SR Cost Problem

Consider a manufacturing firm operating a given scale of plant. Assume that the only input that the firm can change the amount of that can be used during the time period considered is labor (L).

Assume that the production function between Labor (L) and Total Product (Q) is given in the first two columns of the table below.

Labor (L) Total Product (Q) Labor (L) Total Product (Q)

1 100 10 1,234

2 250 11 1,314

3 410 12 1,384

4 560 13 1,444

5 700 14 1,494

6 830 15 1,534

7 945 16 1,564

8 1,050 17 1,584

9 1,146 18 1,594

Assume that depreciation on the plant and equipment, interest on borrowed money, property taxes, insurance, etc., i.e., Total Fixed Costs (TFC), are $220, and that the price of a unit of labor (PL) is $100.

To gain experience with a valuable piece of business software, it is strongly suggested that the student use a spreadsheet software program to perform the calculations and to construct the graphs described in parts A and B below. Any spreadsheet program may be used although students may be most familiar with MS EXCEL. It is assumed that the student is familiar with making calculations using a spreadsheet program.

As indicated on the course Syllabus, it is suggested that MS OFFICE, which includes EXCEL, be installed on external computers that are used. It is installed on all the computers located on the Gannon main campus.

A. Calculations

Instructions. Open a spreadsheet program, such as MS EXCEL. Open a new worksheet. Enter the above data for L in column 1 and the above data for Q in column 2.

For each level of output (Q) shown in the second column in the above table, calculate a value for each of the following cost measures: Total Fixed Cost (TFC), Total Variable Cost (TVC), Total Cost (TC), Average Fixed Cost (AFC), Average Variable Cost (AVC), Average Total Cost (ATC) and Marginal Cost (MC). Refer to the Lecture Notes entitled “Short Run Cost Functions” for the formulas used for calculating the cost measures. [Note: In calculating the average cost measures be sure to divide the corresponding total cost measure by Q and NOT by L.]

Ideally, MC would be calculated between each row and placed on a new row created with an amount of output (Q) equal to ½ of the two amounts of output used in the calculation. In other words, the MC calculated between 100 and 250 units of Q would be calculated using the discrete formula and placed on a newly created row corresponding to 175 units of Q. But this is not necessary. Each MC calculation may be placed on the row corresponding to the higher of the two levels of output used in the calculation. For example, the MC calculated between 100 and 250 units of Q using the discrete formula may be placed on the row corresponding to 250 units of Q.

Copy the above calculations in the EXCEL program and insert, i.e., paste, here into this document.

B. Graphs

1. Using the EXCEL chart feature, on one diagram graph the relationship between Total Product (Q) and all three of the total cost measures, i.e., TFC, TVC, and TC.

There is a tutorial on using the EXCEL chart tool available at:

Copy the above graphs in the EXCEL program and insert, i.e., paste, here into this document.

On the graph be sure to label the axes and provide a label or legend for each curve. Be sure to place output (Q) on the horizontal axis and be sure that the scale for Q is correct.

Copy the above graph in the EXCEL program and insert, i.e., paste, here into this document.

2. Using the EXCEL chart feature, on another diagram, graph the relationship between Total Product (Q) and the average and marginal cost measures, i.e., AFC, AVC, ATC, and MC. Ideally, MC would be plotted midway between the two amounts of output (Q) used in the calculation, but this is not necessary. It may be plotted corresponding to the higher of the two levels of output used in each calculation. For example, the MC calculated between 100 and 250 units of Q may be plotted corresponding to 250 units of Q.

On the graph be sure to label the axes and provide a label or legend for each curve. Be sure to place output (Q) on the horizontal axis and be sure that the scale for Q is correct.

There is a tutorial on using the EXCEL chart tool available at:

Copy the above graph in the EXCEL program and insert, i.e., paste, here into this document.

C. Relationships

1. What happens to the value of each of the total cost measures, i.e., TC, TVC, and TFC, as Q increases (increases, decreases, remains constant?).

2. What happens to the value of AFC as Q increases?

3. How long does AFC decrease?

4. AVC decreases over the range of output from _____ to _____. Over this range of output what is happening to the values of AFC and ATC as output increases?

