Dr. Barry Haworth University of Louisville Department of Economics Honors Econ 201-01 Spring 2012 ## Homework #3 (due by 9:00pm on Thurs, March 8)

1.   A firm has the following costs (q = output, TC = total costs, MC = marginal costs):

TC = \$10                                                       if q = 0

TC = q 3 - 4q 2 + 10q + 12                               if q > 0

[MC = 3q 2 - 8q + 10                                      if q > 0]

Based on the equations above, please calculate the various types of cost below.

a. When this firm produces 3 units of output, what is this firm’s average cost (AC)?

b. When this firm produces 3 units of output, what is this firm’s average variable cost (AVC)?

c. When this firm produces 3 units of output, what is this firm’s average fixed cost (AFC)?

d. What is the amount of this firm’s sunk cost?

e. When this firm produces 3 units of output, what is this firm’s recoverable fixed cost?

2. Assume that a profit-maximizing, perfectly competitive firm is producing where economic profit is equal to zero.   The firm’s output is 10 units and the market price is \$100.   The firm has \$150 in sunk costs and an average variable cost of \$80.

What is the amount of recoverable fixed costs for this firm?

3. Assume that a profit-maximizing, perfectly competitive firm (not the firm in the previous question) is producing at what we defined in class as the shut down point.   The firm’s output is 100 units and the market price is \$50.   The firm has \$400 in sunk costs and an average variable cost of \$40.

What are the profits of this firm?

4. Assume that a firm has the following costs (q = output, TC = total costs, MC = marginal costs):

TC = \$400                                                     if q = 0

TC = 2q 2 + 20q + 500                                   if q > 0

[MC = 4q + 20                                              if q > 0]

Based on the equations above, please calculate the various types of cost below. Remember, be sure to express your answer in terms of dollars and cents.

a. Assume this firm operates under profit maximizing principles and that the market price is \$60. What is the firm’s average cost (AC)?

b. Assume this firm operates under profit maximizing principles and that the market price is \$80. What is the firm’s total variable cost (TVC)?

c. Assume this firm operates under profit maximizing principles and that the firm is producing 20 units of output.   What would be their profit from producing those 20 units?

5. Firm A is a relatively small distribution firm that transports the goods produced by different manufacturers to various retail locations in the Greater Louisville area.   The firm has its own capital, secretarial staff and managers, but hires all other laborers (dock workers and drivers) on a daily basis from a temporary services company.

Given the above, we can state the following about firm A:

·          Labor is variable.   I.e., the output of firm A depends entirely on how many dock workers and drivers are hired on any given day.

·          Capital is fixed.   I.e., no matter how much output may change from day to day, firm A uses the same fixed quantity of capital (e.g. warehouse, office space, forklifts and trucks).

If the production function doesn’t appear correctly on your computer, it should say that Q = 50 multiplied by the square root of “5 x L” (where L is a variable for the quantity of labor).

a. What is the average product of labor (APL) when 20 units of labor are hired?

b. What is the marginal product of labor (MPL) when the firm increases labor from 20 to 21?

6. Let’s assume that you run a company where labor is the only variable factor (both capital and land are fixed factors). You sell widgets that are very inexpensive and you hire low skilled labor (because making cheap widgets doesn’t require much skill), so the wage is fairly low (assume no minimum wage). Assume further that you have a production function equation which tells you how much output you get for different amounts of labor.

The information described above is given below.  Use this information to answer the question.

• Price of widgets:   P = \$1
• Wage (of each unit of labor that produces widgets):   w = \$5

If the production function doesn’t appear correctly on your computer, it should say that Q = 20 multiplied by the square root of “L” (where L is a variable for the quantity of labor).

At this point, you’re contemplating how much labor to hire.  Start with zero units of labor and assume you'll hire labor 1 unit at a time.  If so, then how many units of labor should you hire? ( note : you should use marginal analysis, such as working with marginal benefit and marginal cost, in answering this question)

a. 1 unit of labor

b. 2 units of labor

c. 3 units of labor

d. 4 units of labor

e. 5 units of labor

f. 6 units of labor

g. 7 units of labor

h. 8 units of labor

i.   9 units of labor

j . none of the above

7. The questions in parts a-d below relate to Output-Cost table at the bottom of the page.   Assume that the information in this table is taken from a single perfectly competitive firm that follows the basic profit maximizing principles discussed in class and the textbook.   Remember to express your answers in terms of dollars and cents.   To avoid “round off error” in the calculation of profit – please calculate profit using the following equation:   p = (PQ - TC)

a. Assume that this perfectly competitive firm is operating as a profit maximizer when producing 15 units of output.   If so, then what must be this firm’s current profits?

Today, the market price is \$3.60 (i.e. P = 3.6)

b. What are the highest possible profits in this situation?

Suppose industry demand increases, causing the market price to become \$4.50 (i.e. P = 4.5)

c. What are the highest possible profits in this situation?

Industry demand increases again, causing the market price to become \$10.70 (i.e. P = 10.7)

d. What are the highest possible profits in this situation?

(Multiple Choice) Question #8 also refers to the Output-Cost table (below).

8. If the market price is currently given as \$9.80 (i.e. P = 9.8), then how will this market change (adapt) over the long run?

b. Firms in this market will shut down in the long run

c. Existing firms in this market will either contract or exit the market in the long run

d. Existing firms in this market will expand or new firms will enter this market in the long run.

Firm A’s Output and Costs:

Average

Firm's             Total            Marginal         Variable

output            Costs               Costs               Costs

0                  80.0                    -                      -

1                  84.8                  4.6                   4.8

2                  89.3                  4.3                   4.6

3                  93.5                  4.1                   4.5

4                  97.4                  3.9                   4.4

5                 101.3                 3.8                   4.3

6                 105.0                 3.7                   4.2

7                 108.6                 3.6                   4.1

8                 112.3                 3.7                  4.04

9                 116.1                 3.8                  4.01

10                120.0                 4.0                   4.0

11                124.1                 4.2                  4.01

12                128.5                 4.5                  4.04

13                133.2                 4.9                   4.1

14                138.2                 5.3                   4.2

15                143.8                 5.8                   4.3

16                149.8                 6.3                   4.4

17                156.3                 6.9                   4.5

18                163.5                 7.5                   4.6

19                171.4                 8.2                   4.8

20                180.0                 9.0                   5.0

21                189.4                 9.8                   5.2

22                199.7                10.7                  5.4

23                210.9                11.7                  5.7

24                223.0                12.7                  6.0

25                236.3                13.8                  6.3

Note: The values in each (cost) column were rounded off to the nearest single decimal point – except when it was important to distinguish between various rows. Round-off error may arise in the calculation of profit, causing answers to vary slightly between the two approaches discussed in class (i.e. between the (P – AC )Q approach and the (PQ – TC) approach). #### IMAGES

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