, you could use marginal analysis to determine the number of hours that you should
spend studying in this course.
Marginal analysis is defined as the analysis of the benefits and costs of one additional
unit of a good or service or one additional unit of input. It can be broken into four steps.
In the first step of marginal analysis, you identify the control variable. The goal of
marginal analysis is to determine if the control variable should be increased by one unit.
For example, a business manager may want to know if the business should hire one more
person (i.e., input). In this case, the control variable is the number of workers.
In the second step of marginal analysis, you determine the benefit from increasing the
control variable by one unit. The benefit from one additional unit of the control variable
is referred to as the marginal benefit. For example, the marginal benefit to a business
from hiring one more person may be $3,000 in additional sales per month.
In the third step of marginal analysis, you determine the cost of increasing the control
variable by one unit. The cost of one additional unit of the control variable is referred to
as the marginal cost. For example, the marginal cost to a business of hiring one more
person may be $2,500 per month.
2
In the fourth step of marginal analysis, you decide if the control variable should be
increased by one unit or not. You should increase the control variable by one unit if the
marginal benefit of this action is greater than or equal to its marginal cost. If the
marginal benefit of one more unit of the control variable is less than the marginal cost of
this action, you should not increase the control variable by one unit. For example, a
business should hire one more person if the marginal benefit of this action is $3,000 per
month and the marginal cost is $2,500 per month.
Please answer the questions below using the following information. You may want
to refer to your notebook, lecture notes, and textbook.
Let's suppose that you are the manager of a company that sells agricultural chemicals.
You would like to determine if your business should hire one more salesperson. You
currently employ 3 people. You pay your employees $23,000 per year, which is the rate
at which you would hire another person.
Fill in the blanks in the table below.
Number of
Employees
Total Annual
Salary
Total Sales
0
Marginal Cost
of this Unit of
Labor
0
0
Marginal
Benefit of this
Unit of Labor
0
0
1
23,000
23,000
$33,000
33,000
2
46,000
23,000
$64,000
31,000
3
69,000
23,000
$92,000
28,000
4
92,000
23,000
$116,000
24,000
5
115,000
23,000
$135,000
19,000
Should you hire a fourth person? Explain your answer.
Yes! Marginal benefit = $24,000 > Marginal cost = $23,000
What salary would you be willing to pay a fifth employee?
$19,000 or less.
3
Please answer the questions below using the following information. You may want
to refer to your notebook, lecture notes, and textbook.
Let's suppose that you are the manager of a company that makes garden arbors. The
arbors sell for $50.00 each. The cost of the materials in an arbor is $37.50. The fixed
cost of production is $10.00 per hour (e.g., rent on building). You pay your employees
$15.00 per hour. This exercise will help you determine how many people to hire.
Fill in the blanks in the table on the next page.
How many people should you hire? Explain your answer.
Hire 3 people because MB = 100 > MC = 90
At 4 persons hired MB = 50 < MC = 52.50
After you determine the optimal number of people that you should hire, let's suppose that
an opportunity arises for you to hire another person at less than $15 per hour. How much
money would you be willing to pay another person on a per hour basis?
We need to lower MC by $2.50 per hour. If we were able to pay the fourth
employee $15.00 per hour - $2.50 per hour = $12.50 or less, then we would hire the
fourth employee.
4
Number of
Employees
Number of
Arbors
Made per
Hour
Total
Salary per
Hour
Total Cost
Fixed Cost
of Materials per Hour
per Hour
Total Cost
of
Production
per Hour
Marginal
Cost of this
Unit of
Labor
Total
Revenue
from
Production
per Hour
Marginal
Revenue 1
from this
Unit of
Labor
0
0
0
0
$10
$10
0
0
0
1
2
15
75
10
100
90
100
100
2
5
30
187.5
10
227.50
127.5
250
150
3
7
45
262.5
10
317.50
90
350
100
4
8
60
300
10
370
52.5
400
50
5
8
75
300
10
385
15
400
0
1
The marginal benefit in this exercise is equal to the marginal revenue.
