Question

Name: Section: Homework Assignment: Production and Cost in the Firm (Chapter 7) On the back of this page is a table, partially filled in, with employment i.e., units of labor) output and cost data for a firm. The first part of the assignment is to complete all the missing cells. You are encouraged to use Excel and the table on back is available as an Excel Workbook on Blackboard. For the three rightmost columns, display the cost data in dollars and cents (e.g., $3.33). You will need cents to answer questions 3 and 4 Now, using the data in this table, answer the following questions. 1) As units of labor are added the costs will change. At what unit of labor does the Law of Diminishing Marginal Returns become apparent? There are two ways of determining this from the numbers in the table. Identify both. 2) At what unit of labor does Marginal Cost begin to exceed Average Variable Cost? 3) What starts happening to Average Variable Cost at that unit of labor? 4) At what unit of labor does Marginal Cost begin to exceed Average Total Cost? 5) What starts happening to Average Total Cost at that unit of labor? 6) Generate a graph of Marginal Cost, Average Variable Cost and Average Total Cost for Units of Labor 1 thru 9, and attach it to this sheet with a staple. 7) Thought for consideration: given this cost data, how many units of labor would be optimal for the firm to employ? This assignment is due Thursday October 24. Hard copy submission required. Make sure your name appears on your work. See the syllabus regarding homework assignments and the treatment of late submissions.

Answer 1

Here “MP” is the additional production by hiring additional unit of labor. So, for “L=1” the MP is “(80-0)/(1-0) = 80”, for “L=2” the MP is “(200-80)/(2-1) = 120”. In this way we can calculate the MP for different level of labor.

Now, FC is the amount of cost when production is “0”. So, for “L=0” the total cost is “1000”, => the FC is “1000” for all level of production and employment. Total cost is the sum of “FC” and “VC”. We have the data on “FC” and “VC”, => we can calculate the TC for different level of production. So, for “L=0” the TC is “1000+0 = 1000”, for “L=1” the TC is “1000+400 = 1400”, for “L=3” the TC is “1000+800 = 1800”.

Marginal cost is the additional cost for additional unit of production. So, for “L=1” the MC is “(1400-1000)/(80-0) = 5”, for “L=2” the MC is “(1800-1400)/(200-80) = 3.33” and so on. Now, average variable cost is the “variable cost” per unit of output production. So, for “L=1” the AVC is “400/80 = 5”, for “L=2” the AVC is “800/200 = 4” and so on.

Finally, average total cost is the “total cost” per unit of output production. So, for “L=1” the ATC is “1400/80 = 17.5”, for “L=2” the ATC is “1800/200 = 9” and so on.

L AVC ATC 120 600 vouwNO MP 0 80 200 340 460 560 640 700 740 760 760 FCVC 10000 80 1000 400 120 1000 800 140 1000 1200 1000 1600 100 1000 2000 80 1000 2400 60 1000 2800 1000 3200 20 1000 1000 3600 1000 4000 TCMC 1000 1400 5 1800 3.33 2200 2.86 2600 3.33 3000 4 3400 5 3800 6.67 4200 10 4600 20 5000 5 4 3.53 3.48 3.57 3.75 4 4.32 4.74 5.26 17.5 9 6.47 5.65 5.36 5.31 5.43 5.68 6.05 6.58 9

1).

The “Diminishing Marginal Returns” starts when MP starts falling. So, here from “L=4” the MP starts falling and “MC” starts rising, => “Diminishing Marginal Returns” starts. So, there are two ways to determine the “Diminishing Marginal Returns” by “MP” and “MC”.

2).

At “L=4” the MC is “3.33” which is less than “AVC”. Now, at “L=5” the MC is “4” which is more than “AVC” implied at “L=5” the MC begin to exceed the AVC.

3).

Initially the AVC is falling but at that level of labor it starts rising.

4).

At “L=6” the MC is “5” which is less than “ATC”. Now, at “L=7” the MC is “6.67” which is more than “ATC” implied at “L=7” the MC begin to exceed the ATC.

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