ECO 520 Case Study One: Production and Cost Guidelines and Rubric Overview This course includes two case studies. These exercises are designed to actively involve you in microeconomic reasoning and decision making and to help you apply the concepts covered in the course to complex real-world situations. The case studies provide practice reading and interpreting both quantitative and qualitative analysis. You will then use your analysis to make decisions and predictions. These exercises provide practice communicating reasoning in a professional manner. Prompt Case Study One: Production and Costfocuses on a perfectly competitive industry. Each competitive firm in this industry has a Cobb-Douglas production function: 5 . 0 5 . 0 02 . 0 L K q = . These firms combine capital and labor to produce output. In task 3-2 you will use graphs and equations to analyze competitive firm decisions, the interaction between those decisions, and the competitive market determination of price. Skills needed to complete this case study: 1. The ability to enter data, enter formulas, and create charts in Excel (Note: use the data provided in the Case Study One Data document.) 2. The ability to use basic algebra To complete Case Study One, follow the steps below: 1. Use algebra to derive the cost function: · To solve for K as a function of q and L. Show your work, and verify that you have this solution: L q K 2 2 02 . 0 = . · Write the cost function. Cost is equal to the sum of the expenditures to purchase capital plus the expenditures to purchase labor. Each of these expenditures is equal to the price of the input multiplied by the quantity of the input. Use the letter r to denote the price of capital and w to denote the price of labor. 2. Use Excel to create and graph isoquant curves: · Use column A to store possible values for L. Use the first row to label the column. Put a zero (use the number 0) in the second row. Put the formula =a2+5 in the third row. Copy this formula in rows 4-25. · Use column B to store the quantity of K that is needed to combine with each possible value of L to produce 5 units. Use the equation from Step 1, with q = 5. · Use column C to store the quantity of K that is needed to combine with each possible value of L to produce 10 units. Use the equation from Step 1, with q = 10. · Use column D to store the quantity of K that is needed to combine with each possible value of L to produce 15 units. Use the equation from Step 1, with q = 15. · Use scatter-plot to graph the isoquants. Print the graph, and use this graph to complete the following table: Q quantity of L that must be combined with K=5000 to produce each quantity of output (q) 5 10 15 3. Consider the short run situation in which K is fixed at 5000. Assume r = .05 and w = 40. Open a new Excel worksheet for cost information. Note the difference between your production worksheet, in which the first column stored possible values of L, and this new cost worksheet in ...

1. ECO 520 Case Study One: Production and Cost Guidelines and
Rubric
Overview
This course includes two case studies. These exercises are
designed to actively involve you in microeconomic reasoning
and decision making and to help you apply the concepts covered
in the course to complex real-world situations. The case studies
provide practice reading and interpreting both quantitative and
qualitative analysis. You will then use your analysis to make
decisions and predictions. These exercises provide practice
communicating reasoning in a professional manner.
Prompt
Case Study One: Production and Costfocuses on a perfectly
competitive industry. Each competitive firm in this industry has
a Cobb-Douglas production function:
5
.
0
5
.
0
02
.
0
L
K
q
=
. These firms combine capital and labor to produce output. In
task 3-2 you will use graphs and equations to analyze
competitive firm decisions, the interaction between those

2. decisions, and the competitive market determination of price.
Skills needed to complete this case study:
1. The ability to enter data, enter formulas, and create charts in
Excel (Note: use the data provided in the Case Study One Data
document.)
2. The ability to use basic algebra
To complete Case Study One, follow the steps below:
1. Use algebra to derive the cost function:
· To solve for K as a function of q and L. Show your work, and
verify that you have this solution:
L
q
K
2
2
02
.
0
=
.
· Write the cost function. Cost is equal to the sum of the
expenditures to purchase capital plus the expenditures to
purchase labor. Each of these expenditures is equal to the price
of the input multiplied by the quantity of the input. Use the
letter r to denote the price of capital and w to denote the price
of labor.
2. Use Excel to create and graph isoquant curves:
· Use column A to store possible values for L. Use the first row
to label the column. Put a zero (use the number 0) in the second

