ECO 520 Case Study One

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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 Cost focuses on a perfectly competitive industry. Each competitive firm in this industry has a Cobb-Douglas production function: . 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.)

1. 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: .

· 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 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 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: .

· 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.

· 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

· 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. 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 ; 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, .

· 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.

· 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

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

· S=D in market

· You will need equations that describe these two facts (fill in the blanks):

· ATC = MC

= _________________________

· D = S

720-0.5Q = 40Q/n; where

· 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

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 (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

Represent a competitive firm, and the resulting profit according to directions

(10)

N/A

No graph and analysis provided

(0)

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)

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

(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)

Earned Total

Comments:

100%

market Q	Demand	LR Supply
(Impact on taxes) 0	720	0
100	670	12
200	620	24
300	570	37
400	520	49
500	470	61
600	420	73
700	370	86
800	320	98
900	270	110
1,000	220	122
1,100	170	135
1,200	120	147
1,300	70	159
1,400	20	171
1,500	-30	183
1,600	-80	196
1,700	-130	208
1,800	-180	220

(Market S & D)

market Q

Demand

Supply

720

100

670

200

620

300

570

120

400

520

160

500

470

200

600

420

240

700

370

280

800

320

900

270

360

110

1,000

220

400

122

1,100

170

440

135

1,200

120

480

147

1,300

520

159

1,400

560

171

1,500

-30

600

183

1,600

-80

640

196

1,700

-130

680

208

1,800

-180

720

220

q	TFC	TVC	TC	AFC	AVC	ATC	MC-subt	MC-EQ
0	250	0	250					0
1	250	20	270	250	20	270	20	40
2	250	80	330	125	40	165	60	80
3	250	180	430	83	60	143	100	120
4	250	320	570	63	80	143	140	160
5	250	500	750	50	100	150	180	200
6	250	720	970	42	120	162	220	240
7	250	980	1,230	36	140	176	260	280
8	250	1,280	1,530	31	160	191	300	320
9	250	1,620	1,870	28	180	208	340	360
10	250	2,000	2,250	25	200	225	380	400
11	250	2,420	2,670	23	220	243	420	440
12	250	2,880	3,130	21	240	261	460	480
13	250	3,380	3,630	19	260	279	500	520
14	250	3,920	4,170	18	280	298	540	560
15	250	4,500	4,750	17	300	317	580	600
16	250	5,120	5,370	16	320	336	620	640
17	250	5,780	6,030	15	340	355	660	680
18	250	6,480	6,730	14	360	374	700	720

AFC

AVC

ATC

MC-EQ

250

270

125

165

143

120

143

160

100

150

200

120

162

240

140

176

280

160

191

320

180

208

360

200

225

400

220

243

440

240

261

480

260

279

520

280

298

560

300

317

600

320

336

640

340

355

680

360

374

720

Production

Kfor Q=5

Kfor Q=10

Kfor Q=15

12,500

6,250

25,000

4,167

16,667

3,125

12,500

28,125

2,500

10,000

22,500

2,083

8,333

18,750

1,786

7,143

16,071

1,563

6,250

14,063

1,389

5,556

12,500

1,250

5,000

11,250

1,136

4,545

10,227

1,042

4,167

9,375

962

3,846

8,654

893

3,571

8,036

833

3,333

7,500

781

3,125

7,031

735

2,941

6,618

694

2,778

6,250

658

2,632

5,921

100

625

2,500

5,625

105

595

2,381

5,357

110

568

2,273

5,114

115

543

2,174

4,891

AFC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 250 125 83.333333333333329 62.5 50 41.666666666666664 35.714285714285715 31.25 27.777777777777779 25 22.727272727272727 20.833333333333332 19.23076923076923 17.857142857142858 16.666666666666668 15.625 14.705882352941176 13.888888888888889 AVC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 ATC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 270 165 143.33333333333334 142.5 150 161.66666666666666 175.71428571428572 191.25 207.77777777777777 225 242.72727272727272 260.83333333333331 279.23076923076923 297.85714285714283 316.66666666666669 335.625 354.70588235294116 373.88888888888891 MC-EQ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 12500 6250 4166.666666666667 3125 2500 2083.3333333333335 1785.7142857142858 1562.5 1388.8888888888887 1250 1136.3636363636363 1041.6666666666667 961.53846153846143 892.85714285714289 833.33333333333326 781.25 735.29411764705878 694.44444444444434 657.89473684210532 625 595.23809523809518 568.18181818181813 543.47826086956525 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 25000 16666.666666666668 12500 10000 8333.3333333333339 7142.8571428571431 6250 5555.5555555555547 5000 4545.454545454545 4166.666666666667 3846.1538461538 457 3571.4285714285716 3333.333333333333 3125 2941.1764705882351 2777.7777777777774 2631.5789473684213 2500 2380.9523809523807 2272.7272727272725 2173.913043478261 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 28125 22500 18750 16071.428571428571 14062.5 12499.999999999998 11250 10227.272727272726 9375 8653.8461538461524 8035.7142857142853 7499.9999999999991 7031.25 6617.6470588235288 6249.9999999999991 5921.0526315789475 5625 5357.1428571428569 5113.6363636363631 4891.304347826087

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5000

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100

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5000

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5000

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