5
In reference to the table on the previous page, you may have noticed that each additional
unit of labor in this exercise is less productive than the previous unit (i.e., the physical
efficiency falls). For example, the second employee allowed for three additional units of
output while the third employee allowed for only two additional units of output. This
observation is referred to as the diminishing productivity of labor. If all of your
employees are equally skilled, how can you explain why the third employee you hired is
less productive than the second employee hired?
Capital is held fixed in the analysis.
Please answer the questions below using the following information. You may want
to refer to your notebook, lecture notes, and textbook.
Let's suppose that you are the manager of a company that makes cookies. The cookies
sell for $13.00 per box. The cost of the materials in a box of cookies is $8.00. The fixed
cost of production is $12.00 per hour (e.g., rent on store). You pay your employees $9.00
per hour. This exercise will help you determine how many people to hire.
Fill in the blanks in the table on the next page.
How many people should you hire? Explain your answer.
4 people should be hired because MB = 26 > MC = 25
6
Number of
Employees
Boxes of
Cookies
Made per
Hour
Total
Salary per
Hour
Total Cost
Fixed Cost
of Materials per Hour
per Hour
Total Cost
of
Production
per Hour
Marginal
Cost of this
Unit of
Labor
Total
Revenue
from
Production
per Hour
Marginal
Revenue 2
from this
Unit of
Labor
0
0
0
0
$12
$12
0
0
0
1
10
9
80
12
101
89
130
130
2
16
18
128
12
158
57
208
78
3
20
27
160
12
199
41
260
52
4
22
36
176
12
224
25
286
26
5
23
45
184
12
241
17
299
13
2
The marginal benefit in this exercise is equal to the marginal revenue.
7
After you determine the optimal number of people that you should hire, let's suppose that
an opportunity arises for you to hire another person at less than $9 per hour. How much
money would you be willing to pay another person on a per hour basis?
MB of the 5th person is $13 and MC is $17. We need to lower the MC by $4.00 per
hour. We would be willing to pay $9.00 per hour - $4.00 per hour = $5.00 per hour
or less.
Let's suppose that you are wondering if you should install another oven for baking your
cookies. You are using two ovens in production at this time. What effects do you think
that another oven will have on the physical efficiency of labor? How can you determine
if another oven is economically efficient?
Another oven would increase output for a given level of labor therefore increasing
physical efficiency. To determine if another oven is economically efficient, we would
use marginal analysis, while holding labor constant, to determine if we should
purchase another oven.
What do you think would be a good multiple choice question on the next exam to test
your knowledge of marginal analysis?
8
Reviewing the Fundamentals of Graphing. This exercise will cover graphing in the xy plane, the calculation of slope, and the interpretation of graphs. As we will
demonstrate, a graph is sometimes the best way to convey information. That is, a simple
graph can be "worth" a million words.
A graph is made up of many small points. For example, a line can be thought of as
millions and millions of small dots that are very close together. The proximity of the dots
or points in a line makes it look like the points are connected. Our goal in this exercise is
to review the plotting of the points that make-up a graph and the interpretation of the final
product.
We will plot points in the x-y plane. In this model, the horizontal axis is called the xaxis. The variable that is graphed on the x-axis is called the independent variable. The
vertical axis in the x-y plane is called the y-axis. The variable that is graphed on the yaxis is called the dependent variable. The x-y plane, a line, and a point are demonstrated
in Figure 1.
y-axis
8
6
(3, 6)
4
2
0
1
2
3
4
Figure 1: x-y Plane, a Line, and a Point
5
x-axis
9
The points in a graph have unique addresses or coordinates. For example, the coordinate
of the point demonstrated in Figure 1 is (3, 6). In general, the coordinate of a point is
given in the form (x, y).
The coordinate of a point can be thought of as a set of directions for plotting the point.
For example, let's consider the point (3, 6) in Figure 1. In this case, the directions say
that you should move 3 units along the x-axis from the origin. You should then make a
right-angle turn and go 6 units straight up the y-axis. You are now at the address or
coordinate of the point (3, 6). Put a dot at this location to mark the point, as shown in
Figure 1.
The equally spaced hash marks along the axis in a graph represent the units of the axis.