3. row. Put the formula =a2+5 in the third row. Copy this formula
in rows 4-25.
· Use column B to store the quantity of K that is needed to
combine with each possible value of L to produce 5 units. Use
the equation from Step 1, with q = 5.
· Use column C to store the quantity of K that is needed to
combine with each possible value of L to produce 10 units. Use
the equation from Step 1, with q = 10.
· Use column D to store the quantity of K that is needed to
combine with each possible value of L to produce 15 units. Use
the equation from Step 1, with q = 15.
· Use scatter-plot to graph the isoquants. Print the graph, and
use this graph to complete the following table:
Q
quantity of L that must be combined with K=5000 to produce
each quantity of output (q)
5
10
15
3. Consider the short run situation in which K is fixed at 5000.
Assume r = .05 and w = 40. Open a new Excel worksheet for
cost information. Note the difference between your production
worksheet, in which the first column stored possible values of
L, and this new cost worksheet in which the first column will
store possible values of q. The variable represented in the first
column will be graphed on the horizontal axis of the scatter-
plot. For the isoquant diagram, L is shown on the horizontal
axis. The new cost worksheet will be used to graph cost

4. functions, with quantity of output on the horizontal axis
· Use column A to store possible values of q from 0 through 20.
· Use column B to store Total Fixed Cost (TFC). Fixed cost in
this example is equal to r*K, with K = 5000.
· Use column C to store Total Variable Cost (TVC). Variable
cost in this example is equal to w*L. To compute the quantity of
L that must be combined with K=5000 to produce each possible
value of q, remember that the production function is:
5
.
0
5
.
0
02
.
0
L
K
q
=
.
· Use algebra to solve for L as a function of q and K. Because K
is fixed at 5000 for this short run analysis, the resulting
equation will have L on the left-hand-side and the variable q
will be combined with several constants on the right-hand-side.
Substitute this equation for L to generate the TVC values for
column C. Be careful to enclose the entire denominator in
parentheses.

5. · Use column D to store Total Cost (TC) = TFC + TVC.
· Generate AFC in column E by dividing TFC/q
· Generate AVC in column F by dividing TVC/q
· Generate ATC in column G by dividing TC/q
· Generate one estimate of MC in column H by computing the
change in TC as output increases. Leave the first row blank.
Enter a formula into the third row: =d3-d2. Copy this formula
into the remaining columns. This will provide arc elasticity.
· Generate a second estimate of MC in column I. Point elasticity
is equal to
)
5000
(
02
.
0
)
40
(
2
2
q
· Use scatter-plot to graph TC, TFC and TVC.
· Use scatter-plot to generate a second graph to show ATC,
AFC, AVC and the second estimate of MC.
4. Find equilibrium P & Q in the perfectly competitive market.

6. Demand is represented by the equation: P = 720 - 0.5Q. The
perfectly competitive firms are assumed to be identical. The
quantity supplied by each individual firm is represented by the
firm's MC curve. In order to graph market supply and market
demand, however, we need to focus on market quantity, rather
than individual firm quantity. The market quantity is equal to
nq
Q
=
; where q is the individual firm's quantity.
· Solve for the short-run equilibrium market P & Q using
algebra.
· Generate new columns in Excel to represent demand and
supply. This will require some strategic thinking. You will want
to generate a graph with market quantity on the horizontal axis.
That means that you will need to generate a column of numbers
to represent possible values of market quantity.
· Let column J represent market quantity,
q
Q
100
=
.
· Store values for demand in column K. Store values of supply
in column L. The numbers in column L will be equal to the
numbers representing MC in column I. You can simply copy
these numbers into column L. Alternately, you could enter the
formula for MC, recognizing that the firm-level quantity is
equal to the market quantity stored in column J divided by 100.