5. AVC increases over the range of output from _____ to _____. Over this range of output what is happening to the values of AFC and ATC as output increases?

6. ATC reaches a minimum at a level of output approximately equal to _____ . AVC reaches a minimum at a level of output approximately equal to _____.

7. How would you characterize the shapes of the ATC curve, AVC curve, and the MC curve?

8. Pick a level of Q for which MC < ATC. If Q were to increase, the value of ATC (increases, decreases, stays the same?)

9. Pick a level of Q for which MC > ATC. If Q were to increase, the value of ATC (increases, decreases, stays the same?)

10. The MC curve intersects the ATC at the __________ point on the ATC curve?

11. Referring to the table, over that range of labor usage throughout which MP increases as more L is used, for the corresponding range of output, as Q increases, MC (increases, decreases, remains constant?) .

12. Over that range of labor usage throughout which MP decreases as L increases, for the corresponding range of output, as Q increases, MC (increases, decreases, remains constant?) Explain.

[Hint: The best way to see the relationship between MP and MC and to answer the above two questions is to construct two diagrams, one on top of the other. In the lower diagram, graph the MP curve. In the upper diagram, on the horizontal axis plot the Q corresponding to the amount of labor on the horizontal axis of the bottom diagram, and on the vertical axis plot MC.

Graphical Competitive Firm Problem

Use the below diagram containing a competitive firm’s short run average and marginal cost curves to answer the following questions corresponding to different prices of the firm’s product. Recall that an individual competitive firm has no control over the price of its product. If difficulties are encountered, refer to the section entitled “Amended MR-MC Profit Maximizing Rule for a Competitive Firm,” which is contained in the PC Firm Theory Lecture Notes.

A. Assume the price of the firm’s product is $7.

1. For each level of output, Marginal Revenue (MR) = _____ and Average Revenue (AR) = _____.

2. The level of output for which MC equals MR, which equals price, is approximately ______.

3. For the rate of output indicated in answer to #2 above, ATC is ______ so that TC is _____.

4. For the rate of output indicated in answer to #2 above, TR is ______ so that profits, which equal TR - TC, are _______.

5. The profit maximizing rate of output is ______.

B. Assume the price of the firm’s product is $3.

1. The level of output for which MC equals MR, which equals price, is approximately ______.

2. At the level of output indicated in answer to #1 above, ATC is _____, and TC is ______.

3. At the level of output indicated in answer to #1 above, TR is ______ and profits are _____.

4. At the level of output indicated in answer to #1 above, AVC is approximately ____ so that TVC equals _____ .

5. At the level of output indicated in answer to #2 above, the relationship between P, ATC, and AVC is as follows: _____<_____<_____.

6. At the level of output indicated in answer to #2 above, the relationship between TC, TVC, and TR is as follows: _____<_____<_____.

7. The profit maximizing rate of output is ______. Explain why the firm is better off producing this rate rather than shutting down.

C. Assume the price of the firm’s product is $2.

1. The level of output for which MC equals MR, which equals price, is approximately ______.

2. At the level of output indicated in answer to #1 above, ATC is approximately _____, and TC is ______.

3. At the level of output indicated in answer to #1 above, TR is ______ and profits are _____.

4. At the level of output indicated in answer to #1 above, AVC is approximately ____ so that TVC equals _____ .

5. At the level of output indicated in answer to #1 above, the relationship between ATC, AVC, and P is as follows: _____<_____<_____.

6. At the level of output indicated in answer to #1 above, the relationship between TC, TVC, and TR is as follows: _____<_____<_____.

7 The profit maximizing rate of output is ______. Explain why the firm is better off shutting down rather than producing the rate of output indicated in answer to #1 above.

D. This individual competitive firm’s supply curve corresponds to that portion of the _________ cost curve that lies above the ________ point on the __________ cost curve.

E. The market supply curve for the product that this firm produces corresponds to the horizontal summation of all the individual firm’s ___________ cost curves above the __________ point of the __________ curve.

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