For example, there are hash marks at 2, 4, and 6 units on the y-axis in Figure 1.
It is important to note that the distance between any two adjoining hash marks is the same
along a given axis. For instance, the distance between the hash mark at 6 units and the
hash mark at 4 units on the y-axis in Figure 1 is the same as the distance between the
hash marks at 4 and 2 units.
The distance between the hash marks on an axis is chosen to meet the needs or
requirements of the problem. For example, let's assume that we were graphing the
demand schedule below. In this case, the distance between the hash marks on the x-axis
should be 20 units. The distance between the hash marks on the y-axis should be 100
units. If you were asked to plot the point $750 on the y-axis, you should put a dot
halfway between the hash mark at $700 and the hash mark at $800.
Demand Schedule
Quantity Demanded
Price
20
$900
40
$800
60
$700
80
$600
A direct or positive relationship is said to exist between two variables when an increase
in the independent variable is associated with an increase in the dependent variable (i.e.,
x and y both go up). This type of relationship also holds when a decrease in the
independent variable is associated with a decrease in the dependent variable (i.e., x and y
both go down).
10
An inverse or negative relationship is said to exist between two variables when an
increase in the independent variable is associated with a decrease in the dependent
variable (i.e., x goes up and y goes down). This type of relationship also holds when a
decrease in the independent variable is associated with an increase in the dependent
variable (i.e., x goes down and y goes up). A direct relationship and an inverse
relationship are demonstrated in Figure 2.
dependent variable
dependent variable
Inverse
Relationship
Direct
Relationship
independent variable
independent variable
Figure 2: Direct and Inverse Relationships
The independent variable and the dependent variable are said to have no relationship
when changes in the independent variable are not associated with changes in the
dependent variable. An example of this type of relationship is demonstrated in Figure 3.
dependent variable
No
Relationship
independent variable
Figure 3: No Relationship
dependent variable
No
Relationship
independent variable
11
Answer the questions below. You may want to refer to your notebook and lecture notes.
Let's suppose that you are asked to graph the demand schedule below. The quantity
demanded of the commodity should be graphed on the x-axis.
Demand Schedule
Quantity Demanded Price
30
$60
60
$45
90
$30
120
$15
What should be distance between the hash marks on the x-axis? Provide a sketch of the
x-axis. Place a dot at the point (105, 0) on the x-axis.
0
30
60
90 105 120
150
What should be distance between the hash marks on the y-axis? Provide a sketch of the
y-axis. Place a dot at the point (0, 50) on the y-axis.
12
Let's suppose that you are asked to graph the supply schedule below. The quantity
supplied of the commodity should be graphed on the x-axis.
Supply Schedule
Quantity Supplied Price
12.5
$5.25
25
$10.50
50
$21.00
62.5
$26.25
What should be the distance between the hash marks on the x-axis? Provide a sketch of
the x-axis. Place a dot at the point (18.75, 0) on the x-axis.
What should be the distance between the hash marks on the y-axis? Provide a sketch of
the y-axis. Place a dot at the point (0, 18.375) on the y-axis.
13
Consider the demand schedule below.
Demand Schedule
Quantity Demanded Price
0
$27
1
$24
2
$21
4
$15
5
$12
8
$3
Graph the demand curve. The quantity demanded of the commodity should be graphed
on the x-axis. The price for the commodity should be graphed on the y-axis. Label the
points using the notation (x, y). It is important that you always label the axes in a graph.
What is the relationship between the quantity demanded of the commodity and the price
for the commodity? Inverse or Negative
14
The slope of a line measures the change or adjustment in the dependent variable that is
associated with a one unit change in the independent variable. For example, let's suppose
that the slope of a line is 3.5. Under these circumstances, a change in the independent
variable from 10 to 12 units (i.e., 2 units) will be associated with a change in the
dependent variable of 7 units (i.e., 3.5 x 2).
The slope of a line can be calculated using any two points on the line. It does not matter
which two pairs of points is used in the calculation.
In general, the slope of a line is calculated between points ( x 0 , y 0 ) and (x 1 , y1 ) as
follows:
Slope =
y1 - y 0
x1 - x 0
What is the slope of the demand curve graphed above?
(0,27) and (8,3)
slope = (3-27) / (8-0) = -3
What would be the change in the quantity demanded of the commodity associated with a
change in the price for the commodity from $12 to $6?
Slope = (y1-y0) / (x1-x0)
(y1-y0) = 6-12 = -6
(x1-x0) * -3 = -6
(x1-x0) = +2
15
What is the price for the commodity if the quantity demanded is 3 units?
-3 = (y1 - 12) / (3-5)
y1-12 = 6
y1 = $18
Consider the supply schedule below.
Supply Schedule
Quantity Supplied
Price
1,200
$50
3,600
$150
4,800
$200
6,000
$250
9,600
$400
10,800
$450
Graph the supply curve. The quantity supplied of the commodity should be graphed on
the x-axis. The price for the commodity should be graphed on the y-axis. Label the
points using the notation (x, y). It is important that you always label the axes in a graph.
16
What is the relationship between the quantity supplied of the commodity and the price for
the commodity? Direct or postive.
What is the slope of the supply curve?
(1200,50) and (10,800, 450)
Slope = (y1-y0) / (x1-x0)
Slope = (450-50) / (10,800-1200) = 1/24 = .0416
What would be the change in the quantity supplied of the commodity associated with a
change in the price for the commodity from $350 to $250?
1/24 = (250 - 350) / (x1-x0)
(x1-x0) = -2,400
What is the price for the commodity if the quantity supplied is 7,200 units?
1/24 = (y1 - 50) / (7200 - 1200)
y1 = 250 + 50 = 300
17
A graph can be very useful in conveying information. For example, let's suppose that we
would like to use a graph to illustrate the relationship between the quantity of fertilizer
used on a farm and the farm's profit from operations.
As we all know, crops need fertilizer to grow. A farmer should apply fertilizer to his
fields until the economic efficiency of using another pound of fertilizer is less than or
equal to one. At this point, the marginal benefit from using another pound of fertilizer is
less than or equal to the marginal cost. If the farmer's application of fertilizer exceeds
this optimal rate, the profit from his enterprise will fall.
A rough sketch of the relationship between the quantity of fertilizer used on a farm and
the farm's profit from operations is as follows:
Profit
Pounds of Fertilizer per Acre
Sketch the relationship between the time you spend studying in this course and your
grade. Graph the time spent studying on the x-axis.
grade
Time
18
Sketch a curve demonstrating the relationship between the marginal tax rate and the total
tax collected by the government. Graph the marginal tax rate on the x-axis.
You should keep in mind that no taxes are collected when the marginal tax rate is 0 or
100%. As the marginal tax rate rises from 0, the tax collected by the government will
initially increase. If the marginal tax rate continues to rise, people will eventually decide
that the cost of working is not worth the benefits. At this point, the tax collected will fall.
Taxes
Collected
0
100%
Marginal tax rate
Sketch a curve demonstrating the relationship between the money spent on safety
awareness in a factory and the factory's total expenses. Graph the money spent on safety
awareness on the x-axis.
In general, a factory's total expenses are high when no money is spent on safety
awareness. This is because accident costs are usually very high under these
circumstances. When a factory starts a safety awareness program, the marginal benefit of
the program is usually greater than the marginal cost. As more and more money is spent
on safety training, a point is reached in which the cost of the training is less than the
benefits.
Total
Expenses
Money spent on
safety awareness
19
Sketch a curve demonstrating the relationship between the time a foreman spends
supervising his employees and the total output of his workers. Graph the time a foreman
spends supervising his employees on the x-axis.
Output
Time Supervising
Fill in the blanks in the table below.
Variable on the
x-axis
City's Population
Variable on the
y-axis
Average Cost of a
Home
Type of
Relationship
Direct
Output of Wheat on
a Small Farm in
North Carolina
World Price for
Wheat
None
Value of a College
Degree
Number of College
Students
Direct
The Fine for a
Speeding Ticket
The Percentage of
the Population that
Speeds
Inverse
The Salary for High
School Teachers
Number of High
School Teachers
Direct
Rough Sketch
of Relationship