7. · Graph demand and supply. Verify that the computed
equilibrium P & Q are consistent with the graph.
5. Complete the following table for a firm that is producing the
profit-maximizing level of output.
Revenue
$$$
Optimal firm q
Short-run equilibrium P
Revenue = q*P
Cost
TFC
TVC (incurred by a firm that is producing the optimal Q)
TC = TVC + TFC
Profit
Profit = Revenue - TC

8. 6. Generate a graph to show the optimal quantity that will be
produced by each competitive firm, and the resulting profit.
This graph will include 4 curves to show:
· The short-run equilibrium price (To generate this horizontal
line, use column L to store the values of the equilibrium P.
Because this line is horizontal, all of the numbers stored in this
column are identical.)
· ATC
· AVC
· MC.
Is your graph is consistent with your profit computation?
Explain.
7. Assume that potential entrants will have exactly the same
cost function as the existing firms. Will new firms enter the
market? Why or why not?
8. You work for a firm that produces an input that is used by
these competitive firms. Your marketing vice president has
asked you to provide analysis to support the marketing
department's strategic planning committee. They understand that
the industry is not currently in long-run equilibrium, and they
have asked you to help them estimate the output that will be
produced and the number of firms that will exist when the
industry reaches long-run equilibrium. This will require several
steps:
· Draw the pair of graphs that depict long run competitive
equilibrium. Note that two things are true in LR equilibrium:
· P=MC=ATC for individual firm

9. · S=D in market
· You will need equations that describe these two facts (fill in
the blanks):
· ATC = MC
)
5000
(
02
.
0
40
)
5000
(
05
.
0
2
q
q
+
= _________________________
· D = S
720-0.5Q = 40Q/n; where
nq
Q

10. =
· Solve these two equations for q and n.
· To create graphs, complete the following steps:
· Open a new worksheet
· Use column A to store possible values of the market quantity.
Put zero in the second row. Enter the formula =a2+100 in the
third row. Copy this formula into rows 4-20.
· Enter the formula for market demand into the second column
(=720 - 0.5*A2)
· Enter the formula for the initial market supply into the third
column (=40*A2/100); where n=100 is the number of firms in
the initial market.
· Enter the formula for the final market supply into the fourth
column (=40*a2/n); where n is the long-run equilibrium number
of firms you computed in the previous step.
· Use scatter-plot to create a graph that shows market demand
and both the initial market supply and the long-run equilibrium
market supply. Verify that the short-run and long-run
equilibrium prices and quantities are consistent with your
algebraic solution values.
· Complete the following table:
Long Run Equilibrium
Output of each individual firm
Industry output
Number of firms

11. Format: Case Study One must follow these formatting
guidelines: double spacing, 12-point Times New Roman font,
one-inch margins.
Instructor Feedback: Students can find their feedback in the
Grade Center.
Rubric
Critical Elements
Exemplary
Proficient
Needs Improvement
Not Evident
Value
Section 1
Uses algebra and the Excel spreadsheet to complete the answer.
Analyzes the cost function using economics vocabulary
(10)
N/A
N/A
No graph and analysis provided
(0)
10
Section 2
Uses Excel to create and graph isoquant curves and scatter-plot
according to directions
(10)
N/A
N/A
No graph and analysis provided

12. (0)
10
Section 3
Uses a new Excel Worksheet for cost (see Cost Tab) to
complete the directions for a short run situation
(10)
N/A
N/A
No graph and analysis provided
(0)
10
Section 4
Represent and graph the firm's MC curve according to
directions
(10)
N/A
N/A
No graph and analysis provided
(0)
10
Section 5
Represent a firm profit-maximizing level of output according to
directions
(10)
N/A
N/A
No table and analysis provided
(0)
10
Section 6

13. Represent a competitive firm, and the resulting profit according
to directions
(10)
N/A
N/A
No graph and analysis provided
(0)
10
Section 7
Submission meets “Proficient” and extends explanation to
include additional reasons for the entry into the market
(18-20)
Uses Excel spreadsheet, algebra to determine costs along with a
discussion using economic vocabulary, variables, and reasoning
to make an argument for (or against) entry into the market
(16-17)
Missing one or more of the factors to completing the assignment
(14-15)
Does not include the majority of the assignment components
(0-13)
20
Section 8
Submission meets “Proficient” and extends explanation to
include additional reasons for the strategic plans for long-run
equilibrium market
(18-20)
Follow the steps in the Case Study One document to create
required graphs, scatter plots and tables to support strategic
plans for long-run equilibrium market

14. (16-17)
Missing one or more of the factors to completing the assignment
(14-15)
Does not include the majority of the assignment components
(0-13)
20
Earned Total
Comments:
100%
_1248089426.unknown
_1248089460.unknown
_1248089655.unknown
_1248089362.unknown
_1248089225.unknown
_1248089107.